From 2167e2ff0b8ff9d6e111bdd8f77d340a13a3ce9e Mon Sep 17 00:00:00 2001
From: Cristian C Lalescu <Cristian.Lalescu@mpcdf.mpg.de>
Date: Tue, 4 Jan 2022 12:55:22 +0100
Subject: [PATCH 01/24] tweaks PP file output
---
TurTLE/PP.py | 14 +-
documentation/sphinx_static/convergence.py | 224 +++++++++++++++++++++
2 files changed, 234 insertions(+), 4 deletions(-)
create mode 100644 documentation/sphinx_static/convergence.py
diff --git a/TurTLE/PP.py b/TurTLE/PP.py
index 8382ab13..4703d26a 100644
--- a/TurTLE/PP.py
+++ b/TurTLE/PP.py
@@ -783,9 +783,9 @@ class PP(_code):
if 'field_dtype' in df.keys():
# we don't need to do anything, raw binary files are used
return None
- last_iteration = df['iteration'][...]
- cppf = df['parameters/checkpoints_per_file'][...]
- niter_out = df['parameters/niter_out'][...]
+ last_iteration = df['iteration'][()]
+ cppf = df['parameters/checkpoints_per_file'][()]
+ niter_out = df['parameters/niter_out'][()]
with h5py.File(os.path.join(self.work_dir, self.simname + '_fields.h5'), 'a') as ff:
ff.require_group('vorticity')
ff.require_group('vorticity/complex')
@@ -807,7 +807,13 @@ class PP(_code):
if self.dns_type == 'resize':
with h5py.File(os.path.join(self.work_dir, self.pp_parameters['new_simname'] + '.h5'), 'a') as ff:
for kk in df['parameters'].keys():
- ff['parameters/' + kk] = df['parameters/' + kk][...]
+ ff['parameters/' + kk] = df['parameters/' + kk][()]
+ ff['parameters/nx'][()] = self.pp_parameters['new_nx']
+ ff['parameters/ny'][()] = self.pp_parameters['new_ny']
+ ff['parameters/nz'][()] = self.pp_parameters['new_nz']
+ if 'iteration' not in ff.keys():
+ ff['iteration'] = last_iteration
+ ff['checkpoint'] = df['checkpoint'][()]
return None
def launch_jobs(
self,
diff --git a/documentation/sphinx_static/convergence.py b/documentation/sphinx_static/convergence.py
new file mode 100644
index 00000000..5f8d5343
--- /dev/null
+++ b/documentation/sphinx_static/convergence.py
@@ -0,0 +1,224 @@
+import numpy as np
+import h5py
+import matplotlib.pyplot as plt
+
+import TurTLE
+from TurTLE import DNS, PP
+
+base_niterations = 256
+test_niterations = 32
+
+def run_simulations():
+ # change these two values as neded.
+ # number of MPI processes to use
+ nprocesses = 4
+ # number of OpenMP threads per MPI process to use
+ nthreads_per_process = 2
+
+# 1. Generate quasistationary state to use for initial conditions.
+ # create a dns object
+ c0 = DNS()
+ # launch the simulation
+ c0.launch([
+ 'NSVE',
+ '-n', '32',
+ '--np', '{0}'.format(nprocesses),
+ '--ntpp', '{0}'.format(nthreads_per_process),
+ '--precision', 'double',
+ '--src-simname', 'B32p1e4',
+ '--src-wd', TurTLE.data_dir,
+ '--src-iteration', '0',
+ '--simname', 'base_1x',
+ '--niter_todo', '{0}'.format(base_niterations),
+ '--niter_out', '{0}'.format(base_niterations),
+ '--overwrite-src-parameters',
+ '--kMeta', '1.0',
+ '--niter_stat', '16',
+ '--checkpoints_per_file', '{0}'.format(16)])
+
+# 2. Generate initial conditions for NSVE runs at 2x and 4x the
+# base resolution.
+ for factor in [2, 4]:
+ # create postprocess object
+ cc = PP()
+ # create a larger version of the field at iteration 512
+ cc.launch([
+ 'resize',
+ '--np', '{0}'.format(nprocesses),
+ '--ntpp', '{0}'.format(nthreads_per_process),
+ '--simname', 'base_1x',
+ '--precision', 'double',
+ '--iter0', '{0}'.format(base_niterations),
+ '--iter1', '{0}'.format(base_niterations),
+ '--new_nx', '{0}'.format(factor*32),
+ '--new_ny', '{0}'.format(factor*32),
+ '--new_nz', '{0}'.format(factor*32),
+ '--new_simname', 'base_{0}x'.format(factor)])
+ # update "checkpoint" file, so we can use "base__x" as "src-simname"
+ # this is needed after "resize"
+ f1 = h5py.File('base_{0}x_checkpoint_0.h5'.format(factor), 'a')
+ f1['vorticity/complex/{0}'.format(base_niterations)] = h5py.ExternalLink(
+ 'base_{0}x_fields.h5'.format(factor),
+ 'vorticity/complex/{0}'.format(base_niterations))
+ f1.close()
+
+# 3. Generate initial conditions for NSE runs at 1x, 2x and 4x the
+# base resolution.
+ for factor in [1, 2, 4]:
+ # create postprocess object
+ cc = PP()
+ # compute velocity field at last iteration
+ cc.launch([
+ 'get_velocity',
+ '--np', '{0}'.format(nprocesses),
+ '--ntpp', '{0}'.format(nthreads_per_process),
+ '--simname', 'base_{0}x'.format(factor),
+ '--precision', 'double',
+ '--iter0', '{0}'.format(base_niterations),
+ '--iter1', '{0}'.format(base_niterations)])
+ # we don't need to update "checkpoint" file after "get_velocity"
+
+# 4. Run NSVE for the three resolutions.
+ for factor in [1, 2, 4]:
+ # create dns object
+ cc = DNS()
+ # launch simulation
+ cc.launch([
+ 'NSVE',
+ '-n', '{0}'.format(factor*32),
+ '--np', '{0}'.format(nprocesses),
+ '--ntpp', '{0}'.format(nthreads_per_process),
+ '--src-simname', 'base_{0}x'.format(factor),
+ '--src-iteration', '{0}'.format(base_niterations),
+ '--simname', 'nsve_{0}x'.format(factor),
+ '--precision', 'double',
+ '--dtfactor', '0.3',
+ '--kMeta', '{0}'.format(1.0*factor),
+ '--niter_todo', '{0}'.format(test_niterations*factor),
+ '--niter_out', '{0}'.format(test_niterations*factor),
+ '--niter_stat', '{0}'.format(4*factor)])
+
+# 5. Run NSE for the three resolutions.
+ for factor in [1, 2, 4]:
+ # create dns object
+ cc = DNS()
+ # launch simulation
+ cc.launch([
+ 'NSE',
+ '-n', '{0}'.format(factor*32),
+ '--np', '{0}'.format(nprocesses),
+ '--ntpp', '{0}'.format(nthreads_per_process),
+ '--src-simname', 'base_{0}x'.format(factor),
+ '--src-iteration', '{0}'.format(base_niterations),
+ '--simname', 'nse_{0}x'.format(factor),
+ '--precision', 'double',
+ '--dtfactor', '0.3',
+ '--kMeta', '{0}'.format(1.0*factor),
+ '--niter_todo', '{0}'.format(test_niterations*factor),
+ '--niter_out', '{0}'.format(test_niterations*factor),
+ '--niter_stat', '{0}'.format(4*factor)])
+ return None
+
+def ift(cfield):
+ ff = np.fft.irfftn(cfield, axes = (0, 1, 2))
+ field = np.transpose(ff, (1, 0, 2, 3)).copy()
+ return field
+
+def compute_curl(
+ cc,
+ cfield,
+ inverse_curl = False):
+ kx = cc.get_data_file()['kspace/kx'][()]
+ ky = cc.get_data_file()['kspace/ky'][()]
+ kz = cc.get_data_file()['kspace/kz'][()]
+ ff = cfield.copy()
+ ff[..., 0] = 1j*(ky[:, None, None]*cfield[..., 2] - kz[None, :, None]*cfield[..., 1])
+ ff[..., 1] = 1j*(kz[None, :, None]*cfield[..., 0] - kx[None, None, :]*cfield[..., 2])
+ ff[..., 2] = 1j*(kx[None, None, :]*cfield[..., 1] - ky[:, None, None]*cfield[..., 0])
+ if inverse_curl:
+ k2 = (kx[None, None, :]**2 +
+ ky[ :, None, None]**2 +
+ kz[None, :, None]**2)
+ k2[0, 0, 0] = 1.
+ ff /= k2[:, :, :, None]
+ return ff
+
+def get_velocity(
+ cc,
+ iteration = 0):
+ data_file = h5py.File(
+ cc.get_checkpoint_fname(iteration = iteration),
+ 'r')
+ if 'velocity' in data_file.keys():
+ if 'real' in data_file['velocity'].keys():
+ vel = data_file['velocity/real/{0}'.format(iteration)][()]
+ else:
+ cvel = data_file['velocity/complex/{0}'.format(iteration)][()]
+ vel = ift(cvel)
+ #vel *= cc.parameters['nx']*cc.parameters['ny']*cc.parameters['nz']
+ else:
+ assert('complex' in data_file['vorticity'].keys())
+ cvort = data_file['vorticity/complex/{0}'.format(iteration)][()]
+ cvel = compute_curl(cc, cvort, inverse_curl = True)
+ vel = ift(cvel)
+ data_file.close()
+ return vel
+
+def plot_error():
+ c0_list = [DNS(simname = 'nsve_{0}x'.format(factor))
+ for factor in [1, 2, 4]]
+ c1_list = [DNS(simname = 'nse_{0}x'.format(factor))
+ for factor in [1, 2, 4]]
+ for cc in c0_list + c1_list:
+ cc.compute_statistics()
+
+ factor_list = [1, 2, 4]
+
+ error_list = []
+ for ii in range(len(factor_list)):
+ factor = factor_list[ii]
+ c0 = c0_list[ii]
+ c1 = c1_list[ii]
+ df0 = h5py.File(c0.get_checkpoint_fname(iteration = test_niterations*factor), 'r')
+ df1 = h5py.File(c1.get_checkpoint_fname(iteration = test_niterations*factor), 'r')
+ vel0 = get_velocity(c0, iteration = test_niterations*factor)
+ vel1 = get_velocity(c1, iteration = test_niterations*factor)
+ diff = vel1 - vel0
+ vv = np.sqrt(np.sum(vel0**2, axis = 3))
+ dd = np.sqrt(np.sum(diff**2, axis = 3))
+ err = np.max(dd / vv)
+ error_list.append(err)
+ print('maximum error for factor {0} is {1}'.format(
+ factor, err))
+ df0.close()
+ df1.close()
+
+ f = plt.figure(figsize = (4, 4))
+ a = f.add_subplot(111)
+ fl = np.array(factor_list).astype(np.float)
+ a.plot(fl,
+ error_list,
+ marker = '.',
+ label = 'NSVE vs NSE')
+ a.plot(fl, fl**(-3),
+ dashes = (1, 1),
+ color = 'black',
+ label = '$\propto f^{-3}$')
+ a.set_ylabel('relative error')
+ a.set_xlabel('resolution factor $f$')
+ a.set_xscale('log')
+ a.set_yscale('log')
+ a.legend(loc = 'best')
+ f.tight_layout()
+ f.savefig('field_err_vs_dt.pdf')
+ plt.close(f)
+ return None
+
+def main():
+ run_simulations()
+ plot_error()
+ return None
+
+if __name__ == '__main__':
+ main()
+
--
GitLab
From 87ea3e165c9c584288f029faeeea8cb6f5f9fcd5 Mon Sep 17 00:00:00 2001
From: Cristian C Lalescu <Cristian.Lalescu@mpcdf.mpg.de>
Date: Tue, 4 Jan 2022 13:00:31 +0100
Subject: [PATCH 02/24] moves convergence example to proper folder
---
{documentation/sphinx_static => examples}/convergence.py | 0
1 file changed, 0 insertions(+), 0 deletions(-)
rename {documentation/sphinx_static => examples}/convergence.py (100%)
diff --git a/documentation/sphinx_static/convergence.py b/examples/convergence.py
similarity index 100%
rename from documentation/sphinx_static/convergence.py
rename to examples/convergence.py
--
GitLab
From 233f62b3f6441193219aff299fa50d212c1d8743 Mon Sep 17 00:00:00 2001
From: Cristian C Lalescu <Cristian.Lalescu@mpcdf.mpg.de>
Date: Tue, 4 Jan 2022 13:50:55 +0100
Subject: [PATCH 03/24] adds text to discuss convergence test
---
documentation/index.rst | 2 +
documentation/sphinx_static/convergence.rst | 323 ++++++++++++++++++++
examples/convergence.py | 100 +++---
3 files changed, 375 insertions(+), 50 deletions(-)
create mode 100644 documentation/sphinx_static/convergence.rst
diff --git a/documentation/index.rst b/documentation/index.rst
index 0566f7b4..62a336f0 100644
--- a/documentation/index.rst
+++ b/documentation/index.rst
@@ -18,6 +18,8 @@ Contents:
chapters/api
chapters/cpp_doxygen
+ sphinx_static/convergence
+
Indices and tables
==================
diff --git a/documentation/sphinx_static/convergence.rst b/documentation/sphinx_static/convergence.rst
new file mode 100644
index 00000000..2fc0e6aa
--- /dev/null
+++ b/documentation/sphinx_static/convergence.rst
@@ -0,0 +1,323 @@
+Tutorial: convergence test
+==========================
+
+An essential property of numerical methods is their accuracy. With
+standard approaches to differential equations, one may use
+generic convergence tests to characterize algorithms and/or
+implementations.
+
+
+Navier-Stokes solution
+----------------------
+
+Since TurTLE contains solvers of the Navier Stokes equations in both
+velocity ("NSE") and vorticity formulation ("NSVE"), this allows for a direct
+convergence test: one should use both solvers with identical parameters, and
+compare solutions as the resolution is varied.
+
+Notes:
+
+ * we are discussing a partial differential equation, therefore
+ when we test for convergence we will increase both spatial and
+ temporal resolution.
+
+ * we will test convergence properties for a "statistically
+ stationary initial condition", since the smoothness properties of
+ the field will influence convergence properties in general.
+
+We present here a Python script that performs a simple convergence test
+with TurTLE. The script itself is provided as the file
+`examples/convergence.py`.
+
+The preamble imports standard packages, as well as TurTLE itself:
+
+.. code:: python
+
+ import numpy as np
+ import h5py
+ import matplotlib.pyplot as plt
+
+ import TurTLE
+ from TurTLE import DNS, PP
+
+As explained above, we should test convergence for a statistically
+stationary regime.
+The base simulation will use a real-space grid of :math:`32 \times 32 \times 32` points,
+and experience shows that quasistationarity is reached for this
+problem-size in a few hundred iterations (here `base_niterations`).
+For the convergence test itself, we use a relatively small number
+of iterations (i.e. `test_niterations`), otherwise deterministic chaos will dominate the
+difference between alternative solutions (rather than numerical integration
+errors).
+
+.. code:: python
+
+ base_niterations = 256
+ test_niterations = 32
+
+We distinguish two main steps of this script.
+First, we actually run the numerical simulations.
+Second, we analyze the results (i.e. we compute and plot the integration
+error as it changes with resolution).
+
+.. code:: python
+
+ def main():
+ run_simulations()
+ plot_error()
+ return None
+
+`run_simulations` is a fairly long but simple function.
+In brief, it
+ * generates the initial quasistationary state with the NSVE solver
+ * uses Fourier interpolation to double and quadruple the initial
+ resolution, yielding 3 vorticity fields "1x", "2x" and "4x".
+ * generates the corresponding velocity fields needed for the NSE solver
+ * launches the NSVE solver for the three resolutions
+ * launches the NSE solver for the three resolutions
+We give the full code below.
+We use the `launch` method of the `DNS` and `PP` Python
+classes --- the wrappers around the C++ `direct_numerical_simulation`
+and `postprocess` functionality.
+This means that the current Python code may be translated to a shell
+script directly, only by writing out the arguments (rather than placing
+them in a list of Python strings).
+
+
+.. code:: python
+
+ def run_simulations():
+ # change these two values as neded.
+ # number of MPI processes to use
+ nprocesses = 4
+ # number of OpenMP threads per MPI process to use
+ nthreads_per_process = 2
+
+ # 1. Generate quasistationary state to use for initial conditions.
+ # create a dns object
+ c0 = DNS()
+ # launch the simulation
+ c0.launch([
+ 'NSVE',
+ '-n', '32',
+ '--np', '{0}'.format(nprocesses),
+ '--ntpp', '{0}'.format(nthreads_per_process),
+ '--precision', 'double',
+ '--src-simname', 'B32p1e4',
+ '--src-wd', TurTLE.data_dir,
+ '--src-iteration', '0',
+ '--simname', 'base_1x',
+ '--niter_todo', '{0}'.format(base_niterations),
+ '--niter_out', '{0}'.format(base_niterations),
+ '--overwrite-src-parameters',
+ '--kMeta', '1.0',
+ '--niter_stat', '16',
+ '--checkpoints_per_file', '{0}'.format(16)])
+
+ # 2. Generate initial conditions for NSVE runs at 2x and 4x the
+ # base resolution.
+ for factor in [2, 4]:
+ # create postprocess object
+ cc = PP()
+ # create a larger version of the field at final iteration
+ cc.launch([
+ 'resize',
+ '--np', '{0}'.format(nprocesses),
+ '--ntpp', '{0}'.format(nthreads_per_process),
+ '--simname', 'base_1x',
+ '--precision', 'double',
+ '--iter0', '{0}'.format(base_niterations),
+ '--iter1', '{0}'.format(base_niterations),
+ '--new_nx', '{0}'.format(factor*32),
+ '--new_ny', '{0}'.format(factor*32),
+ '--new_nz', '{0}'.format(factor*32),
+ '--new_simname', 'base_{0}x'.format(factor)])
+ # update "checkpoint" file, so we can use "base__x" as "src-simname"
+ # this is needed after "resize"
+ f1 = h5py.File('base_{0}x_checkpoint_0.h5'.format(factor), 'a')
+ f1['vorticity/complex/{0}'.format(base_niterations)] = h5py.ExternalLink(
+ 'base_{0}x_fields.h5'.format(factor),
+ 'vorticity/complex/{0}'.format(base_niterations))
+ f1.close()
+
+ # 3. Generate initial conditions for NSE runs at 1x, 2x and 4x the
+ # base resolution.
+ for factor in [1, 2, 4]:
+ # create postprocess object
+ cc = PP()
+ # compute velocity field at last iteration
+ cc.launch([
+ 'get_velocity',
+ '--np', '{0}'.format(nprocesses),
+ '--ntpp', '{0}'.format(nthreads_per_process),
+ '--simname', 'base_{0}x'.format(factor),
+ '--precision', 'double',
+ '--iter0', '{0}'.format(base_niterations),
+ '--iter1', '{0}'.format(base_niterations)])
+ # we don't need to update "checkpoint" file after "get_velocity"
+
+ # 4. Run NSVE for the three resolutions.
+ for factor in [1, 2, 4]:
+ # create dns object
+ cc = DNS()
+ # launch simulation
+ cc.launch([
+ 'NSVE',
+ '-n', '{0}'.format(factor*32),
+ '--np', '{0}'.format(nprocesses),
+ '--ntpp', '{0}'.format(nthreads_per_process),
+ '--src-simname', 'base_{0}x'.format(factor),
+ '--src-iteration', '{0}'.format(base_niterations),
+ '--simname', 'nsve_{0}x'.format(factor),
+ '--precision', 'double',
+ '--dtfactor', '0.3',
+ '--kMeta', '{0}'.format(1.0*factor),
+ '--niter_todo', '{0}'.format(test_niterations*factor),
+ '--niter_out', '{0}'.format(test_niterations*factor),
+ '--niter_stat', '{0}'.format(4*factor)])
+
+ # 5. Run NSE for the three resolutions.
+ for factor in [1, 2, 4]:
+ # create dns object
+ cc = DNS()
+ # launch simulation
+ cc.launch([
+ 'NSE',
+ '-n', '{0}'.format(factor*32),
+ '--np', '{0}'.format(nprocesses),
+ '--ntpp', '{0}'.format(nthreads_per_process),
+ '--src-simname', 'base_{0}x'.format(factor),
+ '--src-iteration', '{0}'.format(base_niterations),
+ '--simname', 'nse_{0}x'.format(factor),
+ '--precision', 'double',
+ '--dtfactor', '0.3',
+ '--kMeta', '{0}'.format(1.0*factor),
+ '--niter_todo', '{0}'.format(test_niterations*factor),
+ '--niter_out', '{0}'.format(test_niterations*factor),
+ '--niter_stat', '{0}'.format(4*factor)])
+ return None
+
+Once the runs are finished successfully, the code calls `plot_error`.
+Here we first read the output of the six different runs, and we compute
+their statistics, since the call to `compute_statistics` will in fact also
+perform some sanity checks on the output.
+We then read the velocity fields computed by `NSVE` and `NSE`, and
+compare them (please see the code for `get_velocity` below).
+The results are plotted together with a 3rd order error estimate, for
+subsequent assessment.
+
+.. code:: python
+
+ def plot_error():
+ c0_list = [DNS(simname = 'nsve_{0}x'.format(factor))
+ for factor in [1, 2, 4]]
+ c1_list = [DNS(simname = 'nse_{0}x'.format(factor))
+ for factor in [1, 2, 4]]
+ for cc in c0_list + c1_list:
+ cc.compute_statistics()
+
+ factor_list = [1, 2, 4]
+
+ error_list = []
+ for ii in range(len(factor_list)):
+ factor = factor_list[ii]
+ c0 = c0_list[ii]
+ c1 = c1_list[ii]
+ df0 = h5py.File(c0.get_checkpoint_fname(iteration = test_niterations*factor), 'r')
+ df1 = h5py.File(c1.get_checkpoint_fname(iteration = test_niterations*factor), 'r')
+ vel0 = get_velocity(c0, iteration = test_niterations*factor)
+ vel1 = get_velocity(c1, iteration = test_niterations*factor)
+ diff = vel1 - vel0
+ vv = np.sqrt(np.sum(vel0**2, axis = 3))
+ dd = np.sqrt(np.sum(diff**2, axis = 3))
+ err = np.max(dd / vv)
+ error_list.append(err)
+ print('maximum error for factor {0} is {1}'.format(
+ factor, err))
+ df0.close()
+ df1.close()
+
+ f = plt.figure(figsize = (4, 4))
+ a = f.add_subplot(111)
+ fl = np.array(factor_list).astype(np.float)
+ a.plot(fl,
+ error_list,
+ marker = '.',
+ label = 'NSVE vs NSE')
+ a.plot(fl, fl**(-3),
+ dashes = (1, 1),
+ color = 'black',
+ label = '$\propto f^{-3}$')
+ a.set_ylabel('relative error')
+ a.set_xlabel('resolution factor $f$')
+ a.set_xscale('log')
+ a.set_yscale('log')
+ a.legend(loc = 'best')
+ f.tight_layout()
+ f.savefig('field_err_vs_dt.pdf')
+ plt.close(f)
+ return None
+
+The `get_velocity` function is slightly more elaborate, as it needs to
+check whether the data comes from an `NSVE` run or an `NSE` run.
+Furthermore, in the case of an `NSVE` run we need to explicitly invert
+the curl operator within the Python code in order to obtain the
+velocity.
+Otherwise, we perform an inverse FFT using `numpy`, taking care to
+account for the transposed data layout (which itself is due to the use
+of FFTW).
+
+.. code:: python
+
+ def get_velocity(
+ cc,
+ iteration = 0):
+ data_file = h5py.File(
+ cc.get_checkpoint_fname(iteration = iteration),
+ 'r')
+ if 'velocity' in data_file.keys():
+ if 'real' in data_file['velocity'].keys():
+ vel = data_file['velocity/real/{0}'.format(iteration)][()]
+ else:
+ cvel = data_file['velocity/complex/{0}'.format(iteration)][()]
+ vel = ift(cvel)
+ #vel *= cc.parameters['nx']*cc.parameters['ny']*cc.parameters['nz']
+ else:
+ assert('complex' in data_file['vorticity'].keys())
+ cvort = data_file['vorticity/complex/{0}'.format(iteration)][()]
+ cvel = compute_curl(cc, cvort, inverse_curl = True)
+ vel = ift(cvel)
+ data_file.close()
+ return vel
+
+ def ift(cfield):
+ ff = np.fft.irfftn(cfield, axes = (0, 1, 2))
+ field = np.transpose(ff, (1, 0, 2, 3)).copy()
+ return field
+
+ def compute_curl(
+ cc,
+ cfield,
+ inverse_curl = False):
+ kx = cc.get_data_file()['kspace/kx'][()]
+ ky = cc.get_data_file()['kspace/ky'][()]
+ kz = cc.get_data_file()['kspace/kz'][()]
+ ff = cfield.copy()
+ ff[..., 0] = 1j*(ky[:, None, None]*cfield[..., 2] - kz[None, :, None]*cfield[..., 1])
+ ff[..., 1] = 1j*(kz[None, :, None]*cfield[..., 0] - kx[None, None, :]*cfield[..., 2])
+ ff[..., 2] = 1j*(kx[None, None, :]*cfield[..., 1] - ky[:, None, None]*cfield[..., 0])
+ if inverse_curl:
+ k2 = (kx[None, None, :]**2 +
+ ky[ :, None, None]**2 +
+ kz[None, :, None]**2)
+ k2[0, 0, 0] = 1.
+ ff /= k2[:, :, :, None]
+ return ff
+
+Finally, the script ends with a standard call to `main`:
+
+.. code:: python
+
+ if __name__ == '__main__':
+ main()
+
diff --git a/examples/convergence.py b/examples/convergence.py
index 5f8d5343..6929f77b 100644
--- a/examples/convergence.py
+++ b/examples/convergence.py
@@ -8,6 +8,11 @@ from TurTLE import DNS, PP
base_niterations = 256
test_niterations = 32
+def main():
+ run_simulations()
+ plot_error()
+ return None
+
def run_simulations():
# change these two values as neded.
# number of MPI processes to use
@@ -41,7 +46,7 @@ def run_simulations():
for factor in [2, 4]:
# create postprocess object
cc = PP()
- # create a larger version of the field at iteration 512
+ # create a larger version of the field at final iteration
cc.launch([
'resize',
'--np', '{0}'.format(nprocesses),
@@ -119,51 +124,6 @@ def run_simulations():
'--niter_stat', '{0}'.format(4*factor)])
return None
-def ift(cfield):
- ff = np.fft.irfftn(cfield, axes = (0, 1, 2))
- field = np.transpose(ff, (1, 0, 2, 3)).copy()
- return field
-
-def compute_curl(
- cc,
- cfield,
- inverse_curl = False):
- kx = cc.get_data_file()['kspace/kx'][()]
- ky = cc.get_data_file()['kspace/ky'][()]
- kz = cc.get_data_file()['kspace/kz'][()]
- ff = cfield.copy()
- ff[..., 0] = 1j*(ky[:, None, None]*cfield[..., 2] - kz[None, :, None]*cfield[..., 1])
- ff[..., 1] = 1j*(kz[None, :, None]*cfield[..., 0] - kx[None, None, :]*cfield[..., 2])
- ff[..., 2] = 1j*(kx[None, None, :]*cfield[..., 1] - ky[:, None, None]*cfield[..., 0])
- if inverse_curl:
- k2 = (kx[None, None, :]**2 +
- ky[ :, None, None]**2 +
- kz[None, :, None]**2)
- k2[0, 0, 0] = 1.
- ff /= k2[:, :, :, None]
- return ff
-
-def get_velocity(
- cc,
- iteration = 0):
- data_file = h5py.File(
- cc.get_checkpoint_fname(iteration = iteration),
- 'r')
- if 'velocity' in data_file.keys():
- if 'real' in data_file['velocity'].keys():
- vel = data_file['velocity/real/{0}'.format(iteration)][()]
- else:
- cvel = data_file['velocity/complex/{0}'.format(iteration)][()]
- vel = ift(cvel)
- #vel *= cc.parameters['nx']*cc.parameters['ny']*cc.parameters['nz']
- else:
- assert('complex' in data_file['vorticity'].keys())
- cvort = data_file['vorticity/complex/{0}'.format(iteration)][()]
- cvel = compute_curl(cc, cvort, inverse_curl = True)
- vel = ift(cvel)
- data_file.close()
- return vel
-
def plot_error():
c0_list = [DNS(simname = 'nsve_{0}x'.format(factor))
for factor in [1, 2, 4]]
@@ -214,10 +174,50 @@ def plot_error():
plt.close(f)
return None
-def main():
- run_simulations()
- plot_error()
- return None
+def get_velocity(
+ cc,
+ iteration = 0):
+ data_file = h5py.File(
+ cc.get_checkpoint_fname(iteration = iteration),
+ 'r')
+ if 'velocity' in data_file.keys():
+ if 'real' in data_file['velocity'].keys():
+ vel = data_file['velocity/real/{0}'.format(iteration)][()]
+ else:
+ cvel = data_file['velocity/complex/{0}'.format(iteration)][()]
+ vel = ift(cvel)
+ #vel *= cc.parameters['nx']*cc.parameters['ny']*cc.parameters['nz']
+ else:
+ assert('complex' in data_file['vorticity'].keys())
+ cvort = data_file['vorticity/complex/{0}'.format(iteration)][()]
+ cvel = compute_curl(cc, cvort, inverse_curl = True)
+ vel = ift(cvel)
+ data_file.close()
+ return vel
+
+def ift(cfield):
+ ff = np.fft.irfftn(cfield, axes = (0, 1, 2))
+ field = np.transpose(ff, (1, 0, 2, 3)).copy()
+ return field
+
+def compute_curl(
+ cc,
+ cfield,
+ inverse_curl = False):
+ kx = cc.get_data_file()['kspace/kx'][()]
+ ky = cc.get_data_file()['kspace/ky'][()]
+ kz = cc.get_data_file()['kspace/kz'][()]
+ ff = cfield.copy()
+ ff[..., 0] = 1j*(ky[:, None, None]*cfield[..., 2] - kz[None, :, None]*cfield[..., 1])
+ ff[..., 1] = 1j*(kz[None, :, None]*cfield[..., 0] - kx[None, None, :]*cfield[..., 2])
+ ff[..., 2] = 1j*(kx[None, None, :]*cfield[..., 1] - ky[:, None, None]*cfield[..., 0])
+ if inverse_curl:
+ k2 = (kx[None, None, :]**2 +
+ ky[ :, None, None]**2 +
+ kz[None, :, None]**2)
+ k2[0, 0, 0] = 1.
+ ff /= k2[:, :, :, None]
+ return ff
if __name__ == '__main__':
main()
--
GitLab
From efacb81b059edee97e2d03c93e9dad9694152bfa Mon Sep 17 00:00:00 2001
From: Cristian C Lalescu <Cristian.Lalescu@mpcdf.mpg.de>
Date: Thu, 6 Jan 2022 21:13:02 +0100
Subject: [PATCH 04/24] fixes initial condition check
---
TurTLE/DNS.py | 2 +-
1 file changed, 1 insertion(+), 1 deletion(-)
diff --git a/TurTLE/DNS.py b/TurTLE/DNS.py
index de8b7ff1..4f0ff809 100644
--- a/TurTLE/DNS.py
+++ b/TurTLE/DNS.py
@@ -1128,7 +1128,7 @@ class DNS(_code):
f = h5py.File(self.get_checkpoint_0_fname(), 'r')
try:
dset = f[checkpoint_field + '/complex/0']
- need_field = (dset.shape == (self.parameters['ny'],
+ need_field = (dset.shape != (self.parameters['ny'],
self.parameters['nz'],
self.parameters['nx']//2+1,
3))
--
GitLab
From 2ebb1c88545af4e00ec56d995db620d0edc42b52 Mon Sep 17 00:00:00 2001
From: Cristian C Lalescu <Cristian.Lalescu@mpcdf.mpg.de>
Date: Thu, 6 Jan 2022 21:13:10 +0100
Subject: [PATCH 05/24] adds convergence test for particles
---
examples/convergence.py | 167 ++++++++++++++++++++++++++++++++++++++--
1 file changed, 160 insertions(+), 7 deletions(-)
diff --git a/examples/convergence.py b/examples/convergence.py
index 6929f77b..3289c8c8 100644
--- a/examples/convergence.py
+++ b/examples/convergence.py
@@ -8,12 +8,21 @@ from TurTLE import DNS, PP
base_niterations = 256
test_niterations = 32
+nparticles = 100000
+particle_random_seed = 15
+
def main():
- run_simulations()
- plot_error()
+ generate_initial_conditions()
+
+ run_simulations_field()
+ plot_error_field()
+
+ run_simulations_particles()
+ plot_error_particles()
+ plot_traj_particles()
return None
-def run_simulations():
+def generate_initial_conditions():
# change these two values as neded.
# number of MPI processes to use
nprocesses = 4
@@ -82,8 +91,16 @@ def run_simulations():
'--iter0', '{0}'.format(base_niterations),
'--iter1', '{0}'.format(base_niterations)])
# we don't need to update "checkpoint" file after "get_velocity"
+ return None
-# 4. Run NSVE for the three resolutions.
+def run_simulations_field():
+ # change these two values as neded.
+ # number of MPI processes to use
+ nprocesses = 4
+ # number of OpenMP threads per MPI process to use
+ nthreads_per_process = 2
+
+# 1. Run NSVE for the three resolutions.
for factor in [1, 2, 4]:
# create dns object
cc = DNS()
@@ -103,7 +120,7 @@ def run_simulations():
'--niter_out', '{0}'.format(test_niterations*factor),
'--niter_stat', '{0}'.format(4*factor)])
-# 5. Run NSE for the three resolutions.
+# 2. Run NSE for the three resolutions.
for factor in [1, 2, 4]:
# create dns object
cc = DNS()
@@ -124,7 +141,7 @@ def run_simulations():
'--niter_stat', '{0}'.format(4*factor)])
return None
-def plot_error():
+def plot_error_field():
c0_list = [DNS(simname = 'nsve_{0}x'.format(factor))
for factor in [1, 2, 4]]
c1_list = [DNS(simname = 'nse_{0}x'.format(factor))
@@ -170,7 +187,7 @@ def plot_error():
a.set_yscale('log')
a.legend(loc = 'best')
f.tight_layout()
- f.savefig('field_err_vs_dt.pdf')
+ f.savefig('err_vs_dt_field.pdf')
plt.close(f)
return None
@@ -219,6 +236,142 @@ def compute_curl(
ff /= k2[:, :, :, None]
return ff
+def run_simulations_particles():
+ # change these two values as neded.
+ # number of MPI processes to use
+ nprocesses = 4
+ # number of OpenMP threads per MPI process to use
+ nthreads_per_process = 2
+
+# 1. Run NSVEparticles for resolution 1x, for a few iterations, to build up rhs values.
+ factor = 1
+ # create dns object
+ cc = DNS()
+ # launch simulation
+ cc.launch([
+ 'NSVEparticles',
+ '-n', '{0}'.format(factor*32),
+ '--np', '{0}'.format(nprocesses),
+ '--ntpp', '{0}'.format(nthreads_per_process),
+ '--src-simname', 'base_{0}x'.format(factor),
+ '--src-iteration', '{0}'.format(base_niterations),
+ '--simname', 'nsvep_base'.format(factor),
+ '--precision', 'double',
+ '--dtfactor', '0.3',
+ '--kMeta', '{0}'.format(1.0*factor),
+ '--niter_todo', '{0}'.format(8),
+ '--niter_out', '{0}'.format(8),
+ '--niter_stat', '{0}'.format(8),
+ '--nparticles', '{0}'.format(nparticles),
+ '--niter_part', '{0}'.format(8),
+ '--cpp_random_particles', '{0}'.format(particle_random_seed)])
+
+# 2. Prepare initial conditions
+ for factor in [1, 2, 4]:
+ df = h5py.File('nsvep_{0}x_checkpoint_0.h5'.format(factor), 'w')
+ # field
+ df['vorticity/complex/0'] = h5py.ExternalLink(
+ 'base_{0}x_checkpoint_0.h5'.format(factor),
+ 'vorticity/complex/{0}'.format(base_niterations))
+ # particles
+ df['tracers0/state/0'] = h5py.ExternalLink(
+ 'nsvep_base_checkpoint_0.h5',
+ 'tracers0/state/8')
+ df['tracers0/rhs/0'] = h5py.ExternalLink(
+ 'nsvep_base_checkpoint_0.h5',
+ 'tracers0/rhs/8')
+ df.close()
+
+# 3. Run NSVEparticles
+ for factor in [1, 2, 4]:
+ # create dns object
+ cc = DNS()
+ # launch simulation
+ cc.launch([
+ 'NSVEparticles',
+ '-n', '{0}'.format(factor*32),
+ '--np', '{0}'.format(nprocesses),
+ '--ntpp', '{0}'.format(nthreads_per_process),
+ '--simname', 'nsvep_{0}x'.format(factor),
+ '--precision', 'double',
+ '--dtfactor', '0.3',
+ '--kMeta', '{0}'.format(1.0*factor),
+ '--niter_todo', '{0}'.format(test_niterations*factor),
+ '--niter_out', '{0}'.format(test_niterations*factor),
+ '--niter_stat', '{0}'.format(4*factor),
+ '--nparticles', '{0}'.format(nparticles),
+ '--niter_part', '{0}'.format(2*factor),
+ '--cpp_random_particles', '0' # turn off cpp particle initialization
+ ])
+ return None
+
+def plot_error_particles():
+ f = plt.figure()
+ a = f.add_subplot(111)
+ err_max_list = []
+ err_mean_list = []
+ factor_list = [1, 2]
+ for factor in factor_list:
+ c0 = DNS(simname = 'nsvep_{0}x'.format(factor))
+ c1 = DNS(simname = 'nsvep_{0}x'.format(factor*2))
+ for cc in [c0, c1]:
+ cc.compute_statistics()
+ cc.parameters['niter_part'] = cc.get_data_file()['parameters/niter_part'][()]
+ f0 = h5py.File(c0.get_checkpoint_fname(iteration = test_niterations*factor), 'r')
+ f1 = h5py.File(c1.get_checkpoint_fname(iteration = test_niterations*factor*2), 'r')
+ x0 = f0['tracers0/state/{0}'.format(test_niterations*factor)][()]
+ x1 = f1['tracers0/state/{0}'.format(test_niterations*factor*2)][()]
+ err_max_list.append(np.max(np.abs(x1 - x0)))
+ err_mean_list.append(np.mean(np.abs(x1 - x0)))
+ f0.close()
+ f1.close()
+ factor_list = np.array(factor_list).astype(np.float)
+ err_max_list = np.array(err_max_list)
+ err_mean_list = np.array(err_mean_list)
+ a.plot(factor_list, err_max_list, marker = '.', label = 'max error')
+ a.plot(factor_list, err_mean_list, marker = '.', label = 'mean error')
+ a.plot(factor_list,
+ (1e-2)*factor_list**(-3),
+ color = 'black',
+ dashes = (2, 2),
+ label = '$\propto f^{-3}$')
+ a.plot(factor_list,
+ (1e-2)*factor_list**(-4),
+ color = 'black',
+ dashes = (1, 1),
+ label = '$\propto f^{-4}$')
+ a.set_xscale('log')
+ a.set_yscale('log')
+ a.set_xlabel('resolution factor f')
+ a.set_ylabel('absolute trajectory error [DNS units]')
+ a.legend(loc = 'best')
+ f.tight_layout()
+ f.savefig('err_vs_dt_particle.pdf')
+ plt.close(f)
+ return None
+
+def plot_traj_particles():
+ f = plt.figure()
+ a = f.add_subplot(111)
+ for factor in [1, 2, 4]:
+ cc = DNS(simname = 'nsvep_{0}x'.format(factor))
+ cc.compute_statistics()
+ xx = read_trajectory(cc, 14)
+ a.plot(xx[:, 0], xx[:, 1])
+ f.tight_layout()
+ f.savefig('trajectories.pdf')
+ plt.close(f)
+ return None
+
+def read_trajectory(cc, traj_index):
+ cc.parameters['niter_part'] = cc.get_data_file()['parameters/niter_part'][()]
+ df = cc.get_particle_file()
+ xx = []
+ for ii in range(0, cc.get_data_file()['iteration'][()], cc.parameters['niter_part']):
+ xx.append(df['tracers0/position/{0}'.format(ii)][traj_index])
+ df.close()
+ return np.array(xx)
+
if __name__ == '__main__':
main()
--
GitLab
From 7715c5ec6359a7c750d76b05b1af3f0b1b496264 Mon Sep 17 00:00:00 2001
From: Cristian C Lalescu <Cristian.Lalescu@mpcdf.mpg.de>
Date: Fri, 7 Jan 2022 14:24:37 +0100
Subject: [PATCH 06/24] adds option to control iter0 for DNS class
---
TurTLE/DNS.py | 5 +++--
1 file changed, 3 insertions(+), 2 deletions(-)
diff --git a/TurTLE/DNS.py b/TurTLE/DNS.py
index 4f0ff809..d98367ac 100644
--- a/TurTLE/DNS.py
+++ b/TurTLE/DNS.py
@@ -1213,12 +1213,13 @@ class DNS(_code):
return None
def launch_jobs(
self,
- opt = None):
+ opt = None,
+ iter0 = 0):
if not os.path.exists(self.get_data_file_name()):
if not os.path.isdir(self.work_dir):
os.makedirs(self.work_dir)
self.generate_initial_condition(opt = opt)
- self.write_par()
+ self.write_par(iter0 = iter0)
if (('test' in self.dns_type) or
(self.dns_type in ['kraichnan_field'])):
self.check_current_vorticity_exists = False
--
GitLab
From 67aad83cc31952d796e423d891d34df5f5b3ff2d Mon Sep 17 00:00:00 2001
From: Cristian C Lalescu <Cristian.Lalescu@mpcdf.mpg.de>
Date: Fri, 7 Jan 2022 14:24:50 +0100
Subject: [PATCH 07/24] finalizes convergence tutorial
---
documentation/sphinx_static/convergence.rst | 300 ++++++++++++++++++--
examples/convergence.py | 44 +--
2 files changed, 305 insertions(+), 39 deletions(-)
diff --git a/documentation/sphinx_static/convergence.rst b/documentation/sphinx_static/convergence.rst
index 2fc0e6aa..1c6db97e 100644
--- a/documentation/sphinx_static/convergence.rst
+++ b/documentation/sphinx_static/convergence.rst
@@ -25,7 +25,52 @@ Notes:
stationary initial condition", since the smoothness properties of
the field will influence convergence properties in general.
-We present here a Python script that performs a simple convergence test
+In practice, we compute numerical solutions of NSE and NSVE, convert the
+vorticity of the latter simulation to a velocity field, and compare
+them.
+The time-stepping method is the same 3rd order Runge Kutta algorithm,
+therefore we expect a third order dependency of the "error" on the
+time-step.
+The "spatial discretization" is identical in both cases, since we use
+the same underlying pseudo-spectral framework (including the dealiasing
+method).
+
+The observed numerical differences are due to the simulation of technically
+different PDEs: different arithmetical operations are performed despite
+the fact that "NSVE is simply the curl of NSE".
+In turn, the effects of finite numerical precision and discretization
+are brought into the computation differently, leading to systematic
+deviations between the two DNS.
+
+
+Particle tracking errors
+------------------------
+
+For particle tracking, we use an alternative approach: use the same
+algorithm, and compare results obtained with different resolutions.
+Since we are discussing the numerical solution of an ODE where the right
+hand side is itself a numerical solution from a PDE, we in fact modify
+the resolution of the field PDE (i.e. spatial resolution as well).
+
+There is a more complex mechanism that generates numerical errors for
+particle tracking in this setting.
+In particular, the accuracy of the field itself is relevant, as well as
+the accuracy of the interpolation method coupled to the ODE solver.
+For instance the default particle tracking solver is a 4th order
+Adams Bashforth method in TurTLE, which seems unnecessary since the
+fluid only provides a 3rd order solution.
+The default interpolation method is that of cubic splines, which should
+in fact limit ODE error convergence to 2nd order (because convergence
+relies on existence of relevant Taylor expansion terms, and interpolated
+fields only have a finite number of continuous derivatives).
+This discussion is briefly continued below, but we will not do it justice
+in this tutorial.
+
+
+Python code
+-----------
+
+We present here a Python script that performs simple convergence tests
with TurTLE. The script itself is provided as the file
`examples/convergence.py`.
@@ -55,38 +100,51 @@ errors).
base_niterations = 256
test_niterations = 32
-We distinguish two main steps of this script.
-First, we actually run the numerical simulations.
-Second, we analyze the results (i.e. we compute and plot the integration
-error as it changes with resolution).
+We consider :math:`10^5` particles, and we also choose a specific random
+seed for their initial locations.
+
+.. code:: python
+
+ nparticles = 100000
+ particle_random_seed = 15
+
+We distinguish a few steps of this script.
+First, we generate the statistically quasistationary regime.
+Second, we run the fluid solver and analyze the results.
+Finally, we run the particle simulations and also analyze these results.
+"Analysis" refers here to simple error plots, but more elaborate
+postprocessing can be performed if needed.
.. code:: python
def main():
- run_simulations()
- plot_error()
+ generate_initial_conditions()
+
+ run_simulations_field()
+ plot_error_field()
+
+ run_simulations_particles()
+ plot_error_particles()
return None
-`run_simulations` is a fairly long but simple function.
-In brief, it
- * generates the initial quasistationary state with the NSVE solver
+`generate_initial_conditions` performs a few calls to C++ executable
+codes generated with TurTLE. In brief, it
+ * generates a velocity field in a quasistationary Navier-Stokes
+ regime (using the NSVE solver).
* uses Fourier interpolation to double and quadruple the initial
resolution, yielding 3 vorticity fields "1x", "2x" and "4x".
* generates the corresponding velocity fields needed for the NSE solver
- * launches the NSVE solver for the three resolutions
- * launches the NSE solver for the three resolutions
-We give the full code below.
We use the `launch` method of the `DNS` and `PP` Python
classes --- the wrappers around the C++ `direct_numerical_simulation`
and `postprocess` functionality.
This means that the current Python code may be translated to a shell
script directly, only by writing out the arguments (rather than placing
them in a list of Python strings).
-
+The full function is given below:
.. code:: python
- def run_simulations():
+ def generate_initial_conditions():
# change these two values as neded.
# number of MPI processes to use
nprocesses = 4
@@ -155,8 +213,22 @@ them in a list of Python strings).
'--iter0', '{0}'.format(base_niterations),
'--iter1', '{0}'.format(base_niterations)])
# we don't need to update "checkpoint" file after "get_velocity"
+ return None
+
+`run_simulations_field` runs six DNS (3 resolutions for each of NSE and
+NSVE solvers):
+
- # 4. Run NSVE for the three resolutions.
+.. code:: python
+
+ def run_simulations_field():
+ # change these two values as neded.
+ # number of MPI processes to use
+ nprocesses = 4
+ # number of OpenMP threads per MPI process to use
+ nthreads_per_process = 2
+
+ # 1. Run NSVE for the three resolutions.
for factor in [1, 2, 4]:
# create dns object
cc = DNS()
@@ -176,7 +248,7 @@ them in a list of Python strings).
'--niter_out', '{0}'.format(test_niterations*factor),
'--niter_stat', '{0}'.format(4*factor)])
- # 5. Run NSE for the three resolutions.
+ # 2. Run NSE for the three resolutions.
for factor in [1, 2, 4]:
# create dns object
cc = DNS()
@@ -197,7 +269,8 @@ them in a list of Python strings).
'--niter_stat', '{0}'.format(4*factor)])
return None
-Once the runs are finished successfully, the code calls `plot_error`.
+Once the runs are finished successfully, the code calls
+`plot_error_field`.
Here we first read the output of the six different runs, and we compute
their statistics, since the call to `compute_statistics` will in fact also
perform some sanity checks on the output.
@@ -208,7 +281,7 @@ subsequent assessment.
.. code:: python
- def plot_error():
+ def plot_error_field():
c0_list = [DNS(simname = 'nsve_{0}x'.format(factor))
for factor in [1, 2, 4]]
c1_list = [DNS(simname = 'nse_{0}x'.format(factor))
@@ -255,6 +328,7 @@ subsequent assessment.
a.legend(loc = 'best')
f.tight_layout()
f.savefig('field_err_vs_dt.pdf')
+ f.savefig('field_err_vs_dt.png')
plt.close(f)
return None
@@ -314,6 +388,194 @@ of FFTW).
ff /= k2[:, :, :, None]
return ff
+We then define the function that runs the particle simulations,
+`run_simulations_particles`.
+Because we use an Adams-Bashforth method, we need to know the values of
+the particle velocity (i.e. the right-hand-side of the ODE) at previous
+steps.
+TurTLE accomplishes this by using the Euler integration scheme for "time
+step 0", then using a 2nd order Adams-Bashforth, etc, until the desired
+number of right-hand-side values is stored.
+Thus the code first integrates trajectories for 8 iterations, and the
+output will contain the additional information.
+This happens because such information is crucial for checkpointing ---
+i.e. stopping/restarting the simulation at arbitrary iterations without
+affecting the numerical solution.
+
+To put it simply, for the simulation "nsvep_base" the dataset
+"tracers0/rhs/0" contains only zeros, and TurTLE ignores them.
+However, the "tracers0/rhs/8" dataset for simulation "nsvep_1x" contains
+meaningful values (that are used because we request that `iter0` is
+different from 0).
+
+.. code:: python
+
+ def run_simulations_particles():
+ # change these two values as neded.
+ # number of MPI processes to use
+ nprocesses = 4
+ # number of OpenMP threads per MPI process to use
+ nthreads_per_process = 2
+
+ # 1. Run NSVEparticles for resolution 1x, for a few iterations, to build up rhs values.
+ factor = 1
+ # create dns object
+ cc = DNS()
+ # launch simulation
+ cc.launch([
+ 'NSVEparticles',
+ '-n', '{0}'.format(factor*32),
+ '--np', '{0}'.format(nprocesses),
+ '--ntpp', '{0}'.format(nthreads_per_process),
+ '--src-simname', 'base_{0}x'.format(factor),
+ '--src-iteration', '{0}'.format(base_niterations),
+ '--simname', 'nsvep_base'.format(factor),
+ '--precision', 'double',
+ '--dtfactor', '0.3',
+ '--kMeta', '{0}'.format(1.0*factor),
+ '--niter_todo', '{0}'.format(8),
+ '--niter_out', '{0}'.format(8),
+ '--niter_stat', '{0}'.format(8),
+ '--nparticles', '{0}'.format(nparticles),
+ '--niter_part', '{0}'.format(8),
+ '--cpp_random_particles', '{0}'.format(particle_random_seed)])
+
+ # 2. Prepare initial conditions
+ for factor in [1, 2, 4]:
+ df = h5py.File('nsvep_{0}x_checkpoint_0.h5'.format(factor), 'w')
+ # field
+ df['vorticity/complex/{0}'.format(8*factor)] = h5py.ExternalLink(
+ 'base_{0}x_checkpoint_0.h5'.format(factor),
+ 'vorticity/complex/{0}'.format(base_niterations))
+ # particles
+ df['tracers0/state/{0}'.format(8*factor)] = h5py.ExternalLink(
+ 'nsvep_base_checkpoint_0.h5',
+ 'tracers0/state/8')
+ df['tracers0/rhs/{0}'.format(8*factor)] = h5py.ExternalLink(
+ 'nsvep_base_checkpoint_0.h5',
+ 'tracers0/rhs/8')
+ df.close()
+
+ # 3. Run NSVEparticles
+ for factor in [1, 2, 4]:
+ # create dns object
+ cc = DNS()
+ # launch simulation
+ cc.launch([
+ 'NSVEparticles',
+ '-n', '{0}'.format(factor*32),
+ '--np', '{0}'.format(nprocesses),
+ '--ntpp', '{0}'.format(nthreads_per_process),
+ '--simname', 'nsvep_{0}x'.format(factor),
+ '--precision', 'double',
+ '--dtfactor', '0.3',
+ '--kMeta', '{0}'.format(1.0*factor),
+ '--niter_todo', '{0}'.format(test_niterations*factor),
+ '--niter_out', '{0}'.format(test_niterations*factor),
+ '--niter_stat', '{0}'.format(4*factor),
+ '--nparticles', '{0}'.format(nparticles),
+ '--niter_part', '{0}'.format(2*factor),
+ '--cpp_random_particles', '0'], # turn off cpp particle initialization
+ iter0 = 8*factor)
+ return None
+
+To compute the trajectory integration error, we proceed as explained
+above, and compare each DNS with its corresponding double-the-resolution DNS:
+
+.. code:: python
+
+ def plot_error_particles():
+ f = plt.figure()
+ a = f.add_subplot(111)
+ err_max_list = []
+ err_mean_list = []
+ factor_list = [1, 2]
+ for factor in factor_list:
+ c1 = DNS(simname = 'nsvep_{0}x'.format(factor))
+ c2 = DNS(simname = 'nsvep_{0}x'.format(factor*2))
+ for cc in [c1, c2]:
+ cc.parameters['niter_part'] = cc.get_data_file()['parameters/niter_part'][()]
+ c1.compute_statistics(iter0 = 8*factor)
+ c2.compute_statistics(iter0 = 8*factor*2)
+ final_iter_x1 = c1.get_data_file()['iteration'][()]
+ final_iter_x2 = c2.get_data_file()['iteration'][()]
+ f1 = h5py.File(c1.simname + '_checkpoint_0.h5', 'r')
+ f2 = h5py.File(c2.simname + '_checkpoint_0.h5', 'r')
+ x1 = f1['tracers0/state/{0}'.format(final_iter_x1)][()]
+ x2 = f2['tracers0/state/{0}'.format(final_iter_x2)][()]
+ err_max_list.append(np.max(np.abs(x2 - x1)))
+ err_mean_list.append(np.mean(np.abs(x2 - x1)))
+ f1.close()
+ f2.close()
+ factor_list = np.array(factor_list).astype(np.float)
+ err_max_list = np.array(err_max_list)
+ err_mean_list = np.array(err_mean_list)
+ a.plot(factor_list, err_max_list, marker = '.', label = 'max error')
+ a.plot(factor_list, err_mean_list, marker = '.', label = 'mean error')
+ a.plot(factor_list,
+ (1e-2)*factor_list**(-3),
+ color = 'black',
+ dashes = (2, 2),
+ label = '$\propto f^{-3}$')
+ a.plot(factor_list,
+ (1e-2)*factor_list**(-4),
+ color = 'black',
+ dashes = (1, 1),
+ label = '$\propto f^{-4}$')
+ a.set_xscale('log')
+ a.set_yscale('log')
+ a.set_xlabel('resolution factor f')
+ a.set_ylabel('absolute trajectory error [DNS units]')
+ a.legend(loc = 'best')
+ f.tight_layout()
+ f.savefig('err_vs_dt_particle.pdf')
+ f.savefig('err_vs_dt_particle.png')
+ plt.close(f)
+ return None
+
+Note that we plot two error measures: the maximum error, as well as the
+mean error.
+The plot suggests that these converge at different rates: the mean error
+exhibits 4th order convergence in "factor", whereas the maximum error
+exhibits 3rd order convergence (the limit imposed by the fluid solver
+error).
+While a more detailed investigation would be in order, I speculate that
+for this particular setup the increase of the spatial resolution along
+with the temporal resolution renders the interpolation errors (which should
+decrease the global order to 2) smaller than the simultaneous temporal
+integration errors.
+In any case the interplay of the different error sources is a fairly
+complex subject in itself, which we don't propose to address here in
+full.
+
+For the beginner's convenience, we also provide a method to plot
+individual particle trajectories:
+
+.. code:: python
+
+ def plot_traj_particles():
+ f = plt.figure()
+ a = f.add_subplot(111)
+ for factor in [1, 2, 4]:
+ cc = DNS(simname = 'nsvep_{0}x'.format(factor))
+ cc.compute_statistics(iter0 = 8*factor)
+ xx = read_trajectory(cc, 14, iter0 = 8*factor)
+ a.plot(xx[:, 0], xx[:, 1])
+ f.tight_layout()
+ f.savefig('trajectories.pdf')
+ f.savefig('trajectories.png')
+ plt.close(f)
+ return None
+
+ def read_trajectory(cc, traj_index, iter0):
+ cc.parameters['niter_part'] = cc.get_data_file()['parameters/niter_part'][()]
+ df = cc.get_particle_file()
+ xx = []
+ for ii in range(iter0, cc.get_data_file()['iteration'][()], cc.parameters['niter_part']):
+ xx.append(df['tracers0/position/{0}'.format(ii)][traj_index])
+ df.close()
+ return np.array(xx)
+
Finally, the script ends with a standard call to `main`:
.. code:: python
diff --git a/examples/convergence.py b/examples/convergence.py
index 3289c8c8..f4d6dcd9 100644
--- a/examples/convergence.py
+++ b/examples/convergence.py
@@ -19,6 +19,7 @@ def main():
run_simulations_particles()
plot_error_particles()
+
plot_traj_particles()
return None
@@ -270,14 +271,14 @@ def run_simulations_particles():
for factor in [1, 2, 4]:
df = h5py.File('nsvep_{0}x_checkpoint_0.h5'.format(factor), 'w')
# field
- df['vorticity/complex/0'] = h5py.ExternalLink(
+ df['vorticity/complex/{0}'.format(8*factor)] = h5py.ExternalLink(
'base_{0}x_checkpoint_0.h5'.format(factor),
'vorticity/complex/{0}'.format(base_niterations))
# particles
- df['tracers0/state/0'] = h5py.ExternalLink(
+ df['tracers0/state/{0}'.format(8*factor)] = h5py.ExternalLink(
'nsvep_base_checkpoint_0.h5',
'tracers0/state/8')
- df['tracers0/rhs/0'] = h5py.ExternalLink(
+ df['tracers0/rhs/{0}'.format(8*factor)] = h5py.ExternalLink(
'nsvep_base_checkpoint_0.h5',
'tracers0/rhs/8')
df.close()
@@ -301,8 +302,8 @@ def run_simulations_particles():
'--niter_stat', '{0}'.format(4*factor),
'--nparticles', '{0}'.format(nparticles),
'--niter_part', '{0}'.format(2*factor),
- '--cpp_random_particles', '0' # turn off cpp particle initialization
- ])
+ '--cpp_random_particles', '0'], # turn off cpp particle initialization
+ iter0 = 8*factor)
return None
def plot_error_particles():
@@ -312,19 +313,22 @@ def plot_error_particles():
err_mean_list = []
factor_list = [1, 2]
for factor in factor_list:
- c0 = DNS(simname = 'nsvep_{0}x'.format(factor))
- c1 = DNS(simname = 'nsvep_{0}x'.format(factor*2))
- for cc in [c0, c1]:
- cc.compute_statistics()
+ c1 = DNS(simname = 'nsvep_{0}x'.format(factor))
+ c2 = DNS(simname = 'nsvep_{0}x'.format(factor*2))
+ for cc in [c1, c2]:
cc.parameters['niter_part'] = cc.get_data_file()['parameters/niter_part'][()]
- f0 = h5py.File(c0.get_checkpoint_fname(iteration = test_niterations*factor), 'r')
- f1 = h5py.File(c1.get_checkpoint_fname(iteration = test_niterations*factor*2), 'r')
- x0 = f0['tracers0/state/{0}'.format(test_niterations*factor)][()]
- x1 = f1['tracers0/state/{0}'.format(test_niterations*factor*2)][()]
- err_max_list.append(np.max(np.abs(x1 - x0)))
- err_mean_list.append(np.mean(np.abs(x1 - x0)))
- f0.close()
+ c1.compute_statistics(iter0 = 8*factor)
+ c2.compute_statistics(iter0 = 8*factor*2)
+ final_iter_x1 = c1.get_data_file()['iteration'][()]
+ final_iter_x2 = c2.get_data_file()['iteration'][()]
+ f1 = h5py.File(c1.simname + '_checkpoint_0.h5', 'r')
+ f2 = h5py.File(c2.simname + '_checkpoint_0.h5', 'r')
+ x1 = f1['tracers0/state/{0}'.format(final_iter_x1)][()]
+ x2 = f2['tracers0/state/{0}'.format(final_iter_x2)][()]
+ err_max_list.append(np.max(np.abs(x2 - x1)))
+ err_mean_list.append(np.mean(np.abs(x2 - x1)))
f1.close()
+ f2.close()
factor_list = np.array(factor_list).astype(np.float)
err_max_list = np.array(err_max_list)
err_mean_list = np.array(err_mean_list)
@@ -355,19 +359,19 @@ def plot_traj_particles():
a = f.add_subplot(111)
for factor in [1, 2, 4]:
cc = DNS(simname = 'nsvep_{0}x'.format(factor))
- cc.compute_statistics()
- xx = read_trajectory(cc, 14)
+ cc.compute_statistics(iter0 = 8*factor)
+ xx = read_trajectory(cc, 14, iter0 = 8*factor)
a.plot(xx[:, 0], xx[:, 1])
f.tight_layout()
f.savefig('trajectories.pdf')
plt.close(f)
return None
-def read_trajectory(cc, traj_index):
+def read_trajectory(cc, traj_index, iter0):
cc.parameters['niter_part'] = cc.get_data_file()['parameters/niter_part'][()]
df = cc.get_particle_file()
xx = []
- for ii in range(0, cc.get_data_file()['iteration'][()], cc.parameters['niter_part']):
+ for ii in range(iter0, cc.get_data_file()['iteration'][()], cc.parameters['niter_part']):
xx.append(df['tracers0/position/{0}'.format(ii)][traj_index])
df.close()
return np.array(xx)
--
GitLab
From 843f24ce4a70d2573121be0defdb7b66cfce6be4 Mon Sep 17 00:00:00 2001
From: Cristian C Lalescu <Cristian.Lalescu@mpcdf.mpg.de>
Date: Fri, 7 Jan 2022 21:17:27 +0100
Subject: [PATCH 08/24] adds plots to tutorial
---
documentation/sphinx_static/convergence.rst | 20 +-
.../sphinx_static/err_vs_dt_field.svg | 945 ++++++++++++
.../sphinx_static/err_vs_dt_particle.svg | 1304 +++++++++++++++++
documentation/sphinx_static/trajectories.svg | 960 ++++++++++++
examples/convergence.py | 23 +-
5 files changed, 3243 insertions(+), 9 deletions(-)
create mode 100644 documentation/sphinx_static/err_vs_dt_field.svg
create mode 100644 documentation/sphinx_static/err_vs_dt_particle.svg
create mode 100644 documentation/sphinx_static/trajectories.svg
diff --git a/documentation/sphinx_static/convergence.rst b/documentation/sphinx_static/convergence.rst
index 1c6db97e..f0c296c7 100644
--- a/documentation/sphinx_static/convergence.rst
+++ b/documentation/sphinx_static/convergence.rst
@@ -129,11 +129,13 @@ postprocessing can be performed if needed.
`generate_initial_conditions` performs a few calls to C++ executable
codes generated with TurTLE. In brief, it
+
* generates a velocity field in a quasistationary Navier-Stokes
regime (using the NSVE solver).
* uses Fourier interpolation to double and quadruple the initial
resolution, yielding 3 vorticity fields "1x", "2x" and "4x".
* generates the corresponding velocity fields needed for the NSE solver
+
We use the `launch` method of the `DNS` and `PP` Python
classes --- the wrappers around the C++ `direct_numerical_simulation`
and `postprocess` functionality.
@@ -332,6 +334,15 @@ subsequent assessment.
plt.close(f)
return None
+.. image:: err_vs_dt_field.svg
+
+In the plot, the error for :math:`f = 4` is larger than expected because
+the effects of finite precision arithmetic begin to dominate systematic
+integration errors.
+In practice there are a number of other technical details to consider
+when using resolutions corresponding to :math:`f = 4` (here this means
+:math:`k_M \eta \approx 4`), all of them out of scope for this tutorial.
+
The `get_velocity` function is slightly more elaborate, as it needs to
check whether the data comes from an `NSVE` run or an `NSE` run.
Furthermore, in the case of an `NSVE` run we need to explicitly invert
@@ -535,10 +546,13 @@ above, and compare each DNS with its corresponding double-the-resolution DNS:
Note that we plot two error measures: the maximum error, as well as the
mean error.
+
+.. image:: err_vs_dt_particle.svg
+
The plot suggests that these converge at different rates: the mean error
exhibits 4th order convergence in "factor", whereas the maximum error
-exhibits 3rd order convergence (the limit imposed by the fluid solver
-error).
+seems to converge like :math:`f^{3.5}` (closer to the limit :math:`f^3`
+imposed by the fluid solver error).
While a more detailed investigation would be in order, I speculate that
for this particular setup the increase of the spatial resolution along
with the temporal resolution renders the interpolation errors (which should
@@ -576,6 +590,8 @@ individual particle trajectories:
df.close()
return np.array(xx)
+.. image:: trajectories.svg
+
Finally, the script ends with a standard call to `main`:
.. code:: python
diff --git a/documentation/sphinx_static/err_vs_dt_field.svg b/documentation/sphinx_static/err_vs_dt_field.svg
new file mode 100644
index 00000000..b725f1e0
--- /dev/null
+++ b/documentation/sphinx_static/err_vs_dt_field.svg
@@ -0,0 +1,945 @@
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+ <g id="line2d_19">
+ <path clip-path="url(#p31dcfa20f1)" d="M 431.659545 23.98
+L 400.421456 56.966325
+L 368.470538 88.743919
+L 335.994003 118.63966
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+L 68.101391 279.668187
+" style="fill:none;stroke:#2ca02c;stroke-linecap:square;stroke-width:1.5;"/>
+ </g>
+ <g id="patch_3">
+ <path d="M 46.51 300.76
+L 46.51 10.8
+" style="fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;"/>
+ </g>
+ <g id="patch_4">
+ <path d="M 450 300.76
+L 450 10.8
+" style="fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;"/>
+ </g>
+ <g id="patch_5">
+ <path d="M 46.51 300.76
+L 450 300.76
+" style="fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;"/>
+ </g>
+ <g id="patch_6">
+ <path d="M 46.51 10.8
+L 450 10.8
+" style="fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;"/>
+ </g>
+ <g id="legend_1">
+ <g id="patch_7">
+ <path d="M 53.51 62.834375
+L 107.71 62.834375
+Q 109.71 62.834375 109.71 60.834375
+L 109.71 17.8
+Q 109.71 15.8 107.71 15.8
+L 53.51 15.8
+Q 51.51 15.8 51.51 17.8
+L 51.51 60.834375
+Q 51.51 62.834375 53.51 62.834375
+z
+" style="fill:#ffffff;opacity:0.8;stroke:#cccccc;stroke-linejoin:miter;"/>
+ </g>
+ <g id="line2d_20">
+ <path d="M 55.51 23.898438
+L 75.51 23.898438
+" style="fill:none;stroke:#1f77b4;stroke-linecap:square;stroke-width:1.5;"/>
+ </g>
+ <g id="line2d_21"/>
+ <g id="text_18">
+ <!-- $f = 1$ -->
+ <g transform="translate(83.51 27.398438)scale(0.1 -0.1)">
+ <defs>
+ <path d="M 47.796875 75.984375
+L 46.390625 68.5
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+L 41.21875 54.6875
+L 39.890625 47.703125
+L 25.09375 47.703125
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+L 16.109375 47.703125
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+Q 29.296875 75.984375 39.3125 75.984375
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+ <path d="M 10.59375 45.40625
+L 73.1875 45.40625
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+L 10.59375 37.203125
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+M 10.59375 25.484375
+L 73.1875 25.484375
+L 73.1875 17.1875
+L 10.59375 17.1875
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+ </defs>
+ <use transform="translate(0 0.015625)" xlink:href="#DejaVuSans-Oblique-102"/>
+ <use transform="translate(54.6875 0.015625)" xlink:href="#DejaVuSans-61"/>
+ <use transform="translate(157.958984 0.015625)" xlink:href="#DejaVuSans-49"/>
+ </g>
+ </g>
+ <g id="line2d_22">
+ <path d="M 55.51 38.576563
+L 75.51 38.576563
+" style="fill:none;stroke:#ff7f0e;stroke-linecap:square;stroke-width:1.5;"/>
+ </g>
+ <g id="line2d_23"/>
+ <g id="text_19">
+ <!-- $f = 2$ -->
+ <g transform="translate(83.51 42.076563)scale(0.1 -0.1)">
+ <use transform="translate(0 0.015625)" xlink:href="#DejaVuSans-Oblique-102"/>
+ <use transform="translate(54.6875 0.015625)" xlink:href="#DejaVuSans-61"/>
+ <use transform="translate(157.958984 0.015625)" xlink:href="#DejaVuSans-50"/>
+ </g>
+ </g>
+ <g id="line2d_24">
+ <path d="M 55.51 53.254688
+L 75.51 53.254688
+" style="fill:none;stroke:#2ca02c;stroke-linecap:square;stroke-width:1.5;"/>
+ </g>
+ <g id="line2d_25"/>
+ <g id="text_20">
+ <!-- $f = 4$ -->
+ <g transform="translate(83.51 56.754688)scale(0.1 -0.1)">
+ <use transform="translate(0 0.015625)" xlink:href="#DejaVuSans-Oblique-102"/>
+ <use transform="translate(54.6875 0.015625)" xlink:href="#DejaVuSans-61"/>
+ <use transform="translate(157.958984 0.015625)" xlink:href="#DejaVuSans-52"/>
+ </g>
+ </g>
+ </g>
+ </g>
+ </g>
+ <defs>
+ <clipPath id="p31dcfa20f1">
+ <rect height="289.96" width="403.49" x="46.51" y="10.8"/>
+ </clipPath>
+ </defs>
+</svg>
diff --git a/examples/convergence.py b/examples/convergence.py
index f4d6dcd9..fc16151c 100644
--- a/examples/convergence.py
+++ b/examples/convergence.py
@@ -12,12 +12,12 @@ nparticles = 100000
particle_random_seed = 15
def main():
- generate_initial_conditions()
+ #generate_initial_conditions()
- run_simulations_field()
+ #run_simulations_field()
plot_error_field()
- run_simulations_particles()
+ #run_simulations_particles()
plot_error_particles()
plot_traj_particles()
@@ -189,6 +189,8 @@ def plot_error_field():
a.legend(loc = 'best')
f.tight_layout()
f.savefig('err_vs_dt_field.pdf')
+ f.savefig('err_vs_dt_field.png')
+ f.savefig('err_vs_dt_field.svg')
plt.close(f)
return None
@@ -335,12 +337,12 @@ def plot_error_particles():
a.plot(factor_list, err_max_list, marker = '.', label = 'max error')
a.plot(factor_list, err_mean_list, marker = '.', label = 'mean error')
a.plot(factor_list,
- (1e-2)*factor_list**(-3),
+ (3e-2)*factor_list**(-3.5),
color = 'black',
dashes = (2, 2),
- label = '$\propto f^{-3}$')
+ label = '$\propto f^{-3.5}$')
a.plot(factor_list,
- (1e-2)*factor_list**(-4),
+ (3e-3)*factor_list**(-4),
color = 'black',
dashes = (1, 1),
label = '$\propto f^{-4}$')
@@ -351,6 +353,8 @@ def plot_error_particles():
a.legend(loc = 'best')
f.tight_layout()
f.savefig('err_vs_dt_particle.pdf')
+ f.savefig('err_vs_dt_particle.png')
+ f.savefig('err_vs_dt_particle.svg')
plt.close(f)
return None
@@ -361,9 +365,14 @@ def plot_traj_particles():
cc = DNS(simname = 'nsvep_{0}x'.format(factor))
cc.compute_statistics(iter0 = 8*factor)
xx = read_trajectory(cc, 14, iter0 = 8*factor)
- a.plot(xx[:, 0], xx[:, 1])
+ a.plot(xx[:, 0], xx[:, 1], label = '$f = {0}$'.format(factor))
+ a.legend(loc = 'best')
+ a.set_xlabel('$x$ [code units]')
+ a.set_xlabel('$y$ [code units]')
f.tight_layout()
f.savefig('trajectories.pdf')
+ f.savefig('trajectories.png')
+ f.savefig('trajectories.svg')
plt.close(f)
return None
--
GitLab
From f88d20667835f42f602ebeabadc76bd58a0d10c7 Mon Sep 17 00:00:00 2001
From: Cristian C Lalescu <Cristian.Lalescu@mpcdf.mpg.de>
Date: Fri, 7 Jan 2022 21:19:55 +0100
Subject: [PATCH 09/24] fixes axes label
---
documentation/sphinx_static/trajectories.svg | 279 +++++++++++--------
examples/convergence.py | 2 +-
2 files changed, 158 insertions(+), 123 deletions(-)
diff --git a/documentation/sphinx_static/trajectories.svg b/documentation/sphinx_static/trajectories.svg
index b98f9e06..fd6796fa 100644
--- a/documentation/sphinx_static/trajectories.svg
+++ b/documentation/sphinx_static/trajectories.svg
@@ -7,7 +7,7 @@
<rdf:RDF xmlns:cc="http://creativecommons.org/ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<cc:Work>
<dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
- <dc:date>2022-01-07T21:09:17.278910</dc:date>
+ <dc:date>2022-01-07T21:18:20.267358</dc:date>
<dc:format>image/svg+xml</dc:format>
<dc:creator>
<cc:Agent>
@@ -31,10 +31,10 @@ z
</g>
<g id="axes_1">
<g id="patch_2">
- <path d="M 46.51 300.76
-L 450 300.76
+ <path d="M 63.47 301.9975
+L 450 301.9975
L 450 10.8
-L 46.51 10.8
+L 63.47 10.8
z
" style="fill:#ffffff;"/>
</g>
@@ -44,15 +44,15 @@ z
<defs>
<path d="M 0 0
L 0 3.5
-" id="m8adaaf941d" style="stroke:#000000;stroke-width:0.8;"/>
+" id="m84bd32ba32" style="stroke:#000000;stroke-width:0.8;"/>
</defs>
<g>
- <use style="stroke:#000000;stroke-width:0.8;" x="48.514242" xlink:href="#m8adaaf941d" y="300.76"/>
+ <use style="stroke:#000000;stroke-width:0.8;" x="65.389997" xlink:href="#m84bd32ba32" y="301.9975"/>
</g>
</g>
<g id="text_1">
<!-- 5.60 -->
- <g transform="translate(37.38143 315.358437)scale(0.1 -0.1)">
+ <g transform="translate(54.257185 316.595937)scale(0.1 -0.1)">
<defs>
<path d="M 10.796875 72.90625
L 49.515625 72.90625
@@ -146,12 +146,12 @@ z
<g id="xtick_2">
<g id="line2d_2">
<g>
- <use style="stroke:#000000;stroke-width:0.8;" x="103.339781" xlink:href="#m8adaaf941d" y="300.76"/>
+ <use style="stroke:#000000;stroke-width:0.8;" x="117.91104" xlink:href="#m84bd32ba32" y="301.9975"/>
</g>
</g>
<g id="text_2">
<!-- 5.62 -->
- <g transform="translate(92.206968 315.358437)scale(0.1 -0.1)">
+ <g transform="translate(106.778227 316.595937)scale(0.1 -0.1)">
<defs>
<path d="M 19.1875 8.296875
L 53.609375 8.296875
@@ -188,12 +188,12 @@ z
<g id="xtick_3">
<g id="line2d_3">
<g>
- <use style="stroke:#000000;stroke-width:0.8;" x="158.165319" xlink:href="#m8adaaf941d" y="300.76"/>
+ <use style="stroke:#000000;stroke-width:0.8;" x="170.432082" xlink:href="#m84bd32ba32" y="301.9975"/>
</g>
</g>
<g id="text_3">
<!-- 5.64 -->
- <g transform="translate(147.032507 315.358437)scale(0.1 -0.1)">
+ <g transform="translate(159.29927 316.595937)scale(0.1 -0.1)">
<defs>
<path d="M 37.796875 64.3125
L 12.890625 25.390625
@@ -223,12 +223,12 @@ z
<g id="xtick_4">
<g id="line2d_4">
<g>
- <use style="stroke:#000000;stroke-width:0.8;" x="212.990858" xlink:href="#m8adaaf941d" y="300.76"/>
+ <use style="stroke:#000000;stroke-width:0.8;" x="222.953125" xlink:href="#m84bd32ba32" y="301.9975"/>
</g>
</g>
<g id="text_4">
<!-- 5.66 -->
- <g transform="translate(201.858045 315.358437)scale(0.1 -0.1)">
+ <g transform="translate(211.820312 316.595937)scale(0.1 -0.1)">
<use xlink:href="#DejaVuSans-53"/>
<use x="63.623047" xlink:href="#DejaVuSans-46"/>
<use x="95.410156" xlink:href="#DejaVuSans-54"/>
@@ -239,12 +239,12 @@ z
<g id="xtick_5">
<g id="line2d_5">
<g>
- <use style="stroke:#000000;stroke-width:0.8;" x="267.816396" xlink:href="#m8adaaf941d" y="300.76"/>
+ <use style="stroke:#000000;stroke-width:0.8;" x="275.474167" xlink:href="#m84bd32ba32" y="301.9975"/>
</g>
</g>
<g id="text_5">
<!-- 5.68 -->
- <g transform="translate(256.683584 315.358437)scale(0.1 -0.1)">
+ <g transform="translate(264.341355 316.595937)scale(0.1 -0.1)">
<defs>
<path d="M 31.78125 34.625
Q 24.75 34.625 20.71875 30.859375
@@ -296,12 +296,12 @@ z
<g id="xtick_6">
<g id="line2d_6">
<g>
- <use style="stroke:#000000;stroke-width:0.8;" x="322.641935" xlink:href="#m8adaaf941d" y="300.76"/>
+ <use style="stroke:#000000;stroke-width:0.8;" x="327.99521" xlink:href="#m84bd32ba32" y="301.9975"/>
</g>
</g>
<g id="text_6">
<!-- 5.70 -->
- <g transform="translate(311.509122 315.358437)scale(0.1 -0.1)">
+ <g transform="translate(316.862397 316.595937)scale(0.1 -0.1)">
<defs>
<path d="M 8.203125 72.90625
L 55.078125 72.90625
@@ -323,12 +323,12 @@ z
<g id="xtick_7">
<g id="line2d_7">
<g>
- <use style="stroke:#000000;stroke-width:0.8;" x="377.467473" xlink:href="#m8adaaf941d" y="300.76"/>
+ <use style="stroke:#000000;stroke-width:0.8;" x="380.516252" xlink:href="#m84bd32ba32" y="301.9975"/>
</g>
</g>
<g id="text_7">
<!-- 5.72 -->
- <g transform="translate(366.334661 315.358437)scale(0.1 -0.1)">
+ <g transform="translate(369.383439 316.595937)scale(0.1 -0.1)">
<use xlink:href="#DejaVuSans-53"/>
<use x="63.623047" xlink:href="#DejaVuSans-46"/>
<use x="95.410156" xlink:href="#DejaVuSans-55"/>
@@ -339,12 +339,12 @@ z
<g id="xtick_8">
<g id="line2d_8">
<g>
- <use style="stroke:#000000;stroke-width:0.8;" x="432.293012" xlink:href="#m8adaaf941d" y="300.76"/>
+ <use style="stroke:#000000;stroke-width:0.8;" x="433.037294" xlink:href="#m84bd32ba32" y="301.9975"/>
</g>
</g>
<g id="text_8">
<!-- 5.74 -->
- <g transform="translate(421.160199 315.358437)scale(0.1 -0.1)">
+ <g transform="translate(421.904482 316.595937)scale(0.1 -0.1)">
<use xlink:href="#DejaVuSans-53"/>
<use x="63.623047" xlink:href="#DejaVuSans-46"/>
<use x="95.410156" xlink:href="#DejaVuSans-55"/>
@@ -353,25 +353,23 @@ z
</g>
</g>
<g id="text_9">
- <!-- $y$ [code units] -->
- <g transform="translate(213.855 329.038125)scale(0.1 -0.1)">
+ <!-- $x$ [code units] -->
+ <g transform="translate(222.335 330.274062)scale(0.1 -0.1)">
<defs>
- <path d="M 24.8125 -5.078125
-Q 18.5625 -15.578125 14.625 -18.1875
-Q 10.6875 -20.796875 4.59375 -20.796875
-L -2.484375 -20.796875
-L -0.984375 -13.28125
-L 4.203125 -13.28125
-Q 7.953125 -13.28125 10.59375 -11.234375
-Q 13.234375 -9.1875 16.5 -3.21875
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-L 7.171875 54.6875
-L 16.703125 54.6875
-L 25.78125 12.796875
-L 50.875 54.6875
-L 60.296875 54.6875
-z
-" id="DejaVuSans-Oblique-121"/>
+ <path d="M 60.015625 54.6875
+L 34.90625 27.875
+L 50.296875 0
+L 39.984375 0
+L 28.421875 21.6875
+L 8.296875 0
+L -2.59375 0
+L 24.3125 28.8125
+L 10.015625 54.6875
+L 20.3125 54.6875
+L 30.8125 34.90625
+L 49.125 54.6875
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<path id="DejaVuSans-32"/>
<path d="M 8.59375 75.984375
L 29.296875 75.984375
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z
" id="DejaVuSans-93"/>
</defs>
- <use transform="translate(0 0.015625)" xlink:href="#DejaVuSans-Oblique-121"/>
+ <use transform="translate(0 0.015625)" xlink:href="#DejaVuSans-Oblique-120"/>
<use transform="translate(59.179688 0.015625)" xlink:href="#DejaVuSans-32"/>
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@@ -611,15 +609,15 @@ z
<defs>
<path d="M 0 0
L -3.5 0
-" id="m2bc0edee2e" style="stroke:#000000;stroke-width:0.8;"/>
+" id="m2a24216656" style="stroke:#000000;stroke-width:0.8;"/>
</defs>
<g>
- <use style="stroke:#000000;stroke-width:0.8;" x="46.51" xlink:href="#m2bc0edee2e" y="294.982792"/>
+ <use style="stroke:#000000;stroke-width:0.8;" x="63.47" xlink:href="#m2a24216656" y="296.195636"/>
</g>
</g>
<g id="text_10">
<!-- 3.310 -->
- <g transform="translate(10.881875 298.782011)scale(0.1 -0.1)">
+ <g transform="translate(27.841875 299.994855)scale(0.1 -0.1)">
<defs>
<path d="M 40.578125 39.3125
Q 47.65625 37.796875 51.625 33
@@ -678,12 +676,12 @@ z
<g id="ytick_2">
<g id="line2d_10">
<g>
- <use style="stroke:#000000;stroke-width:0.8;" x="46.51" xlink:href="#m2bc0edee2e" y="255.374956"/>
+ <use style="stroke:#000000;stroke-width:0.8;" x="63.47" xlink:href="#m2a24216656" y="256.41876"/>
</g>
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<g id="text_11">
<!-- 3.315 -->
- <g transform="translate(10.881875 259.174175)scale(0.1 -0.1)">
+ <g transform="translate(27.841875 260.217979)scale(0.1 -0.1)">
<use xlink:href="#DejaVuSans-51"/>
<use x="63.623047" xlink:href="#DejaVuSans-46"/>
<use x="95.410156" xlink:href="#DejaVuSans-51"/>
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<g id="ytick_3">
<g id="line2d_11">
<g>
- <use style="stroke:#000000;stroke-width:0.8;" x="46.51" xlink:href="#m2bc0edee2e" y="215.767119"/>
+ <use style="stroke:#000000;stroke-width:0.8;" x="63.47" xlink:href="#m2a24216656" y="216.641884"/>
</g>
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<g id="text_12">
<!-- 3.320 -->
- <g transform="translate(10.881875 219.566338)scale(0.1 -0.1)">
+ <g transform="translate(27.841875 220.441103)scale(0.1 -0.1)">
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@@ -712,12 +710,12 @@ z
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<g id="line2d_12">
<g>
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+ <use style="stroke:#000000;stroke-width:0.8;" x="63.47" xlink:href="#m2a24216656" y="176.865008"/>
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- <g transform="translate(10.881875 179.958501)scale(0.1 -0.1)">
+ <g transform="translate(27.841875 180.664226)scale(0.1 -0.1)">
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<use x="95.410156" xlink:href="#DejaVuSans-51"/>
@@ -729,12 +727,12 @@ z
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<g id="line2d_13">
<g>
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@@ -746,12 +744,12 @@ z
<g id="ytick_6">
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<g>
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diff --git a/examples/convergence.py b/examples/convergence.py
index fc16151c..6646a2ca 100644
--- a/examples/convergence.py
+++ b/examples/convergence.py
@@ -368,7 +368,7 @@ def plot_traj_particles():
a.plot(xx[:, 0], xx[:, 1], label = '$f = {0}$'.format(factor))
a.legend(loc = 'best')
a.set_xlabel('$x$ [code units]')
- a.set_xlabel('$y$ [code units]')
+ a.set_ylabel('$y$ [code units]')
f.tight_layout()
f.savefig('trajectories.pdf')
f.savefig('trajectories.png')
--
GitLab
From 7b257a9e42c4efc24ec9ee4ad7258634e3130279 Mon Sep 17 00:00:00 2001
From: Cristian C Lalescu <Cristian.Lalescu@mpcdf.mpg.de>
Date: Thu, 13 Jan 2022 17:44:31 +0100
Subject: [PATCH 10/24] updates convergence test
---
examples/convergence.py | 192 +++++++++++++++++++++++++---------------
1 file changed, 121 insertions(+), 71 deletions(-)
diff --git a/examples/convergence.py b/examples/convergence.py
index 6646a2ca..9ee1e6c1 100644
--- a/examples/convergence.py
+++ b/examples/convergence.py
@@ -8,16 +8,21 @@ from TurTLE import DNS, PP
base_niterations = 256
test_niterations = 32
-nparticles = 100000
+nparticles = 1000
particle_random_seed = 15
+base_particle_dt = 0.6
+
+neighbours_smoothness_list = [
+ (1, 1),
+ (1, 0)]
def main():
#generate_initial_conditions()
#run_simulations_field()
- plot_error_field()
+ #plot_error_field()
- #run_simulations_particles()
+ run_simulations_particles()
plot_error_particles()
plot_traj_particles()
@@ -246,11 +251,12 @@ def run_simulations_particles():
# number of OpenMP threads per MPI process to use
nthreads_per_process = 2
-# 1. Run NSVEparticles for resolution 1x, for a few iterations, to build up rhs values.
- factor = 1
+# 1. Run NSVEparticles for a few iterations, to build up rhs values, consistent
+# with the relevant velocity field.
# create dns object
cc = DNS()
# launch simulation
+ factor = 2
cc.launch([
'NSVEparticles',
'-n', '{0}'.format(factor*32),
@@ -258,84 +264,122 @@ def run_simulations_particles():
'--ntpp', '{0}'.format(nthreads_per_process),
'--src-simname', 'base_{0}x'.format(factor),
'--src-iteration', '{0}'.format(base_niterations),
- '--simname', 'nsvep_base'.format(factor),
+ '--simname', 'nsvep_base',
'--precision', 'double',
- '--dtfactor', '0.3',
+ '--dtfactor', '{0}'.format(base_particle_dt/4),
'--kMeta', '{0}'.format(1.0*factor),
- '--niter_todo', '{0}'.format(8),
- '--niter_out', '{0}'.format(8),
- '--niter_stat', '{0}'.format(8),
+ '--niter_todo', '{0}'.format(16),
+ '--niter_out', '{0}'.format(1),
+ '--niter_stat', '{0}'.format(1),
'--nparticles', '{0}'.format(nparticles),
- '--niter_part', '{0}'.format(8),
+ '--niter_part', '{0}'.format(1),
'--cpp_random_particles', '{0}'.format(particle_random_seed)])
# 2. Prepare initial conditions
- for factor in [1, 2, 4]:
- df = h5py.File('nsvep_{0}x_checkpoint_0.h5'.format(factor), 'w')
- # field
- df['vorticity/complex/{0}'.format(8*factor)] = h5py.ExternalLink(
- 'base_{0}x_checkpoint_0.h5'.format(factor),
- 'vorticity/complex/{0}'.format(base_niterations))
- # particles
- df['tracers0/state/{0}'.format(8*factor)] = h5py.ExternalLink(
+ for neighbours, smoothness in neighbours_smoothness_list:
+ interp_name = 'I{0}O{1}'.format(2*neighbours+2, 2*smoothness+1)
+ for factor in [1, 2, 4]:
+ df = h5py.File('nsvep_{0}x_{1}_checkpoint_0.h5'.format(factor, interp_name), 'w')
+ # field
+ df['vorticity/complex/{0}'.format(8*factor)] = h5py.ExternalLink(
'nsvep_base_checkpoint_0.h5',
- 'tracers0/state/8')
- df['tracers0/rhs/{0}'.format(8*factor)] = h5py.ExternalLink(
- 'nsvep_base_checkpoint_0.h5',
- 'tracers0/rhs/8')
- df.close()
+ 'vorticity/complex/16')
+ # particles
+ df['tracers0/state/{0}'.format(8*factor)] = h5py.ExternalLink(
+ 'nsvep_base_checkpoint_0.h5',
+ 'tracers0/state/16')
+ # copy rhs
+ source_file = h5py.File(
+ 'nsvep_base_checkpoint_0.h5', 'r')
+ rhs = source_file['tracers0/rhs/16'][()]
+ if factor == 4:
+ rhs[0] = source_file['tracers0/rhs/16'][0]
+ rhs[1] = source_file['tracers0/rhs/16'][1]
+ rhs[2] = source_file['tracers0/rhs/15'][1]
+ rhs[3] = source_file['tracers0/rhs/14'][1]
+ if factor == 2:
+ rhs[0] = source_file['tracers0/rhs/16'][0]
+ rhs[1] = source_file['tracers0/rhs/15'][1]
+ rhs[2] = source_file['tracers0/rhs/13'][1]
+ rhs[3] = source_file['tracers0/rhs/11'][1]
+ if factor == 1:
+ rhs[0] = source_file['tracers0/rhs/16'][0]
+ rhs[1] = source_file['tracers0/rhs/13'][1]
+ rhs[2] = source_file['tracers0/rhs/9'][1]
+ rhs[3] = source_file['tracers0/rhs/5'][1]
+ df['tracers0/rhs/{0}'.format(8*factor)] = rhs
+ df.close()
# 3. Run NSVEparticles
for factor in [1, 2, 4]:
- # create dns object
- cc = DNS()
- # launch simulation
- cc.launch([
- 'NSVEparticles',
- '-n', '{0}'.format(factor*32),
- '--np', '{0}'.format(nprocesses),
- '--ntpp', '{0}'.format(nthreads_per_process),
- '--simname', 'nsvep_{0}x'.format(factor),
- '--precision', 'double',
- '--dtfactor', '0.3',
- '--kMeta', '{0}'.format(1.0*factor),
- '--niter_todo', '{0}'.format(test_niterations*factor),
- '--niter_out', '{0}'.format(test_niterations*factor),
- '--niter_stat', '{0}'.format(4*factor),
- '--nparticles', '{0}'.format(nparticles),
- '--niter_part', '{0}'.format(2*factor),
- '--cpp_random_particles', '0'], # turn off cpp particle initialization
- iter0 = 8*factor)
+ # Test different interpolations.
+ # The loop iterates over number of neighbours and smoothness.
+ # The simulation names are defined based on "kernel size" and "order
+ # of polynomial".
+ # We do this to emphasize the one-to-one correspondence between
+ # neighbours and kernel size, and smoothness and order of polynomial.
+ for neighbours, smoothness in neighbours_smoothness_list:
+ # create dns object
+ cc = DNS()
+ # launch simulation
+ cc.launch([
+ 'NSVEparticles',
+ '-n', '{0}'.format(64),
+ '--np', '{0}'.format(nprocesses),
+ '--ntpp', '{0}'.format(nthreads_per_process),
+ '--simname', 'nsvep_{0}x_I{1}O{2}'.format(
+ factor,
+ 2*neighbours+2,
+ 2*smoothness+1),
+ '--precision', 'double',
+ '--dtfactor', '{0}'.format(base_particle_dt/factor),
+ '--kMeta', '{0}'.format(2.0),
+ '--niter_todo', '{0}'.format(test_niterations*factor+8*factor),
+ '--niter_out', '{0}'.format(test_niterations*factor+8*factor),
+ '--niter_stat', '{0}'.format(4*factor),
+ '--nparticles', '{0}'.format(nparticles),
+ '--niter_part', '{0}'.format(2*factor),
+ '--tracers0_neighbours', '{0}'.format(neighbours),
+ '--tracers0_smoothness', '{0}'.format(smoothness),
+ '--cpp_random_particles', '0'], # turn off cpp particle initialization
+ iter0 = 8*factor)
return None
def plot_error_particles():
f = plt.figure()
a = f.add_subplot(111)
- err_max_list = []
- err_mean_list = []
factor_list = [1, 2]
- for factor in factor_list:
- c1 = DNS(simname = 'nsvep_{0}x'.format(factor))
- c2 = DNS(simname = 'nsvep_{0}x'.format(factor*2))
- for cc in [c1, c2]:
- cc.parameters['niter_part'] = cc.get_data_file()['parameters/niter_part'][()]
- c1.compute_statistics(iter0 = 8*factor)
- c2.compute_statistics(iter0 = 8*factor*2)
- final_iter_x1 = c1.get_data_file()['iteration'][()]
- final_iter_x2 = c2.get_data_file()['iteration'][()]
- f1 = h5py.File(c1.simname + '_checkpoint_0.h5', 'r')
- f2 = h5py.File(c2.simname + '_checkpoint_0.h5', 'r')
- x1 = f1['tracers0/state/{0}'.format(final_iter_x1)][()]
- x2 = f2['tracers0/state/{0}'.format(final_iter_x2)][()]
- err_max_list.append(np.max(np.abs(x2 - x1)))
- err_mean_list.append(np.mean(np.abs(x2 - x1)))
- f1.close()
- f2.close()
factor_list = np.array(factor_list).astype(np.float)
- err_max_list = np.array(err_max_list)
- err_mean_list = np.array(err_mean_list)
- a.plot(factor_list, err_max_list, marker = '.', label = 'max error')
- a.plot(factor_list, err_mean_list, marker = '.', label = 'mean error')
+ for neighbours, smoothness in neighbours_smoothness_list:
+ interp_name = 'I{0}O{1}'.format(2*neighbours+2, 2*smoothness+1)
+ err_max_list = []
+ err_mean_list = []
+ for factor in factor_list:
+ factor = int(factor)
+ c1 = DNS(simname = 'nsvep_{0}x_'.format(int(factor)) + interp_name)
+ c2 = DNS(simname = 'nsvep_{0}x_'.format(int(factor)*2) + interp_name)
+ for cc in [c1, c2]:
+ cc.parameters['niter_part'] = cc.get_data_file()['parameters/niter_part'][()]
+ c1.compute_statistics(iter0 = 8*factor)
+ c2.compute_statistics(iter0 = 8*factor*2)
+ final_iter_x1 = c1.get_data_file()['iteration'][()]
+ final_iter_x2 = c2.get_data_file()['iteration'][()]
+ f1 = h5py.File(c1.simname + '_checkpoint_0.h5', 'r')
+ f2 = h5py.File(c2.simname + '_checkpoint_0.h5', 'r')
+ print('in error plot')
+ print(final_iter_x1 - 8*factor)
+ print(final_iter_x2 - 8*factor*2)
+ x1 = f1['tracers0/state/{0}'.format(final_iter_x1)][()]
+ x2 = f2['tracers0/state/{0}'.format(final_iter_x2)][()]
+ diff = np.sqrt(np.sum((x2-x1)**2, axis = -1))
+ err_max_list.append(np.max(diff))
+ err_mean_list.append(np.mean(diff))
+ f1.close()
+ f2.close()
+ err_max_list = np.array(err_max_list)
+ err_mean_list = np.array(err_mean_list)
+ a.plot(factor_list, err_max_list, marker = '.', label = 'max error ' + interp_name)
+ a.plot(factor_list, err_mean_list, marker = '.', label = 'mean error ' + interp_name)
a.plot(factor_list,
(3e-2)*factor_list**(-3.5),
color = 'black',
@@ -361,11 +405,17 @@ def plot_error_particles():
def plot_traj_particles():
f = plt.figure()
a = f.add_subplot(111)
- for factor in [1, 2, 4]:
- cc = DNS(simname = 'nsvep_{0}x'.format(factor))
- cc.compute_statistics(iter0 = 8*factor)
- xx = read_trajectory(cc, 14, iter0 = 8*factor)
- a.plot(xx[:, 0], xx[:, 1], label = '$f = {0}$'.format(factor))
+ for neighbours, smoothness in neighbours_smoothness_list:
+ interp_name = 'I{0}O{1}'.format(2*neighbours+2, 2*smoothness+1)
+ for factor in [1, 2, 4]:
+ cc = DNS(simname = 'nsvep_{0}x_'.format(factor) + interp_name)
+ cc.compute_statistics(iter0 = 8*factor)
+ tt = 14
+ xx = read_trajectory(cc, tt, iter0 = 8*factor)
+ #a.plot(xx[:, 0], label = '$f = {0}$'.format(factor), marker = 'x')
+ a.plot(xx[:, 0] - xx[:, 0].mean(),
+ xx[:, 1] - xx[:, 1].mean(),
+ label = '$f = {0}$'.format(factor), marker = 'x')
a.legend(loc = 'best')
a.set_xlabel('$x$ [code units]')
a.set_ylabel('$y$ [code units]')
--
GitLab
From 4203f097b6b1d63343f1c430f81ba3db32e49933 Mon Sep 17 00:00:00 2001
From: Cristian C Lalescu <Cristian.Lalescu@mpcdf.mpg.de>
Date: Fri, 14 Jan 2022 17:18:13 +0100
Subject: [PATCH 11/24] fixes intialization of runs with different
interpolation
---
cpp/full_code/NSVEparticles.cpp | 1 +
examples/convergence.py | 60 ++++++++++++++++++---------------
2 files changed, 34 insertions(+), 27 deletions(-)
diff --git a/cpp/full_code/NSVEparticles.cpp b/cpp/full_code/NSVEparticles.cpp
index f2c53a4e..3f24be40 100644
--- a/cpp/full_code/NSVEparticles.cpp
+++ b/cpp/full_code/NSVEparticles.cpp
@@ -98,6 +98,7 @@ int NSVEparticles<rnumber>::initialize(void)
this->particles_output_writer_mpi->close_file();
}
+ DEBUG_MSG("fs->iteration = %d\n", this->fs->iteration);
DEBUG_MSG_WAIT(MPI_COMM_WORLD, "about to call particles_system_builder\n");
this->ps = particles_system_builder(
this->fs->cvelocity, // (field object)
diff --git a/examples/convergence.py b/examples/convergence.py
index 9ee1e6c1..9560ab4d 100644
--- a/examples/convergence.py
+++ b/examples/convergence.py
@@ -8,13 +8,16 @@ from TurTLE import DNS, PP
base_niterations = 256
test_niterations = 32
-nparticles = 1000
+nparticles = 100
particle_random_seed = 15
-base_particle_dt = 0.6
+base_particle_dt = 0.5
+test_niterations_particles = 128
neighbours_smoothness_list = [
(1, 1),
- (1, 0)]
+ (2, 1),
+ (3, 2),
+ (4, 3)]
def main():
#generate_initial_conditions()
@@ -33,7 +36,7 @@ def generate_initial_conditions():
# number of MPI processes to use
nprocesses = 4
# number of OpenMP threads per MPI process to use
- nthreads_per_process = 2
+ nthreads_per_process = 1
# 1. Generate quasistationary state to use for initial conditions.
# create a dns object
@@ -104,7 +107,7 @@ def run_simulations_field():
# number of MPI processes to use
nprocesses = 4
# number of OpenMP threads per MPI process to use
- nthreads_per_process = 2
+ nthreads_per_process = 1
# 1. Run NSVE for the three resolutions.
for factor in [1, 2, 4]:
@@ -249,22 +252,24 @@ def run_simulations_particles():
# number of MPI processes to use
nprocesses = 4
# number of OpenMP threads per MPI process to use
- nthreads_per_process = 2
+ nthreads_per_process = 3
# 1. Run NSVEparticles for a few iterations, to build up rhs values, consistent
# with the relevant velocity field.
# create dns object
- cc = DNS()
# launch simulation
- factor = 2
- cc.launch([
+ factor = 1
+ for neighbours, smoothness in neighbours_smoothness_list:
+ interp_name = 'I{0}O{1}'.format(2*neighbours+2, 2*smoothness+1)
+ cc = DNS()
+ cc.launch([
'NSVEparticles',
'-n', '{0}'.format(factor*32),
'--np', '{0}'.format(nprocesses),
'--ntpp', '{0}'.format(nthreads_per_process),
'--src-simname', 'base_{0}x'.format(factor),
'--src-iteration', '{0}'.format(base_niterations),
- '--simname', 'nsvep_base',
+ '--simname', 'nsvep_base_' + interp_name,
'--precision', 'double',
'--dtfactor', '{0}'.format(base_particle_dt/4),
'--kMeta', '{0}'.format(1.0*factor),
@@ -273,6 +278,8 @@ def run_simulations_particles():
'--niter_stat', '{0}'.format(1),
'--nparticles', '{0}'.format(nparticles),
'--niter_part', '{0}'.format(1),
+ '--tracers0_neighbours', '{0}'.format(neighbours),
+ '--tracers0_smoothness', '{0}'.format(smoothness),
'--cpp_random_particles', '{0}'.format(particle_random_seed)])
# 2. Prepare initial conditions
@@ -282,15 +289,15 @@ def run_simulations_particles():
df = h5py.File('nsvep_{0}x_{1}_checkpoint_0.h5'.format(factor, interp_name), 'w')
# field
df['vorticity/complex/{0}'.format(8*factor)] = h5py.ExternalLink(
- 'nsvep_base_checkpoint_0.h5',
+ 'nsvep_base_{0}_checkpoint_0.h5'.format(interp_name),
'vorticity/complex/16')
# particles
df['tracers0/state/{0}'.format(8*factor)] = h5py.ExternalLink(
- 'nsvep_base_checkpoint_0.h5',
+ 'nsvep_base_{0}_checkpoint_0.h5'.format(interp_name),
'tracers0/state/16')
# copy rhs
source_file = h5py.File(
- 'nsvep_base_checkpoint_0.h5', 'r')
+ 'nsvep_base_{0}_checkpoint_0.h5'.format(interp_name), 'r')
rhs = source_file['tracers0/rhs/16'][()]
if factor == 4:
rhs[0] = source_file['tracers0/rhs/16'][0]
@@ -324,7 +331,7 @@ def run_simulations_particles():
# launch simulation
cc.launch([
'NSVEparticles',
- '-n', '{0}'.format(64),
+ '-n', '{0}'.format(32),
'--np', '{0}'.format(nprocesses),
'--ntpp', '{0}'.format(nthreads_per_process),
'--simname', 'nsvep_{0}x_I{1}O{2}'.format(
@@ -333,9 +340,9 @@ def run_simulations_particles():
2*smoothness+1),
'--precision', 'double',
'--dtfactor', '{0}'.format(base_particle_dt/factor),
- '--kMeta', '{0}'.format(2.0),
- '--niter_todo', '{0}'.format(test_niterations*factor+8*factor),
- '--niter_out', '{0}'.format(test_niterations*factor+8*factor),
+ '--kMeta', '{0}'.format(1.0),
+ '--niter_todo', '{0}'.format(test_niterations_particles*factor+8*factor),
+ '--niter_out', '{0}'.format(test_niterations_particles*factor+8*factor),
'--niter_stat', '{0}'.format(4*factor),
'--nparticles', '{0}'.format(nparticles),
'--niter_part', '{0}'.format(2*factor),
@@ -366,9 +373,6 @@ def plot_error_particles():
final_iter_x2 = c2.get_data_file()['iteration'][()]
f1 = h5py.File(c1.simname + '_checkpoint_0.h5', 'r')
f2 = h5py.File(c2.simname + '_checkpoint_0.h5', 'r')
- print('in error plot')
- print(final_iter_x1 - 8*factor)
- print(final_iter_x2 - 8*factor*2)
x1 = f1['tracers0/state/{0}'.format(final_iter_x1)][()]
x2 = f2['tracers0/state/{0}'.format(final_iter_x2)][()]
diff = np.sqrt(np.sum((x2-x1)**2, axis = -1))
@@ -410,18 +414,20 @@ def plot_traj_particles():
for factor in [1, 2, 4]:
cc = DNS(simname = 'nsvep_{0}x_'.format(factor) + interp_name)
cc.compute_statistics(iter0 = 8*factor)
- tt = 14
+ tt = 3
xx = read_trajectory(cc, tt, iter0 = 8*factor)
- #a.plot(xx[:, 0], label = '$f = {0}$'.format(factor), marker = 'x')
- a.plot(xx[:, 0] - xx[:, 0].mean(),
- xx[:, 1] - xx[:, 1].mean(),
- label = '$f = {0}$'.format(factor), marker = 'x')
+ a.plot(xx[:, 0],
+ xx[:, 1],
+ label = interp_name + '$f = {0}$'.format(factor),
+ marker = 'x',
+ dashes = (4/factor, 3, 4/factor),
+ alpha = 0.2)
+ #a.plot(xx[:, 0], xx[:, 1], dashes = (4/factor, 3, 4/factor), alpha = 0.2)
a.legend(loc = 'best')
a.set_xlabel('$x$ [code units]')
a.set_ylabel('$y$ [code units]')
f.tight_layout()
f.savefig('trajectories.pdf')
- f.savefig('trajectories.png')
f.savefig('trajectories.svg')
plt.close(f)
return None
@@ -430,7 +436,7 @@ def read_trajectory(cc, traj_index, iter0):
cc.parameters['niter_part'] = cc.get_data_file()['parameters/niter_part'][()]
df = cc.get_particle_file()
xx = []
- for ii in range(iter0, cc.get_data_file()['iteration'][()], cc.parameters['niter_part']):
+ for ii in range(iter0, cc.get_data_file()['iteration'][()]+1, cc.parameters['niter_part']):
xx.append(df['tracers0/position/{0}'.format(ii)][traj_index])
df.close()
return np.array(xx)
--
GitLab
From 1b450924b725317f3cb2338a2a40ea7ecb7a234a Mon Sep 17 00:00:00 2001
From: Cristian C Lalescu <Cristian.Lalescu@mpcdf.mpg.de>
Date: Tue, 18 Jan 2022 11:20:07 +0100
Subject: [PATCH 12/24] adds temporary alternate field convergence test
---
examples/convergence_only_time.py | 281 ++++++++++++++++++++++++++++++
1 file changed, 281 insertions(+)
create mode 100644 examples/convergence_only_time.py
diff --git a/examples/convergence_only_time.py b/examples/convergence_only_time.py
new file mode 100644
index 00000000..1db81aa3
--- /dev/null
+++ b/examples/convergence_only_time.py
@@ -0,0 +1,281 @@
+import numpy as np
+import h5py
+import matplotlib.pyplot as plt
+
+import TurTLE
+from TurTLE import DNS, PP
+
+base_niterations = 512
+test_niterations = 32
+
+def main():
+ generate_initial_conditions()
+
+ run_simulations_field()
+ plot_error_field2()
+ return None
+
+def generate_initial_conditions():
+ # change these two values as neded.
+ # number of MPI processes to use
+ nprocesses = 8
+ # number of OpenMP threads per MPI process to use
+ nthreads_per_process = 1
+
+# 1. Generate quasistationary state to use for initial conditions.
+ # create a dns object
+ c0 = DNS()
+ # launch the simulation
+ c0.launch([
+ 'NSVE',
+ '-n', '64',
+ '--np', '{0}'.format(nprocesses),
+ '--ntpp', '{0}'.format(nthreads_per_process),
+ '--precision', 'double',
+ '--src-simname', 'B32p1e4',
+ '--src-wd', TurTLE.data_dir,
+ '--src-iteration', '0',
+ '--simname', 'base',
+ '--niter_todo', '{0}'.format(base_niterations),
+ '--niter_out', '{0}'.format(base_niterations),
+ '--overwrite-src-parameters',
+ '--kMeta', '1',
+ '--niter_stat', '16',
+ '--checkpoints_per_file', '{0}'.format(16)])
+
+# 3. Generate initial conditions for NSE runs at 1x, 2x and 4x the
+# base resolution.
+ # create postprocess object
+ cc = PP()
+ # compute velocity field at last iteration
+ cc.launch([
+ 'get_velocity',
+ '--np', '{0}'.format(nprocesses),
+ '--ntpp', '{0}'.format(nthreads_per_process),
+ '--simname', 'base',
+ '--precision', 'double',
+ '--iter0', '{0}'.format(base_niterations),
+ '--iter1', '{0}'.format(base_niterations)])
+ # we don't need to update "checkpoint" file after "get_velocity"
+ return None
+
+def run_simulations_field():
+ # change these two values as neded.
+ # number of MPI processes to use
+ nprocesses = 8
+ # number of OpenMP threads per MPI process to use
+ nthreads_per_process = 1
+
+# 1. Run NSVE for the three resolutions.
+ for factor in [1, 2, 4]:
+ # create dns object
+ cc = DNS()
+ # launch simulation
+ cc.launch([
+ 'NSVE',
+ '-n', '{0}'.format(64),
+ '--np', '{0}'.format(nprocesses),
+ '--ntpp', '{0}'.format(nthreads_per_process),
+ '--src-simname', 'base',
+ '--src-iteration', '{0}'.format(base_niterations),
+ '--simname', 'nsve_{0}x'.format(factor),
+ '--precision', 'double',
+ '--dtfactor', '{0}'.format(1.0 / factor),
+ '--niter_todo', '{0}'.format(test_niterations*factor),
+ '--niter_out', '{0}'.format(test_niterations*factor),
+ '--niter_stat', '{0}'.format(4*factor)])
+
+# 2. Run NSE for the three resolutions.
+ for factor in [1, 2, 4]:
+ # create dns object
+ cc = DNS()
+ # launch simulation
+ cc.launch([
+ 'NSE',
+ '-n', '{0}'.format(64),
+ '--np', '{0}'.format(nprocesses),
+ '--ntpp', '{0}'.format(nthreads_per_process),
+ '--src-simname', 'base',
+ '--src-iteration', '{0}'.format(base_niterations),
+ '--simname', 'nse_{0}x'.format(factor),
+ '--precision', 'double',
+ '--dtfactor', '{0}'.format(1.0 / factor),
+ '--niter_todo', '{0}'.format(test_niterations*factor),
+ '--niter_out', '{0}'.format(test_niterations*factor),
+ '--niter_stat', '{0}'.format(4*factor)])
+ return None
+
+def plot_error_field2():
+ c0_list = [DNS(simname = 'nsve_{0}x'.format(factor))
+ for factor in [1, 2, 4]]
+ c1_list = [DNS(simname = 'nse_{0}x'.format(factor))
+ for factor in [1, 2, 4]]
+ cl = [c0_list, c1_list]
+ for cc in c0_list + c1_list:
+ cc.compute_statistics()
+
+ factor_list = [1, 2]
+
+ error_list = [[], []]
+ for ii in range(len(factor_list)):
+ factor = factor_list[ii]
+ for jj in [0, 1]:
+ c0 = cl[jj][ii]
+ c1 = cl[jj][ii+1]
+ df0 = h5py.File(c0.get_checkpoint_fname(iteration = test_niterations*factor), 'r')
+ df1 = h5py.File(c1.get_checkpoint_fname(iteration = test_niterations*2*factor), 'r')
+ vel0 = get_velocity(c0, iteration = test_niterations*factor)
+ vel1 = get_velocity(c1, iteration = test_niterations*2*factor)
+ diff = vel1 - vel0
+ vv = np.sum(vel0**2, axis = 3)
+ dd = np.sum(diff**2, axis = 3)
+ vrms = np.sqrt(np.mean(vv))
+ err = np.mean(dd)**0.5 / vrms
+ error_list[jj].append(err)
+ print('maximum error for factor {0} is {1}'.format(
+ factor, np.max(dd**0.5) / vrms))
+ df0.close()
+ df1.close()
+
+ f = plt.figure(figsize = (4, 4))
+ a = f.add_subplot(111)
+ fl = np.array(factor_list).astype(np.float)
+ a.plot(fl,
+ error_list[0],
+ marker = '.',
+ label = 'NSVE')
+ a.plot(fl,
+ error_list[1],
+ marker = '.',
+ label = 'NSE')
+ a.plot(fl, 1e-3 * fl**(-1),
+ dashes = (1, 1),
+ color = 'black',
+ label = '$\propto f^{-1}$')
+ a.plot(fl, 1e-3 * fl**(-2),
+ dashes = (2, 2),
+ color = 'black',
+ label = '$\propto f^{-2}$')
+ a.plot(fl, 1e-3 * fl**(-3),
+ dashes = (3, 3),
+ color = 'black',
+ label = '$\propto f^{-3}$')
+ a.set_ylabel('relative error')
+ a.set_xlabel('resolution factor $f$')
+ a.set_xscale('log')
+ a.set_yscale('log')
+ a.legend(loc = 'best')
+ f.tight_layout()
+ f.savefig('err_vs_dt_field2.pdf')
+ f.savefig('err_vs_dt_field2.svg')
+ plt.close(f)
+ return None
+
+def plot_error_field():
+ c0_list = [DNS(simname = 'nsve_{0}x'.format(factor))
+ for factor in [1, 2, 4]]
+ c1_list = [DNS(simname = 'nse_{0}x'.format(factor))
+ for factor in [1, 2, 4]]
+ for cc in c0_list + c1_list:
+ cc.compute_statistics()
+
+ factor_list = [1, 2, 4]
+
+ error_list = []
+ for ii in range(len(factor_list)):
+ factor = factor_list[ii]
+ c0 = c0_list[ii]
+ c1 = c1_list[ii]
+ df0 = h5py.File(c0.get_checkpoint_fname(iteration = test_niterations*factor), 'r')
+ df1 = h5py.File(c1.get_checkpoint_fname(iteration = test_niterations*factor), 'r')
+ vel0 = get_velocity(c0, iteration = test_niterations*factor)
+ vel1 = get_velocity(c1, iteration = test_niterations*factor)
+ diff = vel1 - vel0
+ vv = np.sum(vel0**2, axis = 3)
+ dd = np.sum(diff**2, axis = 3)
+ vrms = np.sqrt(np.mean(vv))
+ err = np.mean(dd)**0.5 / vrms
+ error_list.append(err)
+ print('maximum error for factor {0} is {1}'.format(
+ factor, np.max(dd**0.5) / vrms))
+ df0.close()
+ df1.close()
+
+ f = plt.figure(figsize = (4, 4))
+ a = f.add_subplot(111)
+ fl = np.array(factor_list).astype(np.float)
+ a.plot(fl,
+ error_list,
+ marker = '.',
+ label = 'NSVE vs NSE')
+ a.plot(fl, 1e-2 * fl**(-1),
+ dashes = (1, 1),
+ color = 'black',
+ label = '$\propto f^{-1}$')
+ a.plot(fl, 1e-2 * fl**(-2),
+ dashes = (2, 2),
+ color = 'black',
+ label = '$\propto f^{-2}$')
+ a.plot(fl, 1e-2 * fl**(-3),
+ dashes = (3, 3),
+ color = 'black',
+ label = '$\propto f^{-3}$')
+ a.set_ylabel('relative error')
+ a.set_xlabel('resolution factor $f$')
+ a.set_xscale('log')
+ a.set_yscale('log')
+ a.legend(loc = 'best')
+ f.tight_layout()
+ f.savefig('err_vs_dt_field.pdf')
+ f.savefig('err_vs_dt_field.svg')
+ plt.close(f)
+ return None
+
+def get_velocity(
+ cc,
+ iteration = 0):
+ data_file = h5py.File(
+ cc.get_checkpoint_fname(iteration = iteration),
+ 'r')
+ if 'velocity' in data_file.keys():
+ if 'real' in data_file['velocity'].keys():
+ vel = data_file['velocity/real/{0}'.format(iteration)][()]
+ else:
+ cvel = data_file['velocity/complex/{0}'.format(iteration)][()]
+ vel = ift(cvel)
+ #vel *= cc.parameters['nx']*cc.parameters['ny']*cc.parameters['nz']
+ else:
+ assert('complex' in data_file['vorticity'].keys())
+ cvort = data_file['vorticity/complex/{0}'.format(iteration)][()]
+ cvel = compute_curl(cc, cvort, inverse_curl = True)
+ vel = ift(cvel)
+ data_file.close()
+ return vel
+
+def ift(cfield):
+ ff = np.fft.irfftn(cfield, axes = (0, 1, 2))
+ field = np.transpose(ff, (1, 0, 2, 3)).copy()
+ return field
+
+def compute_curl(
+ cc,
+ cfield,
+ inverse_curl = False):
+ kx = cc.get_data_file()['kspace/kx'][()]
+ ky = cc.get_data_file()['kspace/ky'][()]
+ kz = cc.get_data_file()['kspace/kz'][()]
+ ff = cfield.copy()
+ ff[..., 0] = 1j*(ky[:, None, None]*cfield[..., 2] - kz[None, :, None]*cfield[..., 1])
+ ff[..., 1] = 1j*(kz[None, :, None]*cfield[..., 0] - kx[None, None, :]*cfield[..., 2])
+ ff[..., 2] = 1j*(kx[None, None, :]*cfield[..., 1] - ky[:, None, None]*cfield[..., 0])
+ if inverse_curl:
+ k2 = (kx[None, None, :]**2 +
+ ky[ :, None, None]**2 +
+ kz[None, :, None]**2)
+ k2[0, 0, 0] = 1.
+ ff /= k2[:, :, :, None]
+ return ff
+
+if __name__ == '__main__':
+ main()
+
--
GitLab
From 0ec2f584585f10f801492ef9852b3089e4fd657d Mon Sep 17 00:00:00 2001
From: Cristian C Lalescu <Cristian.Lalescu@mpcdf.mpg.de>
Date: Tue, 18 Jan 2022 11:20:47 +0100
Subject: [PATCH 13/24] adds error raise for kspace inconsistency
---
CMakeLists.txt | 7 -------
TurTLE/DNS.py | 12 ++++++++----
cpp/kspace.cpp | 6 ++++--
3 files changed, 12 insertions(+), 13 deletions(-)
diff --git a/CMakeLists.txt b/CMakeLists.txt
index da1d4bd2..627474c6 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -489,13 +489,6 @@ LIST(APPEND source_files ${hpp_for_lib} ${cpp_for_lib})
add_library(TurTLE ${source_files})
-# TODO: we should be using the bit below, but we need to fix everything else about TURTLE_LIBS before we can do that
-#target_link_libraries(TurTLE PUBLIC OpenMP::OpenMP_CXX)
-
-set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} ${OpenMP_CXX_FLAGS}")
-set(CMAKE_EXE_LINKER_FLAGS "${CMAKE_EXE_LINKER_FLAGS} ${OpenMP_EXE_LINKER_FLAGS}")
-list(APPEND TURTLE_LIBS "${OpenMP_CXX_LIB_NAMES}")
-
target_link_libraries(TurTLE ${TURTLE_LIBS})
target_compile_options(TurTLE PRIVATE $<$<CONFIG:DEBUG>:-O1>)
diff --git a/TurTLE/DNS.py b/TurTLE/DNS.py
index d98367ac..3bc6d3a8 100644
--- a/TurTLE/DNS.py
+++ b/TurTLE/DNS.py
@@ -344,13 +344,17 @@ class DNS(_code):
if k in pp_file.keys():
self.statistics[k] = pp_file[k][...]
# sanity check --- Parseval theorem check
- test_energy = (np.max(np.abs(
+ energy_error = np.max(np.abs(
self.statistics['renergy(t)'] -
- self.statistics['energy(t)']) / self.statistics['energy(t)']) < 1e-5)
- test_enstrophy = (np.max(np.abs(
+ self.statistics['energy(t)']) / self.statistics['energy(t)'])
+ test_energy = (energy_error < 1e-5)
+ enstrophy_error = np.max(np.abs(
self.statistics['renstrophy(t)'] -
- self.statistics['enstrophy(t)']) / self.statistics['enstrophy(t)']) < 1e-5)
+ self.statistics['enstrophy(t)']) / self.statistics['enstrophy(t)'])
+ test_enstrophy = (enstrophy_error < 1e-5)
if strict_Parseval_check:
+ #print('energy error', energy_error)
+ #print('enstrophy error', enstrophy_error)
assert(test_energy)
assert(test_enstrophy)
else:
diff --git a/cpp/kspace.cpp b/cpp/kspace.cpp
index 921e498d..369db623 100644
--- a/cpp/kspace.cpp
+++ b/cpp/kspace.cpp
@@ -28,6 +28,7 @@
#include <cstdlib>
#include <algorithm>
#include <cassert>
+#include <stdexcept>
#include "kspace.hpp"
#include "scope_timer.hpp"
#include "shared_array.hpp"
@@ -201,8 +202,9 @@ int kspace<be, dt>::store(hid_t stat_file)
if (this->nshells != int(dims[0]))
{
DEBUG_MSG(
- "ERROR: computed nshells %d not equal to data file nshells %d\n",
- this->nshells, dims[0]);
+ "ERROR: computed nshells %d not equal to data file nshells %d for dealiasing %d\n",
+ this->nshells, dims[0], dt);
+ throw std::runtime_error("Computed nshells not equal to data file nshells. Something is probably wrong with the dealiasing option.\n");
}
H5Dwrite(
dset,
--
GitLab
From fffef06f51d048132c139a5ca9a52832081b77b6 Mon Sep 17 00:00:00 2001
From: Cristian C Lalescu <Cristian.Lalescu@mpcdf.mpg.de>
Date: Tue, 18 Jan 2022 11:21:36 +0100
Subject: [PATCH 14/24] [wip] testing particle convergence
---
examples/convergence.py | 154 +++++++++++++++++-----------------------
1 file changed, 65 insertions(+), 89 deletions(-)
diff --git a/examples/convergence.py b/examples/convergence.py
index 9560ab4d..8d31825d 100644
--- a/examples/convergence.py
+++ b/examples/convergence.py
@@ -5,30 +5,29 @@ import matplotlib.pyplot as plt
import TurTLE
from TurTLE import DNS, PP
-base_niterations = 256
+base_niterations = 512
test_niterations = 32
-nparticles = 100
+nparticles = 4
particle_random_seed = 15
base_particle_dt = 0.5
-test_niterations_particles = 128
+test_niterations_particles = 8
neighbours_smoothness_list = [
- (1, 1),
+ (1, 0),
(2, 1),
- (3, 2),
- (4, 3)]
+ (3, 2)]
def main():
- #generate_initial_conditions()
+ generate_initial_conditions()
- #run_simulations_field()
- #plot_error_field()
+ run_simulations_field()
+ plot_error_field()
- run_simulations_particles()
- plot_error_particles()
+ #run_simulations_particles()
+ #plot_error_particles()
- plot_traj_particles()
+ #plot_traj_particles()
return None
def generate_initial_conditions():
@@ -51,55 +50,28 @@ def generate_initial_conditions():
'--src-simname', 'B32p1e4',
'--src-wd', TurTLE.data_dir,
'--src-iteration', '0',
- '--simname', 'base_1x',
+ '--simname', 'base',
'--niter_todo', '{0}'.format(base_niterations),
'--niter_out', '{0}'.format(base_niterations),
'--overwrite-src-parameters',
- '--kMeta', '1.0',
+ '--kMeta', '2.',
'--niter_stat', '16',
'--checkpoints_per_file', '{0}'.format(16)])
-# 2. Generate initial conditions for NSVE runs at 2x and 4x the
-# base resolution.
- for factor in [2, 4]:
- # create postprocess object
- cc = PP()
- # create a larger version of the field at final iteration
- cc.launch([
- 'resize',
- '--np', '{0}'.format(nprocesses),
- '--ntpp', '{0}'.format(nthreads_per_process),
- '--simname', 'base_1x',
- '--precision', 'double',
- '--iter0', '{0}'.format(base_niterations),
- '--iter1', '{0}'.format(base_niterations),
- '--new_nx', '{0}'.format(factor*32),
- '--new_ny', '{0}'.format(factor*32),
- '--new_nz', '{0}'.format(factor*32),
- '--new_simname', 'base_{0}x'.format(factor)])
- # update "checkpoint" file, so we can use "base__x" as "src-simname"
- # this is needed after "resize"
- f1 = h5py.File('base_{0}x_checkpoint_0.h5'.format(factor), 'a')
- f1['vorticity/complex/{0}'.format(base_niterations)] = h5py.ExternalLink(
- 'base_{0}x_fields.h5'.format(factor),
- 'vorticity/complex/{0}'.format(base_niterations))
- f1.close()
-
# 3. Generate initial conditions for NSE runs at 1x, 2x and 4x the
# base resolution.
- for factor in [1, 2, 4]:
- # create postprocess object
- cc = PP()
- # compute velocity field at last iteration
- cc.launch([
- 'get_velocity',
- '--np', '{0}'.format(nprocesses),
- '--ntpp', '{0}'.format(nthreads_per_process),
- '--simname', 'base_{0}x'.format(factor),
- '--precision', 'double',
- '--iter0', '{0}'.format(base_niterations),
- '--iter1', '{0}'.format(base_niterations)])
- # we don't need to update "checkpoint" file after "get_velocity"
+ # create postprocess object
+ cc = PP()
+ # compute velocity field at last iteration
+ cc.launch([
+ 'get_velocity',
+ '--np', '{0}'.format(nprocesses),
+ '--ntpp', '{0}'.format(nthreads_per_process),
+ '--simname', 'base',
+ '--precision', 'double',
+ '--iter0', '{0}'.format(base_niterations),
+ '--iter1', '{0}'.format(base_niterations)])
+ # we don't need to update "checkpoint" file after "get_velocity"
return None
def run_simulations_field():
@@ -119,12 +91,12 @@ def run_simulations_field():
'-n', '{0}'.format(factor*32),
'--np', '{0}'.format(nprocesses),
'--ntpp', '{0}'.format(nthreads_per_process),
- '--src-simname', 'base_{0}x'.format(factor),
+ '--src-simname', 'base',
'--src-iteration', '{0}'.format(base_niterations),
'--simname', 'nsve_{0}x'.format(factor),
'--precision', 'double',
- '--dtfactor', '0.3',
- '--kMeta', '{0}'.format(1.0*factor),
+ '--dtfactor', '{0}'.format(0.3 / factor),
+ '--kMeta', '{0}'.format(factor*1.0),
'--niter_todo', '{0}'.format(test_niterations*factor),
'--niter_out', '{0}'.format(test_niterations*factor),
'--niter_stat', '{0}'.format(4*factor)])
@@ -139,12 +111,12 @@ def run_simulations_field():
'-n', '{0}'.format(factor*32),
'--np', '{0}'.format(nprocesses),
'--ntpp', '{0}'.format(nthreads_per_process),
- '--src-simname', 'base_{0}x'.format(factor),
+ '--src-simname', 'base',
'--src-iteration', '{0}'.format(base_niterations),
'--simname', 'nse_{0}x'.format(factor),
'--precision', 'double',
- '--dtfactor', '0.3',
- '--kMeta', '{0}'.format(1.0*factor),
+ '--dtfactor', '{0}'.format(0.3 / factor),
+ '--kMeta', '{0}'.format(factor*1.0),
'--niter_todo', '{0}'.format(test_niterations*factor),
'--niter_out', '{0}'.format(test_niterations*factor),
'--niter_stat', '{0}'.format(4*factor)])
@@ -172,10 +144,10 @@ def plot_error_field():
diff = vel1 - vel0
vv = np.sqrt(np.sum(vel0**2, axis = 3))
dd = np.sqrt(np.sum(diff**2, axis = 3))
- err = np.max(dd / vv)
+ err = np.mean(dd / vv)
error_list.append(err)
print('maximum error for factor {0} is {1}'.format(
- factor, err))
+ factor, np.max(dd / vv)))
df0.close()
df1.close()
@@ -186,9 +158,17 @@ def plot_error_field():
error_list,
marker = '.',
label = 'NSVE vs NSE')
- a.plot(fl, fl**(-3),
+ a.plot(fl, 1e-2 * fl**(-1),
dashes = (1, 1),
color = 'black',
+ label = '$\propto f^{-1}$')
+ a.plot(fl, 1e-2 * fl**(-2),
+ dashes = (2, 2),
+ color = 'black',
+ label = '$\propto f^{-2}$')
+ a.plot(fl, 1e-2 * fl**(-3),
+ dashes = (3, 3),
+ color = 'black',
label = '$\propto f^{-3}$')
a.set_ylabel('relative error')
a.set_xlabel('resolution factor $f$')
@@ -197,7 +177,6 @@ def plot_error_field():
a.legend(loc = 'best')
f.tight_layout()
f.savefig('err_vs_dt_field.pdf')
- f.savefig('err_vs_dt_field.png')
f.savefig('err_vs_dt_field.svg')
plt.close(f)
return None
@@ -258,7 +237,7 @@ def run_simulations_particles():
# with the relevant velocity field.
# create dns object
# launch simulation
- factor = 1
+ factor = 2
for neighbours, smoothness in neighbours_smoothness_list:
interp_name = 'I{0}O{1}'.format(2*neighbours+2, 2*smoothness+1)
cc = DNS()
@@ -267,19 +246,20 @@ def run_simulations_particles():
'-n', '{0}'.format(factor*32),
'--np', '{0}'.format(nprocesses),
'--ntpp', '{0}'.format(nthreads_per_process),
- '--src-simname', 'base_{0}x'.format(factor),
+ '--src-simname', 'base',
'--src-iteration', '{0}'.format(base_niterations),
'--simname', 'nsvep_base_' + interp_name,
'--precision', 'double',
'--dtfactor', '{0}'.format(base_particle_dt/4),
- '--kMeta', '{0}'.format(1.0*factor),
- '--niter_todo', '{0}'.format(16),
+ '--kMeta', '{0}'.format(2.0),
+ '--niter_todo', '{0}'.format(20),
'--niter_out', '{0}'.format(1),
'--niter_stat', '{0}'.format(1),
'--nparticles', '{0}'.format(nparticles),
'--niter_part', '{0}'.format(1),
'--tracers0_neighbours', '{0}'.format(neighbours),
'--tracers0_smoothness', '{0}'.format(smoothness),
+ '--tracers0_integration_steps', '5',
'--cpp_random_particles', '{0}'.format(particle_random_seed)])
# 2. Prepare initial conditions
@@ -288,9 +268,10 @@ def run_simulations_particles():
for factor in [1, 2, 4]:
df = h5py.File('nsvep_{0}x_{1}_checkpoint_0.h5'.format(factor, interp_name), 'w')
# field
+ field_iteration = 16
df['vorticity/complex/{0}'.format(8*factor)] = h5py.ExternalLink(
'nsvep_base_{0}_checkpoint_0.h5'.format(interp_name),
- 'vorticity/complex/16')
+ 'vorticity/complex/{0}'.format(field_iteration))
# particles
df['tracers0/state/{0}'.format(8*factor)] = h5py.ExternalLink(
'nsvep_base_{0}_checkpoint_0.h5'.format(interp_name),
@@ -299,21 +280,10 @@ def run_simulations_particles():
source_file = h5py.File(
'nsvep_base_{0}_checkpoint_0.h5'.format(interp_name), 'r')
rhs = source_file['tracers0/rhs/16'][()]
- if factor == 4:
- rhs[0] = source_file['tracers0/rhs/16'][0]
- rhs[1] = source_file['tracers0/rhs/16'][1]
- rhs[2] = source_file['tracers0/rhs/15'][1]
- rhs[3] = source_file['tracers0/rhs/14'][1]
- if factor == 2:
- rhs[0] = source_file['tracers0/rhs/16'][0]
- rhs[1] = source_file['tracers0/rhs/15'][1]
- rhs[2] = source_file['tracers0/rhs/13'][1]
- rhs[3] = source_file['tracers0/rhs/11'][1]
- if factor == 1:
- rhs[0] = source_file['tracers0/rhs/16'][0]
- rhs[1] = source_file['tracers0/rhs/13'][1]
- rhs[2] = source_file['tracers0/rhs/9'][1]
- rhs[3] = source_file['tracers0/rhs/5'][1]
+ for tt in range(1, rhs.shape[0]):
+ ii = 16 - tt*factor + 1
+ print(factor, tt, ii)
+ rhs[tt] = source_file['tracers0/rhs/{0}'.format(16 - tt*factor + 1)][1]
df['tracers0/rhs/{0}'.format(8*factor)] = rhs
df.close()
@@ -331,7 +301,7 @@ def run_simulations_particles():
# launch simulation
cc.launch([
'NSVEparticles',
- '-n', '{0}'.format(32),
+ '-n', '{0}'.format(64),
'--np', '{0}'.format(nprocesses),
'--ntpp', '{0}'.format(nthreads_per_process),
'--simname', 'nsvep_{0}x_I{1}O{2}'.format(
@@ -340,7 +310,7 @@ def run_simulations_particles():
2*smoothness+1),
'--precision', 'double',
'--dtfactor', '{0}'.format(base_particle_dt/factor),
- '--kMeta', '{0}'.format(1.0),
+ '--kMeta', '{0}'.format(2.0),
'--niter_todo', '{0}'.format(test_niterations_particles*factor+8*factor),
'--niter_out', '{0}'.format(test_niterations_particles*factor+8*factor),
'--niter_stat', '{0}'.format(4*factor),
@@ -348,6 +318,7 @@ def run_simulations_particles():
'--niter_part', '{0}'.format(2*factor),
'--tracers0_neighbours', '{0}'.format(neighbours),
'--tracers0_smoothness', '{0}'.format(smoothness),
+ '--tracers0_integration_steps', '5',
'--cpp_random_particles', '0'], # turn off cpp particle initialization
iter0 = 8*factor)
return None
@@ -385,14 +356,19 @@ def plot_error_particles():
a.plot(factor_list, err_max_list, marker = '.', label = 'max error ' + interp_name)
a.plot(factor_list, err_mean_list, marker = '.', label = 'mean error ' + interp_name)
a.plot(factor_list,
- (3e-2)*factor_list**(-3.5),
+ (3e-5)*factor_list**(-2),
color = 'black',
dashes = (2, 2),
- label = '$\propto f^{-3.5}$')
+ label = '$\propto f^{-2}$')
a.plot(factor_list,
- (3e-3)*factor_list**(-4),
+ (3e-5)*factor_list**(-3),
color = 'black',
- dashes = (1, 1),
+ dashes = (3, 3),
+ label = '$\propto f^{-3}$')
+ a.plot(factor_list,
+ (3e-6)*factor_list**(-4),
+ color = 'black',
+ dashes = (4, 4),
label = '$\propto f^{-4}$')
a.set_xscale('log')
a.set_yscale('log')
--
GitLab
From fea49e0de4569401b9cd918d5acdf3007e907639 Mon Sep 17 00:00:00 2001
From: Cristian C Lalescu <Cristian.Lalescu@mpcdf.mpg.de>
Date: Tue, 18 Jan 2022 12:43:39 +0100
Subject: [PATCH 15/24] bugfix: fixes forcing call for NSE
---
cpp/full_code/NSE.cpp | 4 ++--
1 file changed, 2 insertions(+), 2 deletions(-)
diff --git a/cpp/full_code/NSE.cpp b/cpp/full_code/NSE.cpp
index 25a4c395..fac9a0b3 100644
--- a/cpp/full_code/NSE.cpp
+++ b/cpp/full_code/NSE.cpp
@@ -460,7 +460,7 @@ int NSE<rnumber>::ShuOsher(void)
*this->tmp_velocity2 = rnumber(0);
this->add_nonlinear_term(this->tmp_velocity1, this->tmp_velocity2);
- this->add_forcing_term(this->velocity, this->tmp_velocity2);
+ this->add_forcing_term(this->tmp_velocity1, this->tmp_velocity2);
this->kk->CLOOP_K2(
[&](const ptrdiff_t cindex,
const ptrdiff_t xindex,
@@ -482,7 +482,7 @@ int NSE<rnumber>::ShuOsher(void)
*this->tmp_velocity1 = rnumber(0);
this->add_nonlinear_term(this->tmp_velocity2, this->tmp_velocity1);
- this->add_forcing_term(this->velocity, this->tmp_velocity1);
+ this->add_forcing_term(this->tmp_velocity2, this->tmp_velocity1);
this->kk->CLOOP_K2(
[&](const ptrdiff_t cindex,
const ptrdiff_t xindex,
--
GitLab
From 95019c4acafce815c21cb24107f164d366ef35c7 Mon Sep 17 00:00:00 2001
From: Cristian C Lalescu <Cristian.Lalescu@mpcdf.mpg.de>
Date: Tue, 18 Jan 2022 16:39:45 +0100
Subject: [PATCH 16/24] adds cleaner field solver convergence check
---
examples/convergence/fields_base.py | 78 +++++++++
examples/convergence/fields_temporal.py | 202 ++++++++++++++++++++++++
2 files changed, 280 insertions(+)
create mode 100644 examples/convergence/fields_base.py
create mode 100644 examples/convergence/fields_temporal.py
diff --git a/examples/convergence/fields_base.py b/examples/convergence/fields_base.py
new file mode 100644
index 00000000..d2225d32
--- /dev/null
+++ b/examples/convergence/fields_base.py
@@ -0,0 +1,78 @@
+import numpy as np
+import h5py
+import matplotlib.pyplot as plt
+
+def main():
+ return None
+
+def get_velocity(
+ cc,
+ iteration = 0):
+ data_file = h5py.File(
+ cc.get_checkpoint_fname(iteration = iteration),
+ 'r')
+ if 'velocity' in data_file.keys():
+ if 'real' in data_file['velocity'].keys():
+ vel = data_file['velocity/real/{0}'.format(iteration)][()]
+ else:
+ cvel = data_file['velocity/complex/{0}'.format(iteration)][()]
+ vel = ift(cvel)
+ else:
+ assert('complex' in data_file['vorticity'].keys())
+ cvort = data_file['vorticity/complex/{0}'.format(iteration)][()]
+ cvel = compute_curl(cc, cvort, inverse_curl = True)
+ vel = ift(cvel)
+ data_file.close()
+ return vel
+
+def ift(cfield):
+ ff = np.fft.irfftn(cfield, axes = (0, 1, 2))
+ field = np.transpose(ff, (1, 0, 2, 3)).copy()
+ return field*(field.shape[0]*field.shape[1]*field.shape[2])
+
+def compute_curl(
+ cc,
+ cfield,
+ inverse_curl = False):
+ kx = cc.get_data_file()['kspace/kx'][()]
+ ky = cc.get_data_file()['kspace/ky'][()]
+ kz = cc.get_data_file()['kspace/kz'][()]
+ ff = cfield.copy()
+ ff[..., 0] = 1j*(ky[:, None, None]*cfield[..., 2] - kz[None, :, None]*cfield[..., 1])
+ ff[..., 1] = 1j*(kz[None, :, None]*cfield[..., 0] - kx[None, None, :]*cfield[..., 2])
+ ff[..., 2] = 1j*(kx[None, None, :]*cfield[..., 1] - ky[:, None, None]*cfield[..., 0])
+ if inverse_curl:
+ k2 = (kx[None, None, :]**2 +
+ ky[ :, None, None]**2 +
+ kz[None, :, None]**2)
+ k2[0, 0, 0] = 1.
+ ff /= k2[:, :, :, None]
+ return ff
+
+def compute_vector_field_distance(
+ f1, f2,
+ figname = None):
+ diff = f1 - f2
+ rms1 = np.mean(np.sum(f1**2, axis = 3))**0.5
+ rms2 = np.mean(np.sum(f2**2, axis = 3))**0.5
+ rms = np.sqrt(rms1 * rms2)
+ dd = np.sum(diff**2, axis = 3)
+ L2 = np.sqrt(np.mean(dd))
+ max_val = np.max(np.sqrt(dd))
+ if type(figname) != type(None):
+ fig = plt.figure(figsize = (8, 4))
+ a = fig.add_subplot(121)
+ a.imshow(f1[:, 5, :, 2], vmin = -1, vmax = 1, interpolation = 'none')
+ a = fig.add_subplot(122)
+ a.imshow(f2[:, 5, :, 2], vmin = -1, vmax = 1, interpolation = 'none')
+ fig.tight_layout()
+ fig.savefig('field_slice_' + figname + '.pdf')
+ plt.close(fig)
+ return {'L2' : L2,
+ 'L2_rel' : L2 / rms,
+ 'max' : max_val,
+ 'max_rel' : max_val / rms}
+
+if __name__ == '__main__':
+ main()
+
diff --git a/examples/convergence/fields_temporal.py b/examples/convergence/fields_temporal.py
new file mode 100644
index 00000000..3d18a18c
--- /dev/null
+++ b/examples/convergence/fields_temporal.py
@@ -0,0 +1,202 @@
+import numpy as np
+import h5py
+import matplotlib.pyplot as plt
+
+import TurTLE
+from TurTLE import DNS, PP
+
+from fields_base import *
+
+base_niterations = 128
+test_niterations = 32
+grid_size = 128
+
+def main():
+ generate_initial_conditions()
+
+ run_simulations_field()
+ plot_error_field()
+ return None
+
+def generate_initial_conditions():
+ # change these two values as neded.
+ # number of MPI processes to use
+ nprocesses = 8
+ # number of OpenMP threads per MPI process to use
+ nthreads_per_process = 1
+
+# 1. Generate quasistationary state to use for initial conditions.
+ # create a dns object
+ c0 = DNS()
+ # launch the simulation
+ c0.launch([
+ 'NSVE',
+ '-n', '{0}'.format(grid_size),
+ '--np', '{0}'.format(nprocesses),
+ '--ntpp', '{0}'.format(nthreads_per_process),
+ '--precision', 'double',
+ '--src-simname', 'B32p1e4',
+ '--src-wd', TurTLE.data_dir,
+ '--src-iteration', '0',
+ '--simname', 'base',
+ '--niter_todo', '{0}'.format(base_niterations),
+ '--niter_out', '{0}'.format(base_niterations),
+ '--overwrite-src-parameters',
+ '--kMeta', '1.5',
+ '--fk0', '2',
+ '--fk1', '3',
+ '--niter_stat', '16',
+ '--checkpoints_per_file', '{0}'.format(64)])
+
+# 3. Generate initial conditions for NSE runs at 1x, 2x and 4x the
+# base resolution.
+ # create postprocess object
+ cc = PP()
+ # compute velocity field at last iteration
+ cc.launch([
+ 'get_velocity',
+ '--np', '{0}'.format(nprocesses),
+ '--ntpp', '{0}'.format(nthreads_per_process),
+ '--simname', 'base',
+ '--precision', 'double',
+ '--iter0', '{0}'.format(base_niterations),
+ '--iter1', '{0}'.format(base_niterations)])
+ return None
+
+def run_simulations_field():
+ # change these two values as neded.
+ # number of MPI processes to use
+ nprocesses = 8
+ # number of OpenMP threads per MPI process to use
+ nthreads_per_process = 1
+
+# 1. Run NSVE for the three resolutions.
+ for factor in [1, 2, 4]:
+ # create dns object
+ cc = DNS()
+ # launch simulation
+ cc.launch([
+ 'NSVE',
+ '-n', '{0}'.format(grid_size),
+ '--np', '{0}'.format(nprocesses),
+ '--ntpp', '{0}'.format(nthreads_per_process),
+ '--src-simname', 'base',
+ '--src-iteration', '{0}'.format(base_niterations),
+ '--simname', 'nsve_{0}x'.format(factor),
+ '--precision', 'double',
+ '--dtfactor', '{0}'.format(0.5 / factor),
+ '--niter_todo', '{0}'.format(test_niterations*factor),
+ '--niter_out', '{0}'.format(test_niterations*factor),
+ #'--niter_out', '{0}'.format(factor),
+ '--niter_stat', '{0}'.format(factor)])
+
+# 2. Run NSE for the three resolutions.
+ for factor in [1, 2, 4]:
+ # create dns object
+ cc = DNS()
+ # launch simulation
+ cc.launch([
+ 'NSE',
+ '-n', '{0}'.format(grid_size),
+ '--np', '{0}'.format(nprocesses),
+ '--ntpp', '{0}'.format(nthreads_per_process),
+ '--src-simname', 'base',
+ '--src-iteration', '{0}'.format(base_niterations),
+ '--simname', 'nse_{0}x'.format(factor),
+ '--precision', 'double',
+ '--dtfactor', '{0}'.format(0.5 / factor),
+ '--niter_todo', '{0}'.format(test_niterations*factor),
+ #'--niter_out', '{0}'.format(factor),
+ '--niter_out', '{0}'.format(test_niterations*factor),
+ '--niter_stat', '{0}'.format(factor)])
+ return None
+
+def plot_error_field():
+ factor_list = [1, 2, 4]
+ c0_list = [DNS(simname = 'nsve_{0}x'.format(factor))
+ for factor in factor_list]
+ c1_list = [DNS(simname = 'nse_{0}x'.format(factor))
+ for factor in factor_list]
+ cl = [c0_list, c1_list]
+ # sanity checks
+ for cc in c0_list + c1_list:
+ cc.compute_statistics()
+
+ # errors for individual solvers
+ error_list = [[], [], []]
+ for ii in range(len(factor_list)-1):
+ factor = factor_list[ii]
+ for jj in [0, 1]:
+ vel1 = get_velocity(cl[jj][ii ], iteration = test_niterations*factor)
+ vel2 = get_velocity(cl[jj][ii+1], iteration = 2*test_niterations*factor)
+ dd = compute_vector_field_distance(vel1, vel2, figname = cl[jj][ii].simname + '_vs_' + cl[jj][ii+1].simname)
+ error_list[jj].append(dd['L2_rel'])
+
+ # comparisons of two solutions
+ for ii in range(len(factor_list)):
+ factor = factor_list[ii]
+ vel1 = get_velocity(cl[0][ii], iteration = test_niterations*factor)
+ vel2 = get_velocity(cl[1][ii], iteration = test_niterations*factor)
+ dd = compute_vector_field_distance(vel1, vel2)
+ error_list[2].append(dd['L2_rel'])
+
+ f = plt.figure(figsize = (4, 4))
+ a = f.add_subplot(111)
+ a.plot(factor_list[:len(error_list[0])],
+ error_list[0],
+ marker = '.',
+ dashes = (2, 3),
+ label = 'NSVE')
+ a.plot(factor_list[:len(error_list[1])],
+ error_list[1],
+ marker = '.',
+ dashes = (3, 5),
+ label = 'NSE')
+ a.plot(factor_list,
+ error_list[2],
+ marker = '.',
+ label = 'NSVE vs NSE')
+ fl = np.array(factor_list).astype(np.float)
+ for ee in [1, 2, 3]:
+ a.plot(fl, error_list[0][0] * fl**(-ee),
+ dashes = (ee, ee),
+ color = 'black',
+ label = '$\propto f^{{-{0}}}$'.format(ee),
+ zorder = -ee)
+ a.set_ylabel('relative error')
+ a.set_xlabel('resolution factor $f$')
+ a.set_xscale('log')
+ a.set_yscale('log')
+ a.legend(loc = 'best', fontsize = 6)
+ f.tight_layout()
+ f.savefig('err_vs_dt_field.pdf')
+ f.savefig('err_vs_dt_field.svg')
+ plt.close(f)
+
+ #t = range(test_niterations+1)
+ #err_vs_t = [[], [], []]
+ ## comparisons of two solvers
+ #for ii in range(len(factor_list)):
+ # factor = factor_list[ii]
+ # for tt in t:
+ # vel1 = get_velocity(cl[0][ii], iteration = tt*factor)
+ # vel2 = get_velocity(cl[1][ii], iteration = tt*factor)
+ # dd = compute_vector_field_distance(vel1, vel2)
+ # err_vs_t[ii].append(dd['L2_rel'])
+ ## distance between NSVE and NSE as a function of time
+ #f = plt.figure(figsize = (4, 4))
+ #a = f.add_subplot(111)
+ #a.plot(t, err_vs_t[0], label = 'f = 1')
+ #a.plot(t, err_vs_t[1], label = 'f = 2')
+ #a.plot(t, err_vs_t[2], label = 'f = 4')
+ #a.set_yscale('log')
+ #a.legend(loc = 'best', fontsize = 6)
+ #f.tight_layout()
+ #f.savefig('err_vs_t_field.pdf')
+ #f.savefig('err_vs_t_field.svg')
+ #plt.close(f)
+ return None
+
+if __name__ == '__main__':
+ main()
+
--
GitLab
From 7e6fe17b85f20b4bf4298e5018ea24374afb63a9 Mon Sep 17 00:00:00 2001
From: Cristian C Lalescu <Cristian.Lalescu@mpcdf.mpg.de>
Date: Tue, 18 Jan 2022 16:50:42 +0100
Subject: [PATCH 17/24] fixes viscosity value for decaying case
---
TurTLE/DNS.py | 7 ++++++-
1 file changed, 6 insertions(+), 1 deletion(-)
diff --git a/TurTLE/DNS.py b/TurTLE/DNS.py
index 3bc6d3a8..99962bf5 100644
--- a/TurTLE/DNS.py
+++ b/TurTLE/DNS.py
@@ -824,7 +824,7 @@ class DNS(_code):
kM = opt.n * 0.5
if opt.dealias_type == 1:
kM *= 0.8
- # tweak forcing/viscosity based on forcint type
+ # tweak forcing/viscosity based on forcing type
if opt.forcing_type == 'linear':
# custom famplitude for 288 and 576
if opt.n == 288:
@@ -837,6 +837,11 @@ class DNS(_code):
opt.nu = (
opt.injection_rate *
(opt.kMeta / kM)**4)**(1./3)
+ if opt.injection_rate == 0:
+ opt.nu = (
+ (opt.kMeta / kM)**(4./3) *
+ (np.pi / 1.5)**(1./3) *
+ (2*self.parameters['energy'] / 3)**0.5)
elif opt.forcing_type == 'fixed_energy':
kf = 1. / (1./opt.fk0 +
1./opt.fk1)
--
GitLab
From 1c51da3d6b518e8e705fa3033d557c72cdc029b2 Mon Sep 17 00:00:00 2001
From: Cristian C Lalescu <Cristian.Lalescu@mpcdf.mpg.de>
Date: Tue, 18 Jan 2022 17:30:06 +0100
Subject: [PATCH 18/24] tweaks field error analysis
---
examples/convergence/fields_temporal.py | 70 +++---
examples/convergence_only_time.py | 281 ------------------------
2 files changed, 38 insertions(+), 313 deletions(-)
delete mode 100644 examples/convergence_only_time.py
diff --git a/examples/convergence/fields_temporal.py b/examples/convergence/fields_temporal.py
index 3d18a18c..85ada49f 100644
--- a/examples/convergence/fields_temporal.py
+++ b/examples/convergence/fields_temporal.py
@@ -14,8 +14,10 @@ grid_size = 128
def main():
generate_initial_conditions()
- run_simulations_field()
- plot_error_field()
+ run_simulations_field(
+ err_vs_t = False)
+ plot_error_field(
+ err_vs_t = False)
return None
def generate_initial_conditions():
@@ -48,11 +50,10 @@ def generate_initial_conditions():
'--niter_stat', '16',
'--checkpoints_per_file', '{0}'.format(64)])
-# 3. Generate initial conditions for NSE runs at 1x, 2x and 4x the
-# base resolution.
+# 3. Generate initial conditions for NSE runs.
# create postprocess object
cc = PP()
- # compute velocity field at last iteration
+ # launches code to compute velocity field at last iteration
cc.launch([
'get_velocity',
'--np', '{0}'.format(nprocesses),
@@ -63,13 +64,18 @@ def generate_initial_conditions():
'--iter1', '{0}'.format(base_niterations)])
return None
-def run_simulations_field():
+def run_simulations_field(err_vs_t = False):
# change these two values as neded.
# number of MPI processes to use
nprocesses = 8
# number of OpenMP threads per MPI process to use
nthreads_per_process = 1
+ if err_vs_t:
+ niter_out_factor = 1
+ else:
+ niter_out_factor = test_niterations
+
# 1. Run NSVE for the three resolutions.
for factor in [1, 2, 4]:
# create dns object
@@ -86,8 +92,7 @@ def run_simulations_field():
'--precision', 'double',
'--dtfactor', '{0}'.format(0.5 / factor),
'--niter_todo', '{0}'.format(test_niterations*factor),
- '--niter_out', '{0}'.format(test_niterations*factor),
- #'--niter_out', '{0}'.format(factor),
+ '--niter_out', '{0}'.format(niter_out_factor*factor),
'--niter_stat', '{0}'.format(factor)])
# 2. Run NSE for the three resolutions.
@@ -106,12 +111,12 @@ def run_simulations_field():
'--precision', 'double',
'--dtfactor', '{0}'.format(0.5 / factor),
'--niter_todo', '{0}'.format(test_niterations*factor),
- #'--niter_out', '{0}'.format(factor),
+ '--niter_out', '{0}'.format(niter_out_factor*factor),
'--niter_out', '{0}'.format(test_niterations*factor),
'--niter_stat', '{0}'.format(factor)])
return None
-def plot_error_field():
+def plot_error_field(err_vs_t = False):
factor_list = [1, 2, 4]
c0_list = [DNS(simname = 'nsve_{0}x'.format(factor))
for factor in factor_list]
@@ -173,28 +178,29 @@ def plot_error_field():
f.savefig('err_vs_dt_field.svg')
plt.close(f)
- #t = range(test_niterations+1)
- #err_vs_t = [[], [], []]
- ## comparisons of two solvers
- #for ii in range(len(factor_list)):
- # factor = factor_list[ii]
- # for tt in t:
- # vel1 = get_velocity(cl[0][ii], iteration = tt*factor)
- # vel2 = get_velocity(cl[1][ii], iteration = tt*factor)
- # dd = compute_vector_field_distance(vel1, vel2)
- # err_vs_t[ii].append(dd['L2_rel'])
- ## distance between NSVE and NSE as a function of time
- #f = plt.figure(figsize = (4, 4))
- #a = f.add_subplot(111)
- #a.plot(t, err_vs_t[0], label = 'f = 1')
- #a.plot(t, err_vs_t[1], label = 'f = 2')
- #a.plot(t, err_vs_t[2], label = 'f = 4')
- #a.set_yscale('log')
- #a.legend(loc = 'best', fontsize = 6)
- #f.tight_layout()
- #f.savefig('err_vs_t_field.pdf')
- #f.savefig('err_vs_t_field.svg')
- #plt.close(f)
+ if err_vs_t:
+ t = range(test_niterations+1)
+ err_vs_t = [[], [], []]
+ # comparisons of two solvers
+ for ii in range(len(factor_list)):
+ factor = factor_list[ii]
+ for tt in t:
+ vel1 = get_velocity(cl[0][ii], iteration = tt*factor)
+ vel2 = get_velocity(cl[1][ii], iteration = tt*factor)
+ dd = compute_vector_field_distance(vel1, vel2)
+ err_vs_t[ii].append(dd['L2_rel'])
+ # distance between NSVE and NSE as a function of time
+ f = plt.figure(figsize = (4, 4))
+ a = f.add_subplot(111)
+ a.plot(t, err_vs_t[0], label = 'f = 1')
+ a.plot(t, err_vs_t[1], label = 'f = 2')
+ a.plot(t, err_vs_t[2], label = 'f = 4')
+ a.set_yscale('log')
+ a.legend(loc = 'best', fontsize = 6)
+ f.tight_layout()
+ f.savefig('err_vs_t_field.pdf')
+ f.savefig('err_vs_t_field.svg')
+ plt.close(f)
return None
if __name__ == '__main__':
diff --git a/examples/convergence_only_time.py b/examples/convergence_only_time.py
deleted file mode 100644
index 1db81aa3..00000000
--- a/examples/convergence_only_time.py
+++ /dev/null
@@ -1,281 +0,0 @@
-import numpy as np
-import h5py
-import matplotlib.pyplot as plt
-
-import TurTLE
-from TurTLE import DNS, PP
-
-base_niterations = 512
-test_niterations = 32
-
-def main():
- generate_initial_conditions()
-
- run_simulations_field()
- plot_error_field2()
- return None
-
-def generate_initial_conditions():
- # change these two values as neded.
- # number of MPI processes to use
- nprocesses = 8
- # number of OpenMP threads per MPI process to use
- nthreads_per_process = 1
-
-# 1. Generate quasistationary state to use for initial conditions.
- # create a dns object
- c0 = DNS()
- # launch the simulation
- c0.launch([
- 'NSVE',
- '-n', '64',
- '--np', '{0}'.format(nprocesses),
- '--ntpp', '{0}'.format(nthreads_per_process),
- '--precision', 'double',
- '--src-simname', 'B32p1e4',
- '--src-wd', TurTLE.data_dir,
- '--src-iteration', '0',
- '--simname', 'base',
- '--niter_todo', '{0}'.format(base_niterations),
- '--niter_out', '{0}'.format(base_niterations),
- '--overwrite-src-parameters',
- '--kMeta', '1',
- '--niter_stat', '16',
- '--checkpoints_per_file', '{0}'.format(16)])
-
-# 3. Generate initial conditions for NSE runs at 1x, 2x and 4x the
-# base resolution.
- # create postprocess object
- cc = PP()
- # compute velocity field at last iteration
- cc.launch([
- 'get_velocity',
- '--np', '{0}'.format(nprocesses),
- '--ntpp', '{0}'.format(nthreads_per_process),
- '--simname', 'base',
- '--precision', 'double',
- '--iter0', '{0}'.format(base_niterations),
- '--iter1', '{0}'.format(base_niterations)])
- # we don't need to update "checkpoint" file after "get_velocity"
- return None
-
-def run_simulations_field():
- # change these two values as neded.
- # number of MPI processes to use
- nprocesses = 8
- # number of OpenMP threads per MPI process to use
- nthreads_per_process = 1
-
-# 1. Run NSVE for the three resolutions.
- for factor in [1, 2, 4]:
- # create dns object
- cc = DNS()
- # launch simulation
- cc.launch([
- 'NSVE',
- '-n', '{0}'.format(64),
- '--np', '{0}'.format(nprocesses),
- '--ntpp', '{0}'.format(nthreads_per_process),
- '--src-simname', 'base',
- '--src-iteration', '{0}'.format(base_niterations),
- '--simname', 'nsve_{0}x'.format(factor),
- '--precision', 'double',
- '--dtfactor', '{0}'.format(1.0 / factor),
- '--niter_todo', '{0}'.format(test_niterations*factor),
- '--niter_out', '{0}'.format(test_niterations*factor),
- '--niter_stat', '{0}'.format(4*factor)])
-
-# 2. Run NSE for the three resolutions.
- for factor in [1, 2, 4]:
- # create dns object
- cc = DNS()
- # launch simulation
- cc.launch([
- 'NSE',
- '-n', '{0}'.format(64),
- '--np', '{0}'.format(nprocesses),
- '--ntpp', '{0}'.format(nthreads_per_process),
- '--src-simname', 'base',
- '--src-iteration', '{0}'.format(base_niterations),
- '--simname', 'nse_{0}x'.format(factor),
- '--precision', 'double',
- '--dtfactor', '{0}'.format(1.0 / factor),
- '--niter_todo', '{0}'.format(test_niterations*factor),
- '--niter_out', '{0}'.format(test_niterations*factor),
- '--niter_stat', '{0}'.format(4*factor)])
- return None
-
-def plot_error_field2():
- c0_list = [DNS(simname = 'nsve_{0}x'.format(factor))
- for factor in [1, 2, 4]]
- c1_list = [DNS(simname = 'nse_{0}x'.format(factor))
- for factor in [1, 2, 4]]
- cl = [c0_list, c1_list]
- for cc in c0_list + c1_list:
- cc.compute_statistics()
-
- factor_list = [1, 2]
-
- error_list = [[], []]
- for ii in range(len(factor_list)):
- factor = factor_list[ii]
- for jj in [0, 1]:
- c0 = cl[jj][ii]
- c1 = cl[jj][ii+1]
- df0 = h5py.File(c0.get_checkpoint_fname(iteration = test_niterations*factor), 'r')
- df1 = h5py.File(c1.get_checkpoint_fname(iteration = test_niterations*2*factor), 'r')
- vel0 = get_velocity(c0, iteration = test_niterations*factor)
- vel1 = get_velocity(c1, iteration = test_niterations*2*factor)
- diff = vel1 - vel0
- vv = np.sum(vel0**2, axis = 3)
- dd = np.sum(diff**2, axis = 3)
- vrms = np.sqrt(np.mean(vv))
- err = np.mean(dd)**0.5 / vrms
- error_list[jj].append(err)
- print('maximum error for factor {0} is {1}'.format(
- factor, np.max(dd**0.5) / vrms))
- df0.close()
- df1.close()
-
- f = plt.figure(figsize = (4, 4))
- a = f.add_subplot(111)
- fl = np.array(factor_list).astype(np.float)
- a.plot(fl,
- error_list[0],
- marker = '.',
- label = 'NSVE')
- a.plot(fl,
- error_list[1],
- marker = '.',
- label = 'NSE')
- a.plot(fl, 1e-3 * fl**(-1),
- dashes = (1, 1),
- color = 'black',
- label = '$\propto f^{-1}$')
- a.plot(fl, 1e-3 * fl**(-2),
- dashes = (2, 2),
- color = 'black',
- label = '$\propto f^{-2}$')
- a.plot(fl, 1e-3 * fl**(-3),
- dashes = (3, 3),
- color = 'black',
- label = '$\propto f^{-3}$')
- a.set_ylabel('relative error')
- a.set_xlabel('resolution factor $f$')
- a.set_xscale('log')
- a.set_yscale('log')
- a.legend(loc = 'best')
- f.tight_layout()
- f.savefig('err_vs_dt_field2.pdf')
- f.savefig('err_vs_dt_field2.svg')
- plt.close(f)
- return None
-
-def plot_error_field():
- c0_list = [DNS(simname = 'nsve_{0}x'.format(factor))
- for factor in [1, 2, 4]]
- c1_list = [DNS(simname = 'nse_{0}x'.format(factor))
- for factor in [1, 2, 4]]
- for cc in c0_list + c1_list:
- cc.compute_statistics()
-
- factor_list = [1, 2, 4]
-
- error_list = []
- for ii in range(len(factor_list)):
- factor = factor_list[ii]
- c0 = c0_list[ii]
- c1 = c1_list[ii]
- df0 = h5py.File(c0.get_checkpoint_fname(iteration = test_niterations*factor), 'r')
- df1 = h5py.File(c1.get_checkpoint_fname(iteration = test_niterations*factor), 'r')
- vel0 = get_velocity(c0, iteration = test_niterations*factor)
- vel1 = get_velocity(c1, iteration = test_niterations*factor)
- diff = vel1 - vel0
- vv = np.sum(vel0**2, axis = 3)
- dd = np.sum(diff**2, axis = 3)
- vrms = np.sqrt(np.mean(vv))
- err = np.mean(dd)**0.5 / vrms
- error_list.append(err)
- print('maximum error for factor {0} is {1}'.format(
- factor, np.max(dd**0.5) / vrms))
- df0.close()
- df1.close()
-
- f = plt.figure(figsize = (4, 4))
- a = f.add_subplot(111)
- fl = np.array(factor_list).astype(np.float)
- a.plot(fl,
- error_list,
- marker = '.',
- label = 'NSVE vs NSE')
- a.plot(fl, 1e-2 * fl**(-1),
- dashes = (1, 1),
- color = 'black',
- label = '$\propto f^{-1}$')
- a.plot(fl, 1e-2 * fl**(-2),
- dashes = (2, 2),
- color = 'black',
- label = '$\propto f^{-2}$')
- a.plot(fl, 1e-2 * fl**(-3),
- dashes = (3, 3),
- color = 'black',
- label = '$\propto f^{-3}$')
- a.set_ylabel('relative error')
- a.set_xlabel('resolution factor $f$')
- a.set_xscale('log')
- a.set_yscale('log')
- a.legend(loc = 'best')
- f.tight_layout()
- f.savefig('err_vs_dt_field.pdf')
- f.savefig('err_vs_dt_field.svg')
- plt.close(f)
- return None
-
-def get_velocity(
- cc,
- iteration = 0):
- data_file = h5py.File(
- cc.get_checkpoint_fname(iteration = iteration),
- 'r')
- if 'velocity' in data_file.keys():
- if 'real' in data_file['velocity'].keys():
- vel = data_file['velocity/real/{0}'.format(iteration)][()]
- else:
- cvel = data_file['velocity/complex/{0}'.format(iteration)][()]
- vel = ift(cvel)
- #vel *= cc.parameters['nx']*cc.parameters['ny']*cc.parameters['nz']
- else:
- assert('complex' in data_file['vorticity'].keys())
- cvort = data_file['vorticity/complex/{0}'.format(iteration)][()]
- cvel = compute_curl(cc, cvort, inverse_curl = True)
- vel = ift(cvel)
- data_file.close()
- return vel
-
-def ift(cfield):
- ff = np.fft.irfftn(cfield, axes = (0, 1, 2))
- field = np.transpose(ff, (1, 0, 2, 3)).copy()
- return field
-
-def compute_curl(
- cc,
- cfield,
- inverse_curl = False):
- kx = cc.get_data_file()['kspace/kx'][()]
- ky = cc.get_data_file()['kspace/ky'][()]
- kz = cc.get_data_file()['kspace/kz'][()]
- ff = cfield.copy()
- ff[..., 0] = 1j*(ky[:, None, None]*cfield[..., 2] - kz[None, :, None]*cfield[..., 1])
- ff[..., 1] = 1j*(kz[None, :, None]*cfield[..., 0] - kx[None, None, :]*cfield[..., 2])
- ff[..., 2] = 1j*(kx[None, None, :]*cfield[..., 1] - ky[:, None, None]*cfield[..., 0])
- if inverse_curl:
- k2 = (kx[None, None, :]**2 +
- ky[ :, None, None]**2 +
- kz[None, :, None]**2)
- k2[0, 0, 0] = 1.
- ff /= k2[:, :, :, None]
- return ff
-
-if __name__ == '__main__':
- main()
-
--
GitLab
From 9d952856fc2251a6ffe6035d7f7d07e447be8ce6 Mon Sep 17 00:00:00 2001
From: Cristian C Lalescu <Cristian.Lalescu@mpcdf.mpg.de>
Date: Tue, 18 Jan 2022 19:05:33 +0100
Subject: [PATCH 19/24] fixes Heun test
---
TurTLE/test/particle_set/NSVEparticle_set.cpp | 1 +
1 file changed, 1 insertion(+)
diff --git a/TurTLE/test/particle_set/NSVEparticle_set.cpp b/TurTLE/test/particle_set/NSVEparticle_set.cpp
index ee89c2e3..da986349 100644
--- a/TurTLE/test/particle_set/NSVEparticle_set.cpp
+++ b/TurTLE/test/particle_set/NSVEparticle_set.cpp
@@ -205,6 +205,7 @@ int NSVEparticle_set<rnumber>::read_parameters(void)
this->tracers0_neighbours = hdf5_tools::read_value<int>(parameter_file, "parameters/tracers0_neighbours");
this->tracers0_smoothness = hdf5_tools::read_value<int>(parameter_file, "parameters/tracers0_smoothness");
H5Fclose(parameter_file);
+ MPI_Barrier(this->comm);
return EXIT_SUCCESS;
}
--
GitLab
From 41309bce9fd027c3a32049416ec3e51c323723c7 Mon Sep 17 00:00:00 2001
From: Cristian C Lalescu <Cristian.Lalescu@mpcdf.mpg.de>
Date: Wed, 19 Jan 2022 13:10:08 +0100
Subject: [PATCH 20/24] fixes particle convergence test
---
cpp/field.cpp | 2 +-
.../particles_temporal.py} | 303 ++++++------------
2 files changed, 101 insertions(+), 204 deletions(-)
rename examples/{convergence.py => convergence/particles_temporal.py} (55%)
diff --git a/cpp/field.cpp b/cpp/field.cpp
index 6e950ad4..7dd5889f 100644
--- a/cpp/field.cpp
+++ b/cpp/field.cpp
@@ -210,7 +210,7 @@ int field<rnumber, be, fc>::io(
}
if (read)
{
- DEBUG_MSG("field::io trying to read field from file %s\n", fname.c_str());
+ DEBUG_MSG("field::io trying to read field %s from file %s\n", dset_name.c_str(), fname.c_str());
assert(file_exists);
file_id = H5Fopen(fname.c_str(), H5F_ACC_RDONLY, plist_id);
}
diff --git a/examples/convergence.py b/examples/convergence/particles_temporal.py
similarity index 55%
rename from examples/convergence.py
rename to examples/convergence/particles_temporal.py
index 8d31825d..013126db 100644
--- a/examples/convergence.py
+++ b/examples/convergence/particles_temporal.py
@@ -5,35 +5,30 @@ import matplotlib.pyplot as plt
import TurTLE
from TurTLE import DNS, PP
-base_niterations = 512
-test_niterations = 32
+base_niterations = 256
-nparticles = 4
+nparticles = 1000
particle_random_seed = 15
base_particle_dt = 0.5
-test_niterations_particles = 8
+test_niterations_particles = 128
neighbours_smoothness_list = [
- (1, 0),
- (2, 1),
+ (1, 1),
(3, 2)]
def main():
- generate_initial_conditions()
-
- run_simulations_field()
- plot_error_field()
+ #generate_initial_conditions()
#run_simulations_particles()
- #plot_error_particles()
+ plot_error_particles()
- #plot_traj_particles()
+ plot_traj_particles()
return None
def generate_initial_conditions():
# change these two values as neded.
# number of MPI processes to use
- nprocesses = 4
+ nprocesses = 8
# number of OpenMP threads per MPI process to use
nthreads_per_process = 1
@@ -54,7 +49,7 @@ def generate_initial_conditions():
'--niter_todo', '{0}'.format(base_niterations),
'--niter_out', '{0}'.format(base_niterations),
'--overwrite-src-parameters',
- '--kMeta', '2.',
+ '--kMeta', '1.',
'--niter_stat', '16',
'--checkpoints_per_file', '{0}'.format(16)])
@@ -74,170 +69,18 @@ def generate_initial_conditions():
# we don't need to update "checkpoint" file after "get_velocity"
return None
-def run_simulations_field():
- # change these two values as neded.
- # number of MPI processes to use
- nprocesses = 4
- # number of OpenMP threads per MPI process to use
- nthreads_per_process = 1
-
-# 1. Run NSVE for the three resolutions.
- for factor in [1, 2, 4]:
- # create dns object
- cc = DNS()
- # launch simulation
- cc.launch([
- 'NSVE',
- '-n', '{0}'.format(factor*32),
- '--np', '{0}'.format(nprocesses),
- '--ntpp', '{0}'.format(nthreads_per_process),
- '--src-simname', 'base',
- '--src-iteration', '{0}'.format(base_niterations),
- '--simname', 'nsve_{0}x'.format(factor),
- '--precision', 'double',
- '--dtfactor', '{0}'.format(0.3 / factor),
- '--kMeta', '{0}'.format(factor*1.0),
- '--niter_todo', '{0}'.format(test_niterations*factor),
- '--niter_out', '{0}'.format(test_niterations*factor),
- '--niter_stat', '{0}'.format(4*factor)])
-
-# 2. Run NSE for the three resolutions.
- for factor in [1, 2, 4]:
- # create dns object
- cc = DNS()
- # launch simulation
- cc.launch([
- 'NSE',
- '-n', '{0}'.format(factor*32),
- '--np', '{0}'.format(nprocesses),
- '--ntpp', '{0}'.format(nthreads_per_process),
- '--src-simname', 'base',
- '--src-iteration', '{0}'.format(base_niterations),
- '--simname', 'nse_{0}x'.format(factor),
- '--precision', 'double',
- '--dtfactor', '{0}'.format(0.3 / factor),
- '--kMeta', '{0}'.format(factor*1.0),
- '--niter_todo', '{0}'.format(test_niterations*factor),
- '--niter_out', '{0}'.format(test_niterations*factor),
- '--niter_stat', '{0}'.format(4*factor)])
- return None
-
-def plot_error_field():
- c0_list = [DNS(simname = 'nsve_{0}x'.format(factor))
- for factor in [1, 2, 4]]
- c1_list = [DNS(simname = 'nse_{0}x'.format(factor))
- for factor in [1, 2, 4]]
- for cc in c0_list + c1_list:
- cc.compute_statistics()
-
- factor_list = [1, 2, 4]
-
- error_list = []
- for ii in range(len(factor_list)):
- factor = factor_list[ii]
- c0 = c0_list[ii]
- c1 = c1_list[ii]
- df0 = h5py.File(c0.get_checkpoint_fname(iteration = test_niterations*factor), 'r')
- df1 = h5py.File(c1.get_checkpoint_fname(iteration = test_niterations*factor), 'r')
- vel0 = get_velocity(c0, iteration = test_niterations*factor)
- vel1 = get_velocity(c1, iteration = test_niterations*factor)
- diff = vel1 - vel0
- vv = np.sqrt(np.sum(vel0**2, axis = 3))
- dd = np.sqrt(np.sum(diff**2, axis = 3))
- err = np.mean(dd / vv)
- error_list.append(err)
- print('maximum error for factor {0} is {1}'.format(
- factor, np.max(dd / vv)))
- df0.close()
- df1.close()
-
- f = plt.figure(figsize = (4, 4))
- a = f.add_subplot(111)
- fl = np.array(factor_list).astype(np.float)
- a.plot(fl,
- error_list,
- marker = '.',
- label = 'NSVE vs NSE')
- a.plot(fl, 1e-2 * fl**(-1),
- dashes = (1, 1),
- color = 'black',
- label = '$\propto f^{-1}$')
- a.plot(fl, 1e-2 * fl**(-2),
- dashes = (2, 2),
- color = 'black',
- label = '$\propto f^{-2}$')
- a.plot(fl, 1e-2 * fl**(-3),
- dashes = (3, 3),
- color = 'black',
- label = '$\propto f^{-3}$')
- a.set_ylabel('relative error')
- a.set_xlabel('resolution factor $f$')
- a.set_xscale('log')
- a.set_yscale('log')
- a.legend(loc = 'best')
- f.tight_layout()
- f.savefig('err_vs_dt_field.pdf')
- f.savefig('err_vs_dt_field.svg')
- plt.close(f)
- return None
-
-def get_velocity(
- cc,
- iteration = 0):
- data_file = h5py.File(
- cc.get_checkpoint_fname(iteration = iteration),
- 'r')
- if 'velocity' in data_file.keys():
- if 'real' in data_file['velocity'].keys():
- vel = data_file['velocity/real/{0}'.format(iteration)][()]
- else:
- cvel = data_file['velocity/complex/{0}'.format(iteration)][()]
- vel = ift(cvel)
- #vel *= cc.parameters['nx']*cc.parameters['ny']*cc.parameters['nz']
- else:
- assert('complex' in data_file['vorticity'].keys())
- cvort = data_file['vorticity/complex/{0}'.format(iteration)][()]
- cvel = compute_curl(cc, cvort, inverse_curl = True)
- vel = ift(cvel)
- data_file.close()
- return vel
-
-def ift(cfield):
- ff = np.fft.irfftn(cfield, axes = (0, 1, 2))
- field = np.transpose(ff, (1, 0, 2, 3)).copy()
- return field
-
-def compute_curl(
- cc,
- cfield,
- inverse_curl = False):
- kx = cc.get_data_file()['kspace/kx'][()]
- ky = cc.get_data_file()['kspace/ky'][()]
- kz = cc.get_data_file()['kspace/kz'][()]
- ff = cfield.copy()
- ff[..., 0] = 1j*(ky[:, None, None]*cfield[..., 2] - kz[None, :, None]*cfield[..., 1])
- ff[..., 1] = 1j*(kz[None, :, None]*cfield[..., 0] - kx[None, None, :]*cfield[..., 2])
- ff[..., 2] = 1j*(kx[None, None, :]*cfield[..., 1] - ky[:, None, None]*cfield[..., 0])
- if inverse_curl:
- k2 = (kx[None, None, :]**2 +
- ky[ :, None, None]**2 +
- kz[None, :, None]**2)
- k2[0, 0, 0] = 1.
- ff /= k2[:, :, :, None]
- return ff
-
def run_simulations_particles():
# change these two values as neded.
# number of MPI processes to use
- nprocesses = 4
+ nprocesses = 8
# number of OpenMP threads per MPI process to use
- nthreads_per_process = 3
+ nthreads_per_process = 1
# 1. Run NSVEparticles for a few iterations, to build up rhs values, consistent
# with the relevant velocity field.
# create dns object
# launch simulation
- factor = 2
+ factor = 1
for neighbours, smoothness in neighbours_smoothness_list:
interp_name = 'I{0}O{1}'.format(2*neighbours+2, 2*smoothness+1)
cc = DNS()
@@ -251,7 +94,7 @@ def run_simulations_particles():
'--simname', 'nsvep_base_' + interp_name,
'--precision', 'double',
'--dtfactor', '{0}'.format(base_particle_dt/4),
- '--kMeta', '{0}'.format(2.0),
+ '--kMeta', '{0}'.format(factor*1.0),
'--niter_todo', '{0}'.format(20),
'--niter_out', '{0}'.format(1),
'--niter_stat', '{0}'.format(1),
@@ -259,7 +102,7 @@ def run_simulations_particles():
'--niter_part', '{0}'.format(1),
'--tracers0_neighbours', '{0}'.format(neighbours),
'--tracers0_smoothness', '{0}'.format(smoothness),
- '--tracers0_integration_steps', '5',
+ '--tracers0_integration_steps', '4',
'--cpp_random_particles', '{0}'.format(particle_random_seed)])
# 2. Prepare initial conditions
@@ -281,9 +124,9 @@ def run_simulations_particles():
'nsvep_base_{0}_checkpoint_0.h5'.format(interp_name), 'r')
rhs = source_file['tracers0/rhs/16'][()]
for tt in range(1, rhs.shape[0]):
- ii = 16 - tt*factor + 1
- print(factor, tt, ii)
- rhs[tt] = source_file['tracers0/rhs/{0}'.format(16 - tt*factor + 1)][1]
+ ii = 16 - tt*4//factor + 1
+ #print(factor, tt, ii)
+ rhs[tt] = source_file['tracers0/rhs/{0}'.format(16 - tt*4//factor + 1)][1]
df['tracers0/rhs/{0}'.format(8*factor)] = rhs
df.close()
@@ -296,31 +139,42 @@ def run_simulations_particles():
# We do this to emphasize the one-to-one correspondence between
# neighbours and kernel size, and smoothness and order of polynomial.
for neighbours, smoothness in neighbours_smoothness_list:
+ interp_name = 'I{0}O{1}'.format(2*neighbours+2, 2*smoothness+1)
+ source_file = h5py.File('nsvep_base_{0}.h5'.format(interp_name), 'r')
# create dns object
cc = DNS()
# launch simulation
cc.launch([
'NSVEparticles',
- '-n', '{0}'.format(64),
+ '-n', '{0}'.format(source_file['parameters/nx'][()]),
'--np', '{0}'.format(nprocesses),
'--ntpp', '{0}'.format(nthreads_per_process),
- '--simname', 'nsvep_{0}x_I{1}O{2}'.format(
- factor,
- 2*neighbours+2,
- 2*smoothness+1),
+ '--simname', 'nsvep_{0}x_{1}'.format(factor, interp_name),
'--precision', 'double',
'--dtfactor', '{0}'.format(base_particle_dt/factor),
- '--kMeta', '{0}'.format(2.0),
'--niter_todo', '{0}'.format(test_niterations_particles*factor+8*factor),
'--niter_out', '{0}'.format(test_niterations_particles*factor+8*factor),
- '--niter_stat', '{0}'.format(4*factor),
+ '--niter_stat', '{0}'.format(1),
+ ## ensure fluid physics is the same
+ '--dealias_type', '{0}'.format(source_file['parameters/dealias_type'][()]),
+ '--energy', '{0}'.format(source_file['parameters/energy'][()]),
+ '--famplitude', '{0}'.format(source_file['parameters/famplitude'][()]),
+ '--fk0', '{0}'.format(source_file['parameters/fk0'][()]),
+ '--fk1', '{0}'.format(source_file['parameters/fk1'][()]),
+ '--fmode', '{0}'.format(source_file['parameters/fmode'][()]),
+ '--friction_coefficient', '{0}'.format(source_file['parameters/friction_coefficient'][()]),
+ '--injection_rate', '{0}'.format(source_file['parameters/injection_rate'][()]),
+ '--nu', '{0}'.format(source_file['parameters/nu'][()]),
+ '--forcing_type', '{0}'.format(str(source_file['parameters/forcing_type'][()], 'ascii')),
+ ## particle params
'--nparticles', '{0}'.format(nparticles),
- '--niter_part', '{0}'.format(2*factor),
+ '--niter_part', '{0}'.format(1),
'--tracers0_neighbours', '{0}'.format(neighbours),
'--tracers0_smoothness', '{0}'.format(smoothness),
- '--tracers0_integration_steps', '5',
+ '--tracers0_integration_steps', '4',
'--cpp_random_particles', '0'], # turn off cpp particle initialization
iter0 = 8*factor)
+ source_file.close()
return None
def plot_error_particles():
@@ -355,34 +209,25 @@ def plot_error_particles():
err_mean_list = np.array(err_mean_list)
a.plot(factor_list, err_max_list, marker = '.', label = 'max error ' + interp_name)
a.plot(factor_list, err_mean_list, marker = '.', label = 'mean error ' + interp_name)
- a.plot(factor_list,
- (3e-5)*factor_list**(-2),
- color = 'black',
- dashes = (2, 2),
- label = '$\propto f^{-2}$')
- a.plot(factor_list,
- (3e-5)*factor_list**(-3),
- color = 'black',
- dashes = (3, 3),
- label = '$\propto f^{-3}$')
- a.plot(factor_list,
- (3e-6)*factor_list**(-4),
- color = 'black',
- dashes = (4, 4),
- label = '$\propto f^{-4}$')
+ for ee in [2, 3, 4]:
+ a.plot(factor_list,
+ (1e-4)*factor_list**(-ee),
+ color = 'black',
+ dashes = (ee, ee),
+ label = '$\propto f^{{-{0}}}$'.format(ee))
a.set_xscale('log')
a.set_yscale('log')
a.set_xlabel('resolution factor f')
a.set_ylabel('absolute trajectory error [DNS units]')
- a.legend(loc = 'best')
+ a.legend(loc = 'best', fontsize = 7)
f.tight_layout()
f.savefig('err_vs_dt_particle.pdf')
- f.savefig('err_vs_dt_particle.png')
f.savefig('err_vs_dt_particle.svg')
plt.close(f)
return None
def plot_traj_particles():
+ ###########################################################################
f = plt.figure()
a = f.add_subplot(111)
for neighbours, smoothness in neighbours_smoothness_list:
@@ -399,21 +244,73 @@ def plot_traj_particles():
dashes = (4/factor, 3, 4/factor),
alpha = 0.2)
#a.plot(xx[:, 0], xx[:, 1], dashes = (4/factor, 3, 4/factor), alpha = 0.2)
- a.legend(loc = 'best')
+ a.legend(loc = 'best', fontsize = 7)
a.set_xlabel('$x$ [code units]')
a.set_ylabel('$y$ [code units]')
f.tight_layout()
f.savefig('trajectories.pdf')
f.savefig('trajectories.svg')
plt.close(f)
+ ###########################################################################
+ ###########################################################################
+ traj_index = 3
+ for neighbours, smoothness in neighbours_smoothness_list:
+ interp_name = 'I{0}O{1}'.format(2*neighbours+2, 2*smoothness+1)
+ cc = DNS(simname = 'nsvep_base_' + interp_name)
+ cc.compute_statistics()
+ xx_base = read_trajectory(cc, traj_index, iter0 = 0, dset_name = 'velocity')
+ iter0 = 16
+ tt_base = np.array(range(iter0, iter0 + xx_base.shape[0]))*cc.parameters['dt']
+ f = plt.figure()
+ ax_counter = 1
+ for factor in [1, 2, 4]:
+ a = f.add_subplot(310 + ax_counter)
+ ax_counter += 1
+ a.plot(tt_base,
+ xx_base[:, 2],
+ label = 'base_' + interp_name,
+ marker = '+',
+ linewidth = 0.5,
+ alpha = 0.2)
+ cc = DNS(simname = 'nsvep_{0}x_'.format(factor) + interp_name)
+ cc.compute_statistics(iter0 = 8*factor)
+ xx = read_trajectory(cc, traj_index, iter0 = 8*factor, dset_name = 'velocity')
+ tt = np.array(range(8*factor, xx.shape[0]+8*factor))*cc.parameters['dt']
+ a.plot(tt,
+ xx[:, 2],
+ label = interp_name + '$f = {0}$'.format(factor),
+ marker = 'x',
+ dashes = (4/factor, 3, 4/factor),
+ alpha = 0.2)
+ df = h5py.File(cc.simname + '_checkpoint_0.h5', 'r')
+ xx = df['tracers0/rhs/{0}'.format(8*factor)][()]
+ for rhs_index in [1, 2, 3]:
+ a.scatter((8*factor - rhs_index)*cc.parameters['dt'],
+ xx[rhs_index, traj_index, 2],
+ marker = '*',
+ zorder = -10,
+ alpha = 0.5,
+ color = 'black')
+ df.close()
+ a.legend(loc = 'best', fontsize = 7)
+ a.set_xlabel('$t$ [code units]')
+ a.set_ylabel('$v_y$ [code units]')
+ f.tight_layout()
+ f.savefig('velocities_{0}.pdf'.format(interp_name))
+ plt.close(f)
+ ###########################################################################
return None
-def read_trajectory(cc, traj_index, iter0):
+def read_trajectory(
+ cc,
+ traj_index,
+ iter0,
+ dset_name = 'position'):
cc.parameters['niter_part'] = cc.get_data_file()['parameters/niter_part'][()]
df = cc.get_particle_file()
xx = []
for ii in range(iter0, cc.get_data_file()['iteration'][()]+1, cc.parameters['niter_part']):
- xx.append(df['tracers0/position/{0}'.format(ii)][traj_index])
+ xx.append(df['tracers0/' + dset_name + '/{0}'.format(ii)][traj_index])
df.close()
return np.array(xx)
--
GitLab
From 8017d1d3800446593c7297375d5529fd6852d625 Mon Sep 17 00:00:00 2001
From: Cristian C Lalescu <Cristian.Lalescu@mpcdf.mpg.de>
Date: Thu, 20 Jan 2022 10:03:50 +0100
Subject: [PATCH 21/24] [wip] updates convergence text
---
TurTLE/DNS.py | 9 +-
TurTLE/PP.py | 9 +-
TurTLE/tools.py | 7 +-
documentation/index.rst | 2 +
documentation/sphinx_static/bibliography.rst | 21 +
documentation/sphinx_static/convergence.rst | 616 ++----------------
.../sphinx_static/convergence_fields.rst | 281 ++++++++
.../sphinx_static/convergence_particles.rst | 294 +++++++++
.../sphinx_static/err_vs_dt_field.svg | 442 +++++++++----
.../sphinx_static/err_vs_dt_particle.svg | 524 ++++++++++-----
examples/convergence/fields_temporal.py | 6 +-
examples/convergence/particles_temporal.py | 23 +-
12 files changed, 1355 insertions(+), 879 deletions(-)
create mode 100644 documentation/sphinx_static/bibliography.rst
create mode 100644 documentation/sphinx_static/convergence_fields.rst
create mode 100644 documentation/sphinx_static/convergence_particles.rst
diff --git a/TurTLE/DNS.py b/TurTLE/DNS.py
index 99962bf5..d2f7dba6 100644
--- a/TurTLE/DNS.py
+++ b/TurTLE/DNS.py
@@ -387,7 +387,7 @@ class DNS(_code):
Further computation of statistics based on the contents of
``simname_cache.h5``.
Standard quantities are as follows
- (consistent with [Ishihara]_):
+ (consistent with [ishihara2007jfm]_):
.. math::
@@ -403,13 +403,6 @@ class DNS(_code):
Re = \\frac{U_{\\textrm{int}} L_{\\textrm{int}}}{\\nu}, \\hskip
.5cm
R_{\\lambda} = \\frac{U_{\\textrm{int}} \\lambda}{\\nu}
-
- .. [Ishihara] T. Ishihara et al,
- *Small-scale statistics in high-resolution direct numerical
- simulation of turbulence: Reynolds number dependence of
- one-point velocity gradient statistics*.
- J. Fluid Mech.,
- **592**, 335-366, 2007
"""
self.statistics['Uint(t)'] = np.sqrt(2*self.statistics['energy(t)'] / 3)
for key in ['energy',
diff --git a/TurTLE/PP.py b/TurTLE/PP.py
index 4703d26a..4699b52d 100644
--- a/TurTLE/PP.py
+++ b/TurTLE/PP.py
@@ -238,7 +238,7 @@ class PP(_code):
Further computation of statistics based on the contents of
``simname_postprocess.h5``.
Standard quantities are as follows
- (consistent with [Ishihara]_):
+ (consistent with [ishihara2007jfm]_):
.. math::
@@ -254,13 +254,6 @@ class PP(_code):
Re = \\frac{U_{\\textrm{int}} L_{\\textrm{int}}}{\\nu}, \\hskip
.5cm
R_{\\lambda} = \\frac{U_{\\textrm{int}} \\lambda}{\\nu}
-
- .. [Ishihara] T. Ishihara et al,
- *Small-scale statistics in high-resolution direct numerical
- simulation of turbulence: Reynolds number dependence of
- one-point velocity gradient statistics*.
- J. Fluid Mech.,
- **592**, 335-366, 2007
"""
for key in ['energy', 'enstrophy']:
self.statistics[key + '(t)'] = (self.statistics['dk'] *
diff --git a/TurTLE/tools.py b/TurTLE/tools.py
index 7ddbf32d..6d386985 100644
--- a/TurTLE/tools.py
+++ b/TurTLE/tools.py
@@ -230,13 +230,8 @@ def get_fornberg_coeffs(
"""compute finite difference coefficients
Compute finite difference coefficients for a generic grid specified
- by ``x``, according to [Fornberg]_.
+ by ``x``, according to [fornberg1988mc]_.
The function is used by :func:`particle_finite_diff_test`.
-
- .. [Fornberg] B. Fornberg,
- *Generation of Finite Difference Formulas on Arbitrarily Spaced Grids*.
- Mathematics of Computation,
- **51:184**, 699-706, 1988
"""
N = len(a) - 1
d = []
diff --git a/documentation/index.rst b/documentation/index.rst
index 62a336f0..7788a2f2 100644
--- a/documentation/index.rst
+++ b/documentation/index.rst
@@ -20,6 +20,8 @@ Contents:
sphinx_static/convergence
+ sphinx_static/bibliography
+
Indices and tables
==================
diff --git a/documentation/sphinx_static/bibliography.rst b/documentation/sphinx_static/bibliography.rst
new file mode 100644
index 00000000..1b90b082
--- /dev/null
+++ b/documentation/sphinx_static/bibliography.rst
@@ -0,0 +1,21 @@
+Bibliography
+============
+
+.. [fornberg1988mc] B. Fornberg,
+ *Generation of Finite Difference Formulas on Arbitrarily Spaced Grids*.
+ Mathematics of Computation,
+ **51:184**, 699-706, 1988
+
+.. [ishihara2007jfm] T. Ishihara et al,
+ *Small-scale statistics in high-resolution direct numerical
+ simulation of turbulence: Reynolds number dependence of
+ one-point velocity gradient statistics*.
+ J. Fluid Mech.,
+ **592**, 335-366, 2007
+
+.. [lalescu2010jcp] C. C. Lalescu, B. Teaca and D. Carati
+ *Implementation of high order spline interpolations for tracking test
+ particles in discretized fields*.
+ J. Comput. Phys.
+ **229**, 5862-5869, 2010
+
diff --git a/documentation/sphinx_static/convergence.rst b/documentation/sphinx_static/convergence.rst
index f0c296c7..4c05215f 100644
--- a/documentation/sphinx_static/convergence.rst
+++ b/documentation/sphinx_static/convergence.rst
@@ -10,592 +10,88 @@ implementations.
Navier-Stokes solution
----------------------
-Since TurTLE contains solvers of the Navier Stokes equations in both
-velocity ("NSE") and vorticity formulation ("NSVE"), this allows for a direct
-convergence test: one should use both solvers with identical parameters, and
-compare solutions as the resolution is varied.
-
-Notes:
-
- * we are discussing a partial differential equation, therefore
- when we test for convergence we will increase both spatial and
- temporal resolution.
-
- * we will test convergence properties for a "statistically
- stationary initial condition", since the smoothness properties of
- the field will influence convergence properties in general.
-
-In practice, we compute numerical solutions of NSE and NSVE, convert the
-vorticity of the latter simulation to a velocity field, and compare
-them.
-The time-stepping method is the same 3rd order Runge Kutta algorithm,
-therefore we expect a third order dependency of the "error" on the
-time-step.
-The "spatial discretization" is identical in both cases, since we use
-the same underlying pseudo-spectral framework (including the dealiasing
+TurTLE implements two distinct solvers of the Navier-Stokes equations:
+one for their vorticity formulation, and one for the more common velocity
+formulation.
+While there are inescapable differences in the two implementations, they
+both use the same time-stepping algorithm (a 3rd order RungeKutta
method).
-The observed numerical differences are due to the simulation of technically
-different PDEs: different arithmetical operations are performed despite
-the fact that "NSVE is simply the curl of NSE".
-In turn, the effects of finite numerical precision and discretization
-are brought into the computation differently, leading to systematic
-deviations between the two DNS.
+We test convergence properties for a "statistically stationary initial
+condition", since the smoothness properties of the field will influence
+convergence properties in general.
+As an example of the variety of questions that we can address with
+TurTLE, we also perform a direct comparison of the NSVE (vorticity
+solver) and NSE (velocity solver) results.
+
+A basic Python script that performs this convergence test is provided
+under `examples/convergence/fields_temporal.py`, and it is discussed
+below.
+In brief, simulations are performed using the same initial conditions,
+but different time steps.
+Error estimates are computed as differences between the different
+solutions.
+The figure shows the L2 norm of these differences, normalized by
+the root-mean-squared velocity magnitude.
+Note that the actual value of this "relative error" is irrelevant
+(it depends on total integration time, spatial resolution, etc), but the
+plot shows that (1) solutions converge with the 3rd order of the
+timestep and (2) the systematic difference between NSE and NSVE behaves
+quite differently from the two individual error estimates.
+.. image:: err_vs_dt_field.svg
Particle tracking errors
------------------------
-For particle tracking, we use an alternative approach: use the same
-algorithm, and compare results obtained with different resolutions.
-Since we are discussing the numerical solution of an ODE where the right
-hand side is itself a numerical solution from a PDE, we in fact modify
-the resolution of the field PDE (i.e. spatial resolution as well).
-
There is a more complex mechanism that generates numerical errors for
particle tracking in this setting.
In particular, the accuracy of the field itself is relevant, as well as
the accuracy of the interpolation method coupled to the ODE solver.
For instance the default particle tracking solver is a 4th order
-Adams Bashforth method in TurTLE, which seems unnecessary since the
+Adams Bashforth method in TurTLE, which seems at first unnecessary since the
fluid only provides a 3rd order solution.
The default interpolation method is that of cubic splines, which should
-in fact limit ODE error convergence to 2nd order (because convergence
+in principle limit ODE error convergence to 2nd order (because convergence
relies on existence of relevant Taylor expansion terms, and interpolated
fields only have a finite number of continuous derivatives).
This discussion is briefly continued below, but we will not do it justice
in this tutorial.
-
-Python code
------------
-
-We present here a Python script that performs simple convergence tests
-with TurTLE. The script itself is provided as the file
-`examples/convergence.py`.
-
-The preamble imports standard packages, as well as TurTLE itself:
-
-.. code:: python
-
- import numpy as np
- import h5py
- import matplotlib.pyplot as plt
-
- import TurTLE
- from TurTLE import DNS, PP
-
-As explained above, we should test convergence for a statistically
-stationary regime.
-The base simulation will use a real-space grid of :math:`32 \times 32 \times 32` points,
-and experience shows that quasistationarity is reached for this
-problem-size in a few hundred iterations (here `base_niterations`).
-For the convergence test itself, we use a relatively small number
-of iterations (i.e. `test_niterations`), otherwise deterministic chaos will dominate the
-difference between alternative solutions (rather than numerical integration
-errors).
-
-.. code:: python
-
- base_niterations = 256
- test_niterations = 32
-
-We consider :math:`10^5` particles, and we also choose a specific random
-seed for their initial locations.
-
-.. code:: python
-
- nparticles = 100000
- particle_random_seed = 15
-
-We distinguish a few steps of this script.
-First, we generate the statistically quasistationary regime.
-Second, we run the fluid solver and analyze the results.
-Finally, we run the particle simulations and also analyze these results.
-"Analysis" refers here to simple error plots, but more elaborate
-postprocessing can be performed if needed.
-
-.. code:: python
-
- def main():
- generate_initial_conditions()
-
- run_simulations_field()
- plot_error_field()
-
- run_simulations_particles()
- plot_error_particles()
- return None
-
-`generate_initial_conditions` performs a few calls to C++ executable
-codes generated with TurTLE. In brief, it
-
- * generates a velocity field in a quasistationary Navier-Stokes
- regime (using the NSVE solver).
- * uses Fourier interpolation to double and quadruple the initial
- resolution, yielding 3 vorticity fields "1x", "2x" and "4x".
- * generates the corresponding velocity fields needed for the NSE solver
-
-We use the `launch` method of the `DNS` and `PP` Python
-classes --- the wrappers around the C++ `direct_numerical_simulation`
-and `postprocess` functionality.
-This means that the current Python code may be translated to a shell
-script directly, only by writing out the arguments (rather than placing
-them in a list of Python strings).
-The full function is given below:
-
-.. code:: python
-
- def generate_initial_conditions():
- # change these two values as neded.
- # number of MPI processes to use
- nprocesses = 4
- # number of OpenMP threads per MPI process to use
- nthreads_per_process = 2
-
- # 1. Generate quasistationary state to use for initial conditions.
- # create a dns object
- c0 = DNS()
- # launch the simulation
- c0.launch([
- 'NSVE',
- '-n', '32',
- '--np', '{0}'.format(nprocesses),
- '--ntpp', '{0}'.format(nthreads_per_process),
- '--precision', 'double',
- '--src-simname', 'B32p1e4',
- '--src-wd', TurTLE.data_dir,
- '--src-iteration', '0',
- '--simname', 'base_1x',
- '--niter_todo', '{0}'.format(base_niterations),
- '--niter_out', '{0}'.format(base_niterations),
- '--overwrite-src-parameters',
- '--kMeta', '1.0',
- '--niter_stat', '16',
- '--checkpoints_per_file', '{0}'.format(16)])
-
- # 2. Generate initial conditions for NSVE runs at 2x and 4x the
- # base resolution.
- for factor in [2, 4]:
- # create postprocess object
- cc = PP()
- # create a larger version of the field at final iteration
- cc.launch([
- 'resize',
- '--np', '{0}'.format(nprocesses),
- '--ntpp', '{0}'.format(nthreads_per_process),
- '--simname', 'base_1x',
- '--precision', 'double',
- '--iter0', '{0}'.format(base_niterations),
- '--iter1', '{0}'.format(base_niterations),
- '--new_nx', '{0}'.format(factor*32),
- '--new_ny', '{0}'.format(factor*32),
- '--new_nz', '{0}'.format(factor*32),
- '--new_simname', 'base_{0}x'.format(factor)])
- # update "checkpoint" file, so we can use "base__x" as "src-simname"
- # this is needed after "resize"
- f1 = h5py.File('base_{0}x_checkpoint_0.h5'.format(factor), 'a')
- f1['vorticity/complex/{0}'.format(base_niterations)] = h5py.ExternalLink(
- 'base_{0}x_fields.h5'.format(factor),
- 'vorticity/complex/{0}'.format(base_niterations))
- f1.close()
-
- # 3. Generate initial conditions for NSE runs at 1x, 2x and 4x the
- # base resolution.
- for factor in [1, 2, 4]:
- # create postprocess object
- cc = PP()
- # compute velocity field at last iteration
- cc.launch([
- 'get_velocity',
- '--np', '{0}'.format(nprocesses),
- '--ntpp', '{0}'.format(nthreads_per_process),
- '--simname', 'base_{0}x'.format(factor),
- '--precision', 'double',
- '--iter0', '{0}'.format(base_niterations),
- '--iter1', '{0}'.format(base_niterations)])
- # we don't need to update "checkpoint" file after "get_velocity"
- return None
-
-`run_simulations_field` runs six DNS (3 resolutions for each of NSE and
-NSVE solvers):
-
-
-.. code:: python
-
- def run_simulations_field():
- # change these two values as neded.
- # number of MPI processes to use
- nprocesses = 4
- # number of OpenMP threads per MPI process to use
- nthreads_per_process = 2
-
- # 1. Run NSVE for the three resolutions.
- for factor in [1, 2, 4]:
- # create dns object
- cc = DNS()
- # launch simulation
- cc.launch([
- 'NSVE',
- '-n', '{0}'.format(factor*32),
- '--np', '{0}'.format(nprocesses),
- '--ntpp', '{0}'.format(nthreads_per_process),
- '--src-simname', 'base_{0}x'.format(factor),
- '--src-iteration', '{0}'.format(base_niterations),
- '--simname', 'nsve_{0}x'.format(factor),
- '--precision', 'double',
- '--dtfactor', '0.3',
- '--kMeta', '{0}'.format(1.0*factor),
- '--niter_todo', '{0}'.format(test_niterations*factor),
- '--niter_out', '{0}'.format(test_niterations*factor),
- '--niter_stat', '{0}'.format(4*factor)])
-
- # 2. Run NSE for the three resolutions.
- for factor in [1, 2, 4]:
- # create dns object
- cc = DNS()
- # launch simulation
- cc.launch([
- 'NSE',
- '-n', '{0}'.format(factor*32),
- '--np', '{0}'.format(nprocesses),
- '--ntpp', '{0}'.format(nthreads_per_process),
- '--src-simname', 'base_{0}x'.format(factor),
- '--src-iteration', '{0}'.format(base_niterations),
- '--simname', 'nse_{0}x'.format(factor),
- '--precision', 'double',
- '--dtfactor', '0.3',
- '--kMeta', '{0}'.format(1.0*factor),
- '--niter_todo', '{0}'.format(test_niterations*factor),
- '--niter_out', '{0}'.format(test_niterations*factor),
- '--niter_stat', '{0}'.format(4*factor)])
- return None
-
-Once the runs are finished successfully, the code calls
-`plot_error_field`.
-Here we first read the output of the six different runs, and we compute
-their statistics, since the call to `compute_statistics` will in fact also
-perform some sanity checks on the output.
-We then read the velocity fields computed by `NSVE` and `NSE`, and
-compare them (please see the code for `get_velocity` below).
-The results are plotted together with a 3rd order error estimate, for
-subsequent assessment.
-
-.. code:: python
-
- def plot_error_field():
- c0_list = [DNS(simname = 'nsve_{0}x'.format(factor))
- for factor in [1, 2, 4]]
- c1_list = [DNS(simname = 'nse_{0}x'.format(factor))
- for factor in [1, 2, 4]]
- for cc in c0_list + c1_list:
- cc.compute_statistics()
-
- factor_list = [1, 2, 4]
-
- error_list = []
- for ii in range(len(factor_list)):
- factor = factor_list[ii]
- c0 = c0_list[ii]
- c1 = c1_list[ii]
- df0 = h5py.File(c0.get_checkpoint_fname(iteration = test_niterations*factor), 'r')
- df1 = h5py.File(c1.get_checkpoint_fname(iteration = test_niterations*factor), 'r')
- vel0 = get_velocity(c0, iteration = test_niterations*factor)
- vel1 = get_velocity(c1, iteration = test_niterations*factor)
- diff = vel1 - vel0
- vv = np.sqrt(np.sum(vel0**2, axis = 3))
- dd = np.sqrt(np.sum(diff**2, axis = 3))
- err = np.max(dd / vv)
- error_list.append(err)
- print('maximum error for factor {0} is {1}'.format(
- factor, err))
- df0.close()
- df1.close()
-
- f = plt.figure(figsize = (4, 4))
- a = f.add_subplot(111)
- fl = np.array(factor_list).astype(np.float)
- a.plot(fl,
- error_list,
- marker = '.',
- label = 'NSVE vs NSE')
- a.plot(fl, fl**(-3),
- dashes = (1, 1),
- color = 'black',
- label = '$\propto f^{-3}$')
- a.set_ylabel('relative error')
- a.set_xlabel('resolution factor $f$')
- a.set_xscale('log')
- a.set_yscale('log')
- a.legend(loc = 'best')
- f.tight_layout()
- f.savefig('field_err_vs_dt.pdf')
- f.savefig('field_err_vs_dt.png')
- plt.close(f)
- return None
-
-.. image:: err_vs_dt_field.svg
-
-In the plot, the error for :math:`f = 4` is larger than expected because
-the effects of finite precision arithmetic begin to dominate systematic
-integration errors.
-In practice there are a number of other technical details to consider
-when using resolutions corresponding to :math:`f = 4` (here this means
-:math:`k_M \eta \approx 4`), all of them out of scope for this tutorial.
-
-The `get_velocity` function is slightly more elaborate, as it needs to
-check whether the data comes from an `NSVE` run or an `NSE` run.
-Furthermore, in the case of an `NSVE` run we need to explicitly invert
-the curl operator within the Python code in order to obtain the
-velocity.
-Otherwise, we perform an inverse FFT using `numpy`, taking care to
-account for the transposed data layout (which itself is due to the use
-of FFTW).
-
-.. code:: python
-
- def get_velocity(
- cc,
- iteration = 0):
- data_file = h5py.File(
- cc.get_checkpoint_fname(iteration = iteration),
- 'r')
- if 'velocity' in data_file.keys():
- if 'real' in data_file['velocity'].keys():
- vel = data_file['velocity/real/{0}'.format(iteration)][()]
- else:
- cvel = data_file['velocity/complex/{0}'.format(iteration)][()]
- vel = ift(cvel)
- #vel *= cc.parameters['nx']*cc.parameters['ny']*cc.parameters['nz']
- else:
- assert('complex' in data_file['vorticity'].keys())
- cvort = data_file['vorticity/complex/{0}'.format(iteration)][()]
- cvel = compute_curl(cc, cvort, inverse_curl = True)
- vel = ift(cvel)
- data_file.close()
- return vel
-
- def ift(cfield):
- ff = np.fft.irfftn(cfield, axes = (0, 1, 2))
- field = np.transpose(ff, (1, 0, 2, 3)).copy()
- return field
-
- def compute_curl(
- cc,
- cfield,
- inverse_curl = False):
- kx = cc.get_data_file()['kspace/kx'][()]
- ky = cc.get_data_file()['kspace/ky'][()]
- kz = cc.get_data_file()['kspace/kz'][()]
- ff = cfield.copy()
- ff[..., 0] = 1j*(ky[:, None, None]*cfield[..., 2] - kz[None, :, None]*cfield[..., 1])
- ff[..., 1] = 1j*(kz[None, :, None]*cfield[..., 0] - kx[None, None, :]*cfield[..., 2])
- ff[..., 2] = 1j*(kx[None, None, :]*cfield[..., 1] - ky[:, None, None]*cfield[..., 0])
- if inverse_curl:
- k2 = (kx[None, None, :]**2 +
- ky[ :, None, None]**2 +
- kz[None, :, None]**2)
- k2[0, 0, 0] = 1.
- ff /= k2[:, :, :, None]
- return ff
-
-We then define the function that runs the particle simulations,
-`run_simulations_particles`.
-Because we use an Adams-Bashforth method, we need to know the values of
-the particle velocity (i.e. the right-hand-side of the ODE) at previous
-steps.
-TurTLE accomplishes this by using the Euler integration scheme for "time
-step 0", then using a 2nd order Adams-Bashforth, etc, until the desired
-number of right-hand-side values is stored.
-Thus the code first integrates trajectories for 8 iterations, and the
-output will contain the additional information.
-This happens because such information is crucial for checkpointing ---
-i.e. stopping/restarting the simulation at arbitrary iterations without
-affecting the numerical solution.
-
-To put it simply, for the simulation "nsvep_base" the dataset
-"tracers0/rhs/0" contains only zeros, and TurTLE ignores them.
-However, the "tracers0/rhs/8" dataset for simulation "nsvep_1x" contains
-meaningful values (that are used because we request that `iter0` is
-different from 0).
-
-.. code:: python
-
- def run_simulations_particles():
- # change these two values as neded.
- # number of MPI processes to use
- nprocesses = 4
- # number of OpenMP threads per MPI process to use
- nthreads_per_process = 2
-
- # 1. Run NSVEparticles for resolution 1x, for a few iterations, to build up rhs values.
- factor = 1
- # create dns object
- cc = DNS()
- # launch simulation
- cc.launch([
- 'NSVEparticles',
- '-n', '{0}'.format(factor*32),
- '--np', '{0}'.format(nprocesses),
- '--ntpp', '{0}'.format(nthreads_per_process),
- '--src-simname', 'base_{0}x'.format(factor),
- '--src-iteration', '{0}'.format(base_niterations),
- '--simname', 'nsvep_base'.format(factor),
- '--precision', 'double',
- '--dtfactor', '0.3',
- '--kMeta', '{0}'.format(1.0*factor),
- '--niter_todo', '{0}'.format(8),
- '--niter_out', '{0}'.format(8),
- '--niter_stat', '{0}'.format(8),
- '--nparticles', '{0}'.format(nparticles),
- '--niter_part', '{0}'.format(8),
- '--cpp_random_particles', '{0}'.format(particle_random_seed)])
-
- # 2. Prepare initial conditions
- for factor in [1, 2, 4]:
- df = h5py.File('nsvep_{0}x_checkpoint_0.h5'.format(factor), 'w')
- # field
- df['vorticity/complex/{0}'.format(8*factor)] = h5py.ExternalLink(
- 'base_{0}x_checkpoint_0.h5'.format(factor),
- 'vorticity/complex/{0}'.format(base_niterations))
- # particles
- df['tracers0/state/{0}'.format(8*factor)] = h5py.ExternalLink(
- 'nsvep_base_checkpoint_0.h5',
- 'tracers0/state/8')
- df['tracers0/rhs/{0}'.format(8*factor)] = h5py.ExternalLink(
- 'nsvep_base_checkpoint_0.h5',
- 'tracers0/rhs/8')
- df.close()
-
- # 3. Run NSVEparticles
- for factor in [1, 2, 4]:
- # create dns object
- cc = DNS()
- # launch simulation
- cc.launch([
- 'NSVEparticles',
- '-n', '{0}'.format(factor*32),
- '--np', '{0}'.format(nprocesses),
- '--ntpp', '{0}'.format(nthreads_per_process),
- '--simname', 'nsvep_{0}x'.format(factor),
- '--precision', 'double',
- '--dtfactor', '0.3',
- '--kMeta', '{0}'.format(1.0*factor),
- '--niter_todo', '{0}'.format(test_niterations*factor),
- '--niter_out', '{0}'.format(test_niterations*factor),
- '--niter_stat', '{0}'.format(4*factor),
- '--nparticles', '{0}'.format(nparticles),
- '--niter_part', '{0}'.format(2*factor),
- '--cpp_random_particles', '0'], # turn off cpp particle initialization
- iter0 = 8*factor)
- return None
-
-To compute the trajectory integration error, we proceed as explained
-above, and compare each DNS with its corresponding double-the-resolution DNS:
-
-.. code:: python
-
- def plot_error_particles():
- f = plt.figure()
- a = f.add_subplot(111)
- err_max_list = []
- err_mean_list = []
- factor_list = [1, 2]
- for factor in factor_list:
- c1 = DNS(simname = 'nsvep_{0}x'.format(factor))
- c2 = DNS(simname = 'nsvep_{0}x'.format(factor*2))
- for cc in [c1, c2]:
- cc.parameters['niter_part'] = cc.get_data_file()['parameters/niter_part'][()]
- c1.compute_statistics(iter0 = 8*factor)
- c2.compute_statistics(iter0 = 8*factor*2)
- final_iter_x1 = c1.get_data_file()['iteration'][()]
- final_iter_x2 = c2.get_data_file()['iteration'][()]
- f1 = h5py.File(c1.simname + '_checkpoint_0.h5', 'r')
- f2 = h5py.File(c2.simname + '_checkpoint_0.h5', 'r')
- x1 = f1['tracers0/state/{0}'.format(final_iter_x1)][()]
- x2 = f2['tracers0/state/{0}'.format(final_iter_x2)][()]
- err_max_list.append(np.max(np.abs(x2 - x1)))
- err_mean_list.append(np.mean(np.abs(x2 - x1)))
- f1.close()
- f2.close()
- factor_list = np.array(factor_list).astype(np.float)
- err_max_list = np.array(err_max_list)
- err_mean_list = np.array(err_mean_list)
- a.plot(factor_list, err_max_list, marker = '.', label = 'max error')
- a.plot(factor_list, err_mean_list, marker = '.', label = 'mean error')
- a.plot(factor_list,
- (1e-2)*factor_list**(-3),
- color = 'black',
- dashes = (2, 2),
- label = '$\propto f^{-3}$')
- a.plot(factor_list,
- (1e-2)*factor_list**(-4),
- color = 'black',
- dashes = (1, 1),
- label = '$\propto f^{-4}$')
- a.set_xscale('log')
- a.set_yscale('log')
- a.set_xlabel('resolution factor f')
- a.set_ylabel('absolute trajectory error [DNS units]')
- a.legend(loc = 'best')
- f.tight_layout()
- f.savefig('err_vs_dt_particle.pdf')
- f.savefig('err_vs_dt_particle.png')
- plt.close(f)
- return None
-
-Note that we plot two error measures: the maximum error, as well as the
-mean error.
+We present below a Python script that performs a particle tracking
+convergence test, provided as
+`examples/convergence/particles_temporal.py`.
+The figure shows trajectory integration errors, in a fairly simple
+setting, for two interpolation methods: cubic splines (I4O3) and 5th
+order splines on a kernel of 8 points (I8O5).
+Furthermore, we show both the maximum and the mean errors for the same
+set of trajectories.
+While both mean errors seem to converge with the 3rd order of the
+timestep (consistent with the error of the velocity field), the maximum
+error obtained for cubic splines converges with the second order ---
+which is the expected behavior for particle tracking in a field that
+only has one continuous derivative.
.. image:: err_vs_dt_particle.svg
-The plot suggests that these converge at different rates: the mean error
-exhibits 4th order convergence in "factor", whereas the maximum error
-seems to converge like :math:`f^{3.5}` (closer to the limit :math:`f^3`
-imposed by the fluid solver error).
-While a more detailed investigation would be in order, I speculate that
-for this particular setup the increase of the spatial resolution along
-with the temporal resolution renders the interpolation errors (which should
-decrease the global order to 2) smaller than the simultaneous temporal
-integration errors.
-In any case the interplay of the different error sources is a fairly
-complex subject in itself, which we don't propose to address here in
-full.
-
-For the beginner's convenience, we also provide a method to plot
-individual particle trajectories:
+The results would merit a longer and more careful analysis outside the
+scope of this particular tutorial, so we limit ourselves to noting that
+(1) different ODEs will have different numerical properties (i.e.
+rotating particles, or inertial particles) and (2) interpolation errors
+may in general grow with the Reynolds number, since interpolation
+errors depend on values of gradients (however the distribution of
+extreme gradient values also changes with Reynolds number, so the
+overall behavior is complex).
-.. code:: python
- def plot_traj_particles():
- f = plt.figure()
- a = f.add_subplot(111)
- for factor in [1, 2, 4]:
- cc = DNS(simname = 'nsvep_{0}x'.format(factor))
- cc.compute_statistics(iter0 = 8*factor)
- xx = read_trajectory(cc, 14, iter0 = 8*factor)
- a.plot(xx[:, 0], xx[:, 1])
- f.tight_layout()
- f.savefig('trajectories.pdf')
- f.savefig('trajectories.png')
- plt.close(f)
- return None
-
- def read_trajectory(cc, traj_index, iter0):
- cc.parameters['niter_part'] = cc.get_data_file()['parameters/niter_part'][()]
- df = cc.get_particle_file()
- xx = []
- for ii in range(iter0, cc.get_data_file()['iteration'][()], cc.parameters['niter_part']):
- xx.append(df['tracers0/position/{0}'.format(ii)][traj_index])
- df.close()
- return np.array(xx)
+Python code for fields
+----------------------
-.. image:: trajectories.svg
+.. include:: convergence_fields.rst
-Finally, the script ends with a standard call to `main`:
-.. code:: python
+Python code for particles
+-------------------------
- if __name__ == '__main__':
- main()
+.. include:: convergence_particles.rst
diff --git a/documentation/sphinx_static/convergence_fields.rst b/documentation/sphinx_static/convergence_fields.rst
new file mode 100644
index 00000000..45b3aa25
--- /dev/null
+++ b/documentation/sphinx_static/convergence_fields.rst
@@ -0,0 +1,281 @@
+We present here a Python script that performs simple convergence tests
+with TurTLE. The script itself is provided as the file
+`examples/convergence/fields_temporal.py`.
+
+The preamble imports standard packages, TurTLE itself, and a few simple
+tools from `examples/convergence/fields_base.py` (not discussed here):
+
+.. code:: python
+
+ import numpy as np
+ import h5py
+ import matplotlib.pyplot as plt
+
+ import TurTLE
+ from TurTLE import DNS, PP
+
+ from fields_base import *
+
+As explained above, we should test convergence for a statistically
+stationary regime.
+The base simulation will use a real-space grid of :math:`128 \times 128 \times 128` points,
+and experience shows that reasonable quasistationarity is reached for this
+problem-size in a few hundred iterations (here `base_niterations`).
+For the convergence test itself, we use a relatively small number
+of iterations (i.e. `test_niterations`), otherwise deterministic chaos will dominate the
+difference between different solutions (rather than numerical integration
+errors).
+
+.. code:: python
+
+ base_niterations = 512
+ test_niterations = 32
+ grid_size = 128
+
+We distinguish between three steps of this script.
+First, we generate the statistically quasistationary regime.
+Second, we run the fluid solver.
+Finally, we "analyze" the results (i.e. we generate simple error plots).
+
+.. code:: python
+
+ def main():
+ generate_initial_conditions()
+
+ run_simulations_field(
+ err_vs_t = False)
+ plot_error_field(
+ err_vs_t = False)
+ return None
+
+The `err_vs_t` parameter may be used if one is interested in looking at
+the difference between the NSE and NSVE solutions as a function of time.
+It turns on a fine-grained output of the fields in
+`run_simulations_field` and it turns on the corresponding plot in
+`plot_error_field`.
+
+`generate_initial_conditions` performs a few calls to C++ executable
+codes generated with TurTLE. In brief, it
+
+ * generates a vorticity field in a quasistationary Navier-Stokes
+ regime (using the NSVE solver).
+ * generates the corresponding velocity field needed for the NSE solver
+
+We use the `launch` method of the `DNS` and `PP` Python
+classes --- the wrappers around the C++ `direct_numerical_simulation`
+and `postprocess` functionality.
+This means that the current Python code may be translated to a shell
+script directly, only by writing out the arguments (rather than placing
+them in a list of Python strings).
+The full function is given below:
+
+.. code:: python
+
+ def generate_initial_conditions():
+ # change these two values as neded.
+ # number of MPI processes to use
+ nprocesses = 8
+ # number of OpenMP threads per MPI process to use
+ nthreads_per_process = 1
+
+ # 1. Generate quasistationary state to use for initial conditions.
+ # create a dns object
+ c0 = DNS()
+ # launch the simulation
+ c0.launch([
+ 'NSVE',
+ '-n', '{0}'.format(grid_size),
+ '--np', '{0}'.format(nprocesses),
+ '--ntpp', '{0}'.format(nthreads_per_process),
+ '--precision', 'double',
+ '--src-simname', 'B32p1e4',
+ '--src-wd', TurTLE.data_dir,
+ '--src-iteration', '0',
+ '--simname', 'base',
+ '--niter_todo', '{0}'.format(base_niterations),
+ '--niter_out', '{0}'.format(base_niterations),
+ '--overwrite-src-parameters',
+ '--kMeta', '1.5',
+ '--fk0', '2',
+ '--fk1', '3',
+ '--niter_stat', '16',
+ '--checkpoints_per_file', '{0}'.format(64)])
+
+ # 3. Generate initial conditions for NSE runs.
+ # create postprocess object
+ cc = PP()
+ # launches code to compute velocity field at last iteration
+ cc.launch([
+ 'get_velocity',
+ '--np', '{0}'.format(nprocesses),
+ '--ntpp', '{0}'.format(nthreads_per_process),
+ '--simname', 'base',
+ '--precision', 'double',
+ '--iter0', '{0}'.format(base_niterations),
+ '--iter1', '{0}'.format(base_niterations)])
+ return None
+
+`run_simulations_field` runs six DNS (3 resolutions for each of NSE and
+NSVE solvers):
+
+.. code:: python
+
+ def run_simulations_field(err_vs_t = False):
+ # change these two values as neded.
+ # number of MPI processes to use
+ nprocesses = 8
+ # number of OpenMP threads per MPI process to use
+ nthreads_per_process = 1
+
+ if err_vs_t:
+ niter_out_factor = 1
+ else:
+ niter_out_factor = test_niterations
+
+ # 1. Run NSVE for the three resolutions.
+ for factor in [1, 2, 4]:
+ # create dns object
+ cc = DNS()
+ # launch simulation
+ cc.launch([
+ 'NSVE',
+ '-n', '{0}'.format(grid_size),
+ '--np', '{0}'.format(nprocesses),
+ '--ntpp', '{0}'.format(nthreads_per_process),
+ '--src-simname', 'base',
+ '--src-iteration', '{0}'.format(base_niterations),
+ '--simname', 'nsve_{0}x'.format(factor),
+ '--precision', 'double',
+ '--dtfactor', '{0}'.format(0.5 / factor),
+ '--niter_todo', '{0}'.format(test_niterations*factor),
+ '--niter_out', '{0}'.format(niter_out_factor*factor),
+ '--niter_stat', '{0}'.format(factor)])
+
+ # 2. Run NSE for the three resolutions.
+ for factor in [1, 2, 4]:
+ # create dns object
+ cc = DNS()
+ # launch simulation
+ cc.launch([
+ 'NSE',
+ '-n', '{0}'.format(grid_size),
+ '--np', '{0}'.format(nprocesses),
+ '--ntpp', '{0}'.format(nthreads_per_process),
+ '--src-simname', 'base',
+ '--src-iteration', '{0}'.format(base_niterations),
+ '--simname', 'nse_{0}x'.format(factor),
+ '--precision', 'double',
+ '--dtfactor', '{0}'.format(0.5 / factor),
+ '--niter_todo', '{0}'.format(test_niterations*factor),
+ '--niter_out', '{0}'.format(niter_out_factor*factor),
+ '--niter_out', '{0}'.format(test_niterations*factor),
+ '--niter_stat', '{0}'.format(factor)])
+ return None
+
+Once the runs are finished successfully, the code calls
+`plot_error_field`.
+Here we first read the output of the six different runs, and we compute
+their statistics, since the call to `compute_statistics` will also
+perform some sanity checks on the output.
+We then compute the error analysis for each of the two solvers, and also
+compare the two solutions.
+The `get_velocity` and `compute_vector_field_distance` methods are defined in
+`examples/convergence/fields_base.py`.
+
+.. code:: python
+
+ def plot_error_field(err_vs_t = False):
+ factor_list = [1, 2, 4]
+ c0_list = [DNS(simname = 'nsve_{0}x'.format(factor))
+ for factor in factor_list]
+ c1_list = [DNS(simname = 'nse_{0}x'.format(factor))
+ for factor in factor_list]
+ cl = [c0_list, c1_list]
+ # sanity checks
+ for cc in c0_list + c1_list:
+ cc.compute_statistics()
+
+ # errors for individual solvers
+ error_list = [[], [], []]
+ for ii in range(len(factor_list)-1):
+ factor = factor_list[ii]
+ for jj in [0, 1]:
+ vel1 = get_velocity(cl[jj][ii ], iteration = test_niterations*factor)
+ vel2 = get_velocity(cl[jj][ii+1], iteration = 2*test_niterations*factor)
+ dd = compute_vector_field_distance(vel1, vel2, figname = cl[jj][ii].simname + '_vs_' + cl[jj][ii+1].simname)
+ error_list[jj].append(dd['L2_rel'])
+
+ # comparisons of two solutions
+ for ii in range(len(factor_list)):
+ factor = factor_list[ii]
+ vel1 = get_velocity(cl[0][ii], iteration = test_niterations*factor)
+ vel2 = get_velocity(cl[1][ii], iteration = test_niterations*factor)
+ dd = compute_vector_field_distance(vel1, vel2)
+ error_list[2].append(dd['L2_rel'])
+
+ f = plt.figure(figsize = (4, 4))
+ a = f.add_subplot(111)
+ a.plot(factor_list[:len(error_list[0])],
+ error_list[0],
+ marker = '.',
+ dashes = (2, 3),
+ label = 'NSVE')
+ a.plot(factor_list[:len(error_list[1])],
+ error_list[1],
+ marker = '.',
+ dashes = (3, 5),
+ label = 'NSE')
+ a.plot(factor_list,
+ error_list[2],
+ marker = '.',
+ label = 'NSVE vs NSE')
+ fl = np.array(factor_list).astype(np.float)
+ for ee in [2, 3]:
+ a.plot(fl[:2], error_list[0][0] * fl[:2]**(-ee),
+ dashes = (ee, ee),
+ color = 'black',
+ label = '$\propto f^{{-{0}}}$'.format(ee),
+ zorder = -ee)
+ a.set_ylabel('relative error')
+ a.set_xlabel('resolution factor $f$')
+ a.set_xscale('log')
+ a.set_yscale('log')
+ a.legend(loc = 'best', fontsize = 6)
+ f.tight_layout()
+ f.savefig('err_vs_dt_field.pdf')
+ f.savefig('err_vs_dt_field.svg')
+ plt.close(f)
+
+ if err_vs_t:
+ t = range(test_niterations+1)
+ err_vs_t = [[], [], []]
+ # comparisons of two solvers
+ for ii in range(len(factor_list)):
+ factor = factor_list[ii]
+ for tt in t:
+ vel1 = get_velocity(cl[0][ii], iteration = tt*factor)
+ vel2 = get_velocity(cl[1][ii], iteration = tt*factor)
+ dd = compute_vector_field_distance(vel1, vel2)
+ err_vs_t[ii].append(dd['L2_rel'])
+ # distance between NSVE and NSE as a function of time
+ f = plt.figure(figsize = (4, 4))
+ a = f.add_subplot(111)
+ a.plot(t, err_vs_t[0], label = 'f = 1')
+ a.plot(t, err_vs_t[1], label = 'f = 2')
+ a.plot(t, err_vs_t[2], label = 'f = 4')
+ a.set_yscale('log')
+ a.legend(loc = 'best', fontsize = 6)
+ f.tight_layout()
+ f.savefig('err_vs_t_field.pdf')
+ f.savefig('err_vs_t_field.svg')
+ plt.close(f)
+ return None
+
+
+Finally, the script ends with a standard call to `main`:
+
+.. code:: python
+
+ if __name__ == '__main__':
+ main()
+
diff --git a/documentation/sphinx_static/convergence_particles.rst b/documentation/sphinx_static/convergence_particles.rst
new file mode 100644
index 00000000..0d4b2418
--- /dev/null
+++ b/documentation/sphinx_static/convergence_particles.rst
@@ -0,0 +1,294 @@
+We present here a Python script that performs a particle tracking
+convergence test with TurTLE, in the current default configuration (a
+`particles_system` object coupled with an NSVE fluid solver).
+
+The preamble imports standard packages, and TurTLE itself:
+
+.. code:: python
+
+ import numpy as np
+ import h5py
+ import matplotlib.pyplot as plt
+
+ import TurTLE
+ from TurTLE import DNS
+
+We then set a few basic parameters, including a list of interpolation
+parameters.
+In brief, the spline interpolations used in TurTLE are parametrized by
+the size :math:`I` of the interpolation kernel and the order :math:`O` of
+the polynomial.
+In this example code we emphasize two equivalences:
+
+* :math:`I = 2 n + 2` where :math:`n` is the number of neighbouring
+ points (in one orientation) required to interpolate the field
+ within one cell.
+* :math:`O = 2 m + 1` where :math:`m` is the order of highest
+ continuous derivative of the interpolating polynomial.
+
+More details on the interpolation method can be found in
+[lalescu2010jcp]_.
+
+.. code:: python
+
+ base_niterations = 256
+
+ nparticles = 1000
+ particle_random_seed = 15
+ base_particle_dt = 0.5
+ test_niterations_particles = 128
+
+ neighbours_smoothness_list = [
+ (1, 1),
+ (3, 2)]
+
+We distinguish between three main parts of this script: generation of
+initial conditions with statistically stationary regime, computation of
+numerical solutions, analysis of results (plot commands):
+
+.. code:: python
+
+ def main():
+ generate_initial_conditions()
+
+ run_simulations_particles()
+
+ plot_error_particles()
+ plot_traj_particles()
+ return None
+
+`generate_initial_conditions` consists of a single launch of an NSVE
+run:
+
+.. code:: python
+
+ def generate_initial_conditions():
+ # change these two values as neded.
+ # number of MPI processes to use
+ nprocesses = 8
+ # number of OpenMP threads per MPI process to use
+ nthreads_per_process = 1
+
+ # 1. Generate quasistationary state to use for initial conditions.
+ # create a dns object
+ c0 = DNS()
+ # launch the simulation
+ c0.launch([
+ 'NSVE',
+ '-n', '32',
+ '--np', '{0}'.format(nprocesses),
+ '--ntpp', '{0}'.format(nthreads_per_process),
+ '--precision', 'double',
+ '--src-simname', 'B32p1e4',
+ '--src-wd', TurTLE.data_dir,
+ '--src-iteration', '0',
+ '--simname', 'base',
+ '--niter_todo', '{0}'.format(base_niterations),
+ '--niter_out', '{0}'.format(base_niterations),
+ '--overwrite-src-parameters',
+ '--kMeta', '1.',
+ '--niter_stat', '16',
+ '--checkpoints_per_file', '{0}'.format(16)])
+ return None
+
+We then define the function that runs the particle simulations,
+`run_simulations_particles`.
+Because we use an Adams-Bashforth method, we need to know the values of
+the particle velocity (i.e. the right-hand-side of the ODE) at previous
+steps.
+TurTLE accomplishes this by using the Euler integration scheme for "time
+step 0", then using a 2nd order Adams-Bashforth, etc, until the desired
+number of right-hand-side values is stored.
+Thus the code first integrates trajectories for 8 iterations, and the
+output will contain the additional information.
+This happens because such information is crucial for checkpointing ---
+i.e. stopping/restarting the simulation at arbitrary iterations without
+affecting the numerical solution.
+
+To put it simply, for the simulation "nsvep_base" the dataset
+"tracers0/rhs/0" contains only zeros, and TurTLE ignores them.
+However, the "tracers0/rhs/8" dataset for simulation "nsvep_1x" contains
+meaningful values (that are used because we request that `iter0` is
+different from 0).
+
+.. code:: python
+
+ def run_simulations_particles():
+ # change these two values as neded.
+ # number of MPI processes to use
+ nprocesses = 4
+ # number of OpenMP threads per MPI process to use
+ nthreads_per_process = 2
+
+ # 1. Run NSVEparticles for resolution 1x, for a few iterations, to build up rhs values.
+ factor = 1
+ # create dns object
+ cc = DNS()
+ # launch simulation
+ cc.launch([
+ 'NSVEparticles',
+ '-n', '{0}'.format(factor*32),
+ '--np', '{0}'.format(nprocesses),
+ '--ntpp', '{0}'.format(nthreads_per_process),
+ '--src-simname', 'base_{0}x'.format(factor),
+ '--src-iteration', '{0}'.format(base_niterations),
+ '--simname', 'nsvep_base'.format(factor),
+ '--precision', 'double',
+ '--dtfactor', '0.3',
+ '--kMeta', '{0}'.format(1.0*factor),
+ '--niter_todo', '{0}'.format(8),
+ '--niter_out', '{0}'.format(8),
+ '--niter_stat', '{0}'.format(8),
+ '--nparticles', '{0}'.format(nparticles),
+ '--niter_part', '{0}'.format(8),
+ '--cpp_random_particles', '{0}'.format(particle_random_seed)])
+
+ # 2. Prepare initial conditions
+ for factor in [1, 2, 4]:
+ df = h5py.File('nsvep_{0}x_checkpoint_0.h5'.format(factor), 'w')
+ # field
+ df['vorticity/complex/{0}'.format(8*factor)] = h5py.ExternalLink(
+ 'base_{0}x_checkpoint_0.h5'.format(factor),
+ 'vorticity/complex/{0}'.format(base_niterations))
+ # particles
+ df['tracers0/state/{0}'.format(8*factor)] = h5py.ExternalLink(
+ 'nsvep_base_checkpoint_0.h5',
+ 'tracers0/state/8')
+ df['tracers0/rhs/{0}'.format(8*factor)] = h5py.ExternalLink(
+ 'nsvep_base_checkpoint_0.h5',
+ 'tracers0/rhs/8')
+ df.close()
+
+ # 3. Run NSVEparticles
+ for factor in [1, 2, 4]:
+ # create dns object
+ cc = DNS()
+ # launch simulation
+ cc.launch([
+ 'NSVEparticles',
+ '-n', '{0}'.format(factor*32),
+ '--np', '{0}'.format(nprocesses),
+ '--ntpp', '{0}'.format(nthreads_per_process),
+ '--simname', 'nsvep_{0}x'.format(factor),
+ '--precision', 'double',
+ '--dtfactor', '0.3',
+ '--kMeta', '{0}'.format(1.0*factor),
+ '--niter_todo', '{0}'.format(test_niterations*factor),
+ '--niter_out', '{0}'.format(test_niterations*factor),
+ '--niter_stat', '{0}'.format(4*factor),
+ '--nparticles', '{0}'.format(nparticles),
+ '--niter_part', '{0}'.format(2*factor),
+ '--cpp_random_particles', '0'], # turn off cpp particle initialization
+ iter0 = 8*factor)
+ return None
+
+To compute the trajectory integration error, we proceed as explained
+above, and compare each DNS with its corresponding double-the-resolution DNS:
+
+.. code:: python
+
+ def plot_error_particles():
+ f = plt.figure()
+ a = f.add_subplot(111)
+ err_max_list = []
+ err_mean_list = []
+ factor_list = [1, 2]
+ for factor in factor_list:
+ c1 = DNS(simname = 'nsvep_{0}x'.format(factor))
+ c2 = DNS(simname = 'nsvep_{0}x'.format(factor*2))
+ for cc in [c1, c2]:
+ cc.parameters['niter_part'] = cc.get_data_file()['parameters/niter_part'][()]
+ c1.compute_statistics(iter0 = 8*factor)
+ c2.compute_statistics(iter0 = 8*factor*2)
+ final_iter_x1 = c1.get_data_file()['iteration'][()]
+ final_iter_x2 = c2.get_data_file()['iteration'][()]
+ f1 = h5py.File(c1.simname + '_checkpoint_0.h5', 'r')
+ f2 = h5py.File(c2.simname + '_checkpoint_0.h5', 'r')
+ x1 = f1['tracers0/state/{0}'.format(final_iter_x1)][()]
+ x2 = f2['tracers0/state/{0}'.format(final_iter_x2)][()]
+ err_max_list.append(np.max(np.abs(x2 - x1)))
+ err_mean_list.append(np.mean(np.abs(x2 - x1)))
+ f1.close()
+ f2.close()
+ factor_list = np.array(factor_list).astype(np.float)
+ err_max_list = np.array(err_max_list)
+ err_mean_list = np.array(err_mean_list)
+ a.plot(factor_list, err_max_list, marker = '.', label = 'max error')
+ a.plot(factor_list, err_mean_list, marker = '.', label = 'mean error')
+ a.plot(factor_list,
+ (1e-2)*factor_list**(-3),
+ color = 'black',
+ dashes = (2, 2),
+ label = '$\propto f^{-3}$')
+ a.plot(factor_list,
+ (1e-2)*factor_list**(-4),
+ color = 'black',
+ dashes = (1, 1),
+ label = '$\propto f^{-4}$')
+ a.set_xscale('log')
+ a.set_yscale('log')
+ a.set_xlabel('resolution factor f')
+ a.set_ylabel('absolute trajectory error [DNS units]')
+ a.legend(loc = 'best')
+ f.tight_layout()
+ f.savefig('err_vs_dt_particle.pdf')
+ f.savefig('err_vs_dt_particle.png')
+ plt.close(f)
+ return None
+
+Note that we plot two error measures: the maximum error, as well as the
+mean error.
+
+.. image:: err_vs_dt_particle.svg
+
+The plot suggests that these converge at different rates: the mean error
+exhibits 4th order convergence in "factor", whereas the maximum error
+seems to converge like :math:`f^{3.5}` (closer to the limit :math:`f^3`
+imposed by the fluid solver error).
+While a more detailed investigation would be in order, I speculate that
+for this particular setup the increase of the spatial resolution along
+with the temporal resolution renders the interpolation errors (which should
+decrease the global order to 2) smaller than the simultaneous temporal
+integration errors.
+In any case the interplay of the different error sources is a fairly
+complex subject in itself, which we don't propose to address here in
+full.
+
+For the beginner's convenience, we also provide a method to plot
+individual particle trajectories:
+
+.. code:: python
+
+ def plot_traj_particles():
+ f = plt.figure()
+ a = f.add_subplot(111)
+ for factor in [1, 2, 4]:
+ cc = DNS(simname = 'nsvep_{0}x'.format(factor))
+ cc.compute_statistics(iter0 = 8*factor)
+ xx = read_trajectory(cc, 14, iter0 = 8*factor)
+ a.plot(xx[:, 0], xx[:, 1])
+ f.tight_layout()
+ f.savefig('trajectories.pdf')
+ f.savefig('trajectories.png')
+ plt.close(f)
+ return None
+
+ def read_trajectory(cc, traj_index, iter0):
+ cc.parameters['niter_part'] = cc.get_data_file()['parameters/niter_part'][()]
+ df = cc.get_particle_file()
+ xx = []
+ for ii in range(iter0, cc.get_data_file()['iteration'][()], cc.parameters['niter_part']):
+ xx.append(df['tracers0/position/{0}'.format(ii)][traj_index])
+ df.close()
+ return np.array(xx)
+
+.. image:: trajectories.svg
+
+Finally, the script ends with a standard call to `main`:
+
+.. code:: python
+
+ if __name__ == '__main__':
+ main()
+
+
diff --git a/documentation/sphinx_static/err_vs_dt_field.svg b/documentation/sphinx_static/err_vs_dt_field.svg
index b725f1e0..96260bb1 100644
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diff --git a/documentation/sphinx_static/err_vs_dt_particle.svg b/documentation/sphinx_static/err_vs_dt_particle.svg
index a7c5c0cb..354d1447 100644
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<use x="389.408203" xlink:href="#DejaVuSans-111"/>
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- <path d="M 355.059239 38.576563
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+ <g id="line2d_42">
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</g>
- <g id="line2d_35">
+ <g id="line2d_43">
<g>
- <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="365.059239" xlink:href="#m52d3e4d600" y="38.576563"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="69.315346" xlink:href="#md9d020bb03" y="238.748781"/>
</g>
</g>
- <g id="text_12">
- <!-- mean error -->
- <g transform="translate(383.059239 42.076563)scale(0.1 -0.1)">
+ <g id="text_13">
+ <!-- mean error I4O3 -->
+ <g transform="translate(81.915346 241.198781)scale(0.07 -0.07)">
+ <use xlink:href="#DejaVuSans-109"/>
+ <use x="97.412109" xlink:href="#DejaVuSans-101"/>
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+ <g id="line2d_44">
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+ <g id="line2d_45">
+ <g>
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+ </g>
+ </g>
+ <g id="text_14">
+ <!-- max error I8O5 -->
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+ <use x="695.316406" xlink:href="#DejaVuSans-53"/>
+ </g>
+ </g>
+ <g id="line2d_46">
+ <path d="M 62.315346 259.298156
+L 76.315346 259.298156
+" style="fill:none;stroke:#d62728;stroke-linecap:square;stroke-width:1.5;"/>
+ </g>
+ <g id="line2d_47">
+ <g>
+ <use style="fill:#d62728;stroke:#d62728;" x="69.315346" xlink:href="#me87b41afb3" y="259.298156"/>
+ </g>
+ </g>
+ <g id="text_15">
+ <!-- mean error I8O5 -->
+ <g transform="translate(81.915346 261.748156)scale(0.07 -0.07)">
<use xlink:href="#DejaVuSans-109"/>
<use x="97.412109" xlink:href="#DejaVuSans-101"/>
<use x="158.935547" xlink:href="#DejaVuSans-97"/>
@@ -1181,17 +1391,22 @@ L 375.059239 38.576563
<use x="416.267578" xlink:href="#DejaVuSans-114"/>
<use x="455.130859" xlink:href="#DejaVuSans-111"/>
<use x="516.3125" xlink:href="#DejaVuSans-114"/>
+ <use x="557.425781" xlink:href="#DejaVuSans-32"/>
+ <use x="589.212891" xlink:href="#DejaVuSans-73"/>
+ <use x="618.705078" xlink:href="#DejaVuSans-56"/>
+ <use x="682.328125" xlink:href="#DejaVuSans-79"/>
+ <use x="761.039062" xlink:href="#DejaVuSans-53"/>
</g>
</g>
- <g id="line2d_36">
- <path d="M 355.059239 53.254688
-L 375.059239 53.254688
+ <g id="line2d_48">
+ <path d="M 62.315346 269.572844
+L 76.315346 269.572844
" style="fill:none;stroke:#000000;stroke-dasharray:3,3;stroke-dashoffset:0;stroke-width:1.5;"/>
</g>
- <g id="line2d_37"/>
- <g id="text_13">
- <!-- $\propto f^{-3.5}$ -->
- <g transform="translate(383.059239 56.754688)scale(0.1 -0.1)">
+ <g id="line2d_49"/>
+ <g id="text_16">
+ <!-- $\propto f^{-2}$ -->
+ <g transform="translate(81.915346 272.022844)scale(0.07 -0.07)">
<defs>
<path d="M 25.734375 17.71875
Q 33.796875 17.71875 38.625 29.4375
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Q 29.296875 75.984375 39.3125 75.984375
z
" id="DejaVuSans-Oblique-102"/>
- <path d="M 10.796875 72.90625
-L 49.515625 72.90625
-L 49.515625 64.59375
-L 19.828125 64.59375
-L 19.828125 46.734375
-Q 21.96875 47.46875 24.109375 47.828125
-Q 26.265625 48.1875 28.421875 48.1875
-Q 40.625 48.1875 47.75 41.5
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-Q 22.3125 -1.421875 17.546875 -0.640625
-Q 12.796875 0.140625 7.71875 1.703125
-L 7.71875 11.625
-Q 12.109375 9.234375 16.796875 8.0625
-Q 21.484375 6.890625 26.703125 6.890625
-Q 35.15625 6.890625 40.078125 11.328125
-Q 45.015625 15.765625 45.015625 23.390625
-Q 45.015625 31 40.078125 35.4375
-Q 35.15625 39.890625 26.703125 39.890625
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-Q 14.890625 38.140625 10.796875 36.28125
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+ </g>
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+ <g id="line2d_50">
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+L 76.315346 279.847531
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+ </g>
+ <g id="line2d_51"/>
+ <g id="text_17">
+ <!-- $\propto f^{-3}$ -->
+ <g transform="translate(81.915346 282.297531)scale(0.07 -0.07)">
<use transform="translate(19.482422 0.765625)" xlink:href="#DejaVuSans-8733"/>
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-L 375.059239 67.932813
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+ <g id="line2d_52">
+ <path d="M 62.315346 290.122219
+L 76.315346 290.122219
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</g>
- <g id="line2d_39"/>
- <g id="text_14">
+ <g id="line2d_53"/>
+ <g id="text_18">
<!-- $\propto f^{-4}$ -->
- <g transform="translate(383.059239 71.432813)scale(0.1 -0.1)">
+ <g transform="translate(81.915346 292.572219)scale(0.07 -0.07)">
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@@ -1297,8 +1501,8 @@ L 375.059239 67.932813
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</g>
<defs>
- <clipPath id="p15ab6f59e1">
- <rect height="289.528" width="391.921081" x="55.880346" y="10.8"/>
+ <clipPath id="p4f155a8e51">
+ <rect height="289.528" width="391.786081" x="56.015346" y="10.8"/>
</clipPath>
</defs>
</svg>
diff --git a/examples/convergence/fields_temporal.py b/examples/convergence/fields_temporal.py
index 85ada49f..c7111c68 100644
--- a/examples/convergence/fields_temporal.py
+++ b/examples/convergence/fields_temporal.py
@@ -7,7 +7,7 @@ from TurTLE import DNS, PP
from fields_base import *
-base_niterations = 128
+base_niterations = 512
test_niterations = 32
grid_size = 128
@@ -162,8 +162,8 @@ def plot_error_field(err_vs_t = False):
marker = '.',
label = 'NSVE vs NSE')
fl = np.array(factor_list).astype(np.float)
- for ee in [1, 2, 3]:
- a.plot(fl, error_list[0][0] * fl**(-ee),
+ for ee in [2, 3]:
+ a.plot(fl[:2], error_list[0][0] * fl[:2]**(-ee),
dashes = (ee, ee),
color = 'black',
label = '$\propto f^{{-{0}}}$'.format(ee),
diff --git a/examples/convergence/particles_temporal.py b/examples/convergence/particles_temporal.py
index 013126db..054a2538 100644
--- a/examples/convergence/particles_temporal.py
+++ b/examples/convergence/particles_temporal.py
@@ -3,7 +3,7 @@ import h5py
import matplotlib.pyplot as plt
import TurTLE
-from TurTLE import DNS, PP
+from TurTLE import DNS
base_niterations = 256
@@ -17,11 +17,11 @@ neighbours_smoothness_list = [
(3, 2)]
def main():
- #generate_initial_conditions()
+ generate_initial_conditions()
- #run_simulations_particles()
- plot_error_particles()
+ run_simulations_particles()
+ plot_error_particles()
plot_traj_particles()
return None
@@ -52,21 +52,6 @@ def generate_initial_conditions():
'--kMeta', '1.',
'--niter_stat', '16',
'--checkpoints_per_file', '{0}'.format(16)])
-
-# 3. Generate initial conditions for NSE runs at 1x, 2x and 4x the
-# base resolution.
- # create postprocess object
- cc = PP()
- # compute velocity field at last iteration
- cc.launch([
- 'get_velocity',
- '--np', '{0}'.format(nprocesses),
- '--ntpp', '{0}'.format(nthreads_per_process),
- '--simname', 'base',
- '--precision', 'double',
- '--iter0', '{0}'.format(base_niterations),
- '--iter1', '{0}'.format(base_niterations)])
- # we don't need to update "checkpoint" file after "get_velocity"
return None
def run_simulations_particles():
--
GitLab
From dd1359209bb454b08c5c54b8d66b63212c0d6e75 Mon Sep 17 00:00:00 2001
From: Cristian C Lalescu <Cristian.Lalescu@mpcdf.mpg.de>
Date: Wed, 26 Jan 2022 08:50:02 +0100
Subject: [PATCH 22/24] updates convergence text
---
documentation/sphinx_static/convergence.rst | 17 +
.../sphinx_static/convergence_particles.rst | 320 +-
documentation/sphinx_static/trajectories.svg | 3181 ++++++++++++++---
examples/convergence/particles_temporal.py | 6 +-
4 files changed, 2949 insertions(+), 575 deletions(-)
diff --git a/documentation/sphinx_static/convergence.rst b/documentation/sphinx_static/convergence.rst
index 4c05215f..5d0b9574 100644
--- a/documentation/sphinx_static/convergence.rst
+++ b/documentation/sphinx_static/convergence.rst
@@ -6,6 +6,23 @@ standard approaches to differential equations, one may use
generic convergence tests to characterize algorithms and/or
implementations.
+As an example usage of TurTLE, we show here how to characterize
+convergence for the field solver, or the AdamsBashforth
+particle solver.
+The purpose of this tutorial is to introduce TurTLE users to nontrivial
+workflows that involve keeping track of a number of simulations and
+prescribing their initial conditions.
+
+The field solver test is a fairly simple pursuit, showing basic
+operations with the `turtle` launcher.
+
+The particle solver test is also minimal within the methodological
+constraints imposed by the use of the Adams Bashforth integration
+method, leading to a relatively increased complexity.
+The example shows how to account for a number of technical details: full
+control over multi-step method initialization and full control of fluid
+solver forcing parameters.
+
Navier-Stokes solution
----------------------
diff --git a/documentation/sphinx_static/convergence_particles.rst b/documentation/sphinx_static/convergence_particles.rst
index 0d4b2418..35e04080 100644
--- a/documentation/sphinx_static/convergence_particles.rst
+++ b/documentation/sphinx_static/convergence_particles.rst
@@ -96,9 +96,9 @@ We then define the function that runs the particle simulations,
Because we use an Adams-Bashforth method, we need to know the values of
the particle velocity (i.e. the right-hand-side of the ODE) at previous
steps.
-TurTLE accomplishes this by using the Euler integration scheme for "time
-step 0", then using a 2nd order Adams-Bashforth, etc, until the desired
-number of right-hand-side values is stored.
+By default TurTLE accomplishes this by using the Euler integration scheme
+for "time step 0", then using a 2nd order Adams-Bashforth, etc, until
+the desired number of right-hand-side values is stored.
Thus the code first integrates trajectories for 8 iterations, and the
output will contain the additional information.
This happens because such information is crucial for checkpointing ---
@@ -108,7 +108,7 @@ affecting the numerical solution.
To put it simply, for the simulation "nsvep_base" the dataset
"tracers0/rhs/0" contains only zeros, and TurTLE ignores them.
However, the "tracers0/rhs/8" dataset for simulation "nsvep_1x" contains
-meaningful values (that are used because we request that `iter0` is
+meaningful values (that **are** used because we request that `iter0` is
different from 0).
.. code:: python
@@ -116,70 +116,109 @@ different from 0).
def run_simulations_particles():
# change these two values as neded.
# number of MPI processes to use
- nprocesses = 4
+ nprocesses = 8
# number of OpenMP threads per MPI process to use
- nthreads_per_process = 2
+ nthreads_per_process = 1
- # 1. Run NSVEparticles for resolution 1x, for a few iterations, to build up rhs values.
+ # 1. Run NSVEparticles for a few iterations, to build up rhs values, consistent
+ # with the relevant velocity field.
factor = 1
- # create dns object
- cc = DNS()
- # launch simulation
- cc.launch([
+ for neighbours, smoothness in neighbours_smoothness_list:
+ interp_name = 'I{0}O{1}'.format(2*neighbours+2, 2*smoothness+1)
+ # create dns object
+ cc = DNS()
+ # launch simulation
+ cc.launch([
'NSVEparticles',
'-n', '{0}'.format(factor*32),
'--np', '{0}'.format(nprocesses),
'--ntpp', '{0}'.format(nthreads_per_process),
- '--src-simname', 'base_{0}x'.format(factor),
+ '--src-simname', 'base',
'--src-iteration', '{0}'.format(base_niterations),
- '--simname', 'nsvep_base'.format(factor),
+ '--simname', 'nsvep_base_' + interp_name,
'--precision', 'double',
- '--dtfactor', '0.3',
- '--kMeta', '{0}'.format(1.0*factor),
- '--niter_todo', '{0}'.format(8),
- '--niter_out', '{0}'.format(8),
- '--niter_stat', '{0}'.format(8),
+ '--dtfactor', '{0}'.format(base_particle_dt/4),
+ '--kMeta', '{0}'.format(factor*1.0),
+ '--niter_todo', '{0}'.format(20),
+ '--niter_out', '{0}'.format(1),
+ '--niter_stat', '{0}'.format(1),
'--nparticles', '{0}'.format(nparticles),
- '--niter_part', '{0}'.format(8),
+ '--niter_part', '{0}'.format(1),
+ '--tracers0_neighbours', '{0}'.format(neighbours),
+ '--tracers0_smoothness', '{0}'.format(smoothness),
+ '--tracers0_integration_steps', '4',
'--cpp_random_particles', '{0}'.format(particle_random_seed)])
# 2. Prepare initial conditions
- for factor in [1, 2, 4]:
- df = h5py.File('nsvep_{0}x_checkpoint_0.h5'.format(factor), 'w')
- # field
- df['vorticity/complex/{0}'.format(8*factor)] = h5py.ExternalLink(
- 'base_{0}x_checkpoint_0.h5'.format(factor),
- 'vorticity/complex/{0}'.format(base_niterations))
- # particles
- df['tracers0/state/{0}'.format(8*factor)] = h5py.ExternalLink(
- 'nsvep_base_checkpoint_0.h5',
- 'tracers0/state/8')
- df['tracers0/rhs/{0}'.format(8*factor)] = h5py.ExternalLink(
- 'nsvep_base_checkpoint_0.h5',
- 'tracers0/rhs/8')
- df.close()
+ for neighbours, smoothness in neighbours_smoothness_list:
+ interp_name = 'I{0}O{1}'.format(2*neighbours+2, 2*smoothness+1)
+ for factor in [1, 2, 4]:
+ df = h5py.File('nsvep_{0}x_{1}_checkpoint_0.h5'.format(factor, interp_name), 'w')
+ # field
+ field_iteration = 16
+ df['vorticity/complex/{0}'.format(8*factor)] = h5py.ExternalLink(
+ 'nsvep_base_{0}_checkpoint_0.h5'.format(interp_name),
+ 'vorticity/complex/{0}'.format(field_iteration))
+ # particles
+ df['tracers0/state/{0}'.format(8*factor)] = h5py.ExternalLink(
+ 'nsvep_base_{0}_checkpoint_0.h5'.format(interp_name),
+ 'tracers0/state/16')
+ # copy rhs
+ source_file = h5py.File(
+ 'nsvep_base_{0}_checkpoint_0.h5'.format(interp_name), 'r')
+ rhs = source_file['tracers0/rhs/16'][()]
+ for tt in range(1, rhs.shape[0]):
+ ii = 16 - tt*4//factor + 1
+ #print(factor, tt, ii)
+ rhs[tt] = source_file['tracers0/rhs/{0}'.format(16 - tt*4//factor + 1)][1]
+ df['tracers0/rhs/{0}'.format(8*factor)] = rhs
+ df.close()
# 3. Run NSVEparticles
for factor in [1, 2, 4]:
- # create dns object
- cc = DNS()
- # launch simulation
- cc.launch([
- 'NSVEparticles',
- '-n', '{0}'.format(factor*32),
- '--np', '{0}'.format(nprocesses),
- '--ntpp', '{0}'.format(nthreads_per_process),
- '--simname', 'nsvep_{0}x'.format(factor),
- '--precision', 'double',
- '--dtfactor', '0.3',
- '--kMeta', '{0}'.format(1.0*factor),
- '--niter_todo', '{0}'.format(test_niterations*factor),
- '--niter_out', '{0}'.format(test_niterations*factor),
- '--niter_stat', '{0}'.format(4*factor),
- '--nparticles', '{0}'.format(nparticles),
- '--niter_part', '{0}'.format(2*factor),
- '--cpp_random_particles', '0'], # turn off cpp particle initialization
- iter0 = 8*factor)
+ # Test different interpolations.
+ # The loop iterates over number of neighbours and smoothness.
+ # The simulation names are defined based on "kernel size" and "order
+ # of polynomial".
+ # We do this to emphasize the one-to-one correspondence between
+ # neighbours and kernel size, and smoothness and order of polynomial.
+ for neighbours, smoothness in neighbours_smoothness_list:
+ interp_name = 'I{0}O{1}'.format(2*neighbours+2, 2*smoothness+1)
+ source_file = h5py.File('nsvep_base_{0}.h5'.format(interp_name), 'r')
+ # create dns object
+ cc = DNS()
+ # launch simulation
+ cc.launch([
+ 'NSVEparticles',
+ '-n', '{0}'.format(source_file['parameters/nx'][()]),
+ '--np', '{0}'.format(nprocesses),
+ '--ntpp', '{0}'.format(nthreads_per_process),
+ '--simname', 'nsvep_{0}x_{1}'.format(factor, interp_name),
+ '--precision', 'double',
+ '--dtfactor', '{0}'.format(base_particle_dt/factor),
+ '--niter_todo', '{0}'.format(test_niterations_particles*factor+8*factor),
+ '--niter_out', '{0}'.format(test_niterations_particles*factor+8*factor),
+ '--niter_stat', '{0}'.format(1),
+ ## ensure fluid physics is the same
+ '--dealias_type', '{0}'.format(source_file['parameters/dealias_type'][()]),
+ '--energy', '{0}'.format(source_file['parameters/energy'][()]),
+ '--famplitude', '{0}'.format(source_file['parameters/famplitude'][()]),
+ '--fk0', '{0}'.format(source_file['parameters/fk0'][()]),
+ '--fk1', '{0}'.format(source_file['parameters/fk1'][()]),
+ '--fmode', '{0}'.format(source_file['parameters/fmode'][()]),
+ '--friction_coefficient', '{0}'.format(source_file['parameters/friction_coefficient'][()]),
+ '--injection_rate', '{0}'.format(source_file['parameters/injection_rate'][()]),
+ '--nu', '{0}'.format(source_file['parameters/nu'][()]),
+ '--forcing_type', '{0}'.format(str(source_file['parameters/forcing_type'][()], 'ascii')),
+ ## particle params
+ '--nparticles', '{0}'.format(nparticles),
+ '--niter_part', '{0}'.format(1),
+ '--tracers0_neighbours', '{0}'.format(neighbours),
+ '--tracers0_smoothness', '{0}'.format(smoothness),
+ '--tracers0_integration_steps', '4',
+ '--cpp_random_particles', '0'], # turn off C++ particle initialization
+ iter0 = 8*factor)
+ source_file.close()
return None
To compute the trajectory integration error, we proceed as explained
@@ -190,95 +229,146 @@ above, and compare each DNS with its corresponding double-the-resolution DNS:
def plot_error_particles():
f = plt.figure()
a = f.add_subplot(111)
- err_max_list = []
- err_mean_list = []
factor_list = [1, 2]
- for factor in factor_list:
- c1 = DNS(simname = 'nsvep_{0}x'.format(factor))
- c2 = DNS(simname = 'nsvep_{0}x'.format(factor*2))
- for cc in [c1, c2]:
- cc.parameters['niter_part'] = cc.get_data_file()['parameters/niter_part'][()]
- c1.compute_statistics(iter0 = 8*factor)
- c2.compute_statistics(iter0 = 8*factor*2)
- final_iter_x1 = c1.get_data_file()['iteration'][()]
- final_iter_x2 = c2.get_data_file()['iteration'][()]
- f1 = h5py.File(c1.simname + '_checkpoint_0.h5', 'r')
- f2 = h5py.File(c2.simname + '_checkpoint_0.h5', 'r')
- x1 = f1['tracers0/state/{0}'.format(final_iter_x1)][()]
- x2 = f2['tracers0/state/{0}'.format(final_iter_x2)][()]
- err_max_list.append(np.max(np.abs(x2 - x1)))
- err_mean_list.append(np.mean(np.abs(x2 - x1)))
- f1.close()
- f2.close()
factor_list = np.array(factor_list).astype(np.float)
- err_max_list = np.array(err_max_list)
- err_mean_list = np.array(err_mean_list)
- a.plot(factor_list, err_max_list, marker = '.', label = 'max error')
- a.plot(factor_list, err_mean_list, marker = '.', label = 'mean error')
- a.plot(factor_list,
- (1e-2)*factor_list**(-3),
- color = 'black',
- dashes = (2, 2),
- label = '$\propto f^{-3}$')
- a.plot(factor_list,
- (1e-2)*factor_list**(-4),
- color = 'black',
- dashes = (1, 1),
- label = '$\propto f^{-4}$')
+ for neighbours, smoothness in neighbours_smoothness_list:
+ interp_name = 'I{0}O{1}'.format(2*neighbours+2, 2*smoothness+1)
+ err_max_list = []
+ err_mean_list = []
+ for factor in factor_list:
+ factor = int(factor)
+ c1 = DNS(simname = 'nsvep_{0}x_'.format(int(factor)) + interp_name)
+ c2 = DNS(simname = 'nsvep_{0}x_'.format(int(factor)*2) + interp_name)
+ for cc in [c1, c2]:
+ cc.parameters['niter_part'] = cc.get_data_file()['parameters/niter_part'][()]
+ c1.compute_statistics(iter0 = 8*factor)
+ c2.compute_statistics(iter0 = 8*factor*2)
+ final_iter_x1 = c1.get_data_file()['iteration'][()]
+ final_iter_x2 = c2.get_data_file()['iteration'][()]
+ f1 = h5py.File(c1.simname + '_checkpoint_0.h5', 'r')
+ f2 = h5py.File(c2.simname + '_checkpoint_0.h5', 'r')
+ x1 = f1['tracers0/state/{0}'.format(final_iter_x1)][()]
+ x2 = f2['tracers0/state/{0}'.format(final_iter_x2)][()]
+ diff = np.sqrt(np.sum((x2-x1)**2, axis = -1))
+ err_max_list.append(np.max(diff))
+ err_mean_list.append(np.mean(diff))
+ f1.close()
+ f2.close()
+ err_max_list = np.array(err_max_list)
+ err_mean_list = np.array(err_mean_list)
+ a.plot(factor_list, err_max_list, marker = '.', label = 'max error ' + interp_name)
+ a.plot(factor_list, err_mean_list, marker = '.', label = 'mean error ' + interp_name)
+ for ee in [2, 3, 4]:
+ a.plot(factor_list,
+ (1e-4)*factor_list**(-ee),
+ color = 'black',
+ dashes = (ee, ee),
+ label = '$\propto f^{{-{0}}}$'.format(ee))
a.set_xscale('log')
a.set_yscale('log')
a.set_xlabel('resolution factor f')
a.set_ylabel('absolute trajectory error [DNS units]')
- a.legend(loc = 'best')
+ a.legend(loc = 'best', fontsize = 7)
f.tight_layout()
f.savefig('err_vs_dt_particle.pdf')
- f.savefig('err_vs_dt_particle.png')
+ f.savefig('err_vs_dt_particle.svg')
plt.close(f)
return None
-Note that we plot two error measures: the maximum error, as well as the
-mean error.
-
-.. image:: err_vs_dt_particle.svg
-
-The plot suggests that these converge at different rates: the mean error
-exhibits 4th order convergence in "factor", whereas the maximum error
-seems to converge like :math:`f^{3.5}` (closer to the limit :math:`f^3`
-imposed by the fluid solver error).
-While a more detailed investigation would be in order, I speculate that
-for this particular setup the increase of the spatial resolution along
-with the temporal resolution renders the interpolation errors (which should
-decrease the global order to 2) smaller than the simultaneous temporal
-integration errors.
-In any case the interplay of the different error sources is a fairly
-complex subject in itself, which we don't propose to address here in
-full.
-
For the beginner's convenience, we also provide a method to plot
-individual particle trajectories:
+individual particle trajectories.
+Note that the second part of this function is in fact a sanity check for
+the initial conditions: the plot confirms that the data required for the
+multi-step method (explicitly placed in the checkpoint file) is
+consistent with the simulation parameters.
.. code:: python
def plot_traj_particles():
+ ###########################################################################
f = plt.figure()
a = f.add_subplot(111)
- for factor in [1, 2, 4]:
- cc = DNS(simname = 'nsvep_{0}x'.format(factor))
- cc.compute_statistics(iter0 = 8*factor)
- xx = read_trajectory(cc, 14, iter0 = 8*factor)
- a.plot(xx[:, 0], xx[:, 1])
+ for neighbours, smoothness in neighbours_smoothness_list:
+ interp_name = 'I{0}O{1}'.format(2*neighbours+2, 2*smoothness+1)
+ for factor in [1, 2, 4]:
+ cc = DNS(simname = 'nsvep_{0}x_'.format(factor) + interp_name)
+ cc.compute_statistics(iter0 = 8*factor)
+ tt = 3
+ xx = read_trajectory(cc, tt, iter0 = 8*factor)
+ a.plot(xx[:, 0],
+ xx[:, 1],
+ label = interp_name + '$f = {0}$'.format(factor),
+ marker = 'x',
+ dashes = (4/factor, 3, 4/factor),
+ alpha = 0.2)
+ #a.plot(xx[:, 0], xx[:, 1], dashes = (4/factor, 3, 4/factor), alpha = 0.2)
+ a.legend(loc = 'best', fontsize = 7)
+ a.set_xlabel('$x$ [code units]')
+ a.set_ylabel('$y$ [code units]')
f.tight_layout()
f.savefig('trajectories.pdf')
- f.savefig('trajectories.png')
+ f.savefig('trajectories.svg')
plt.close(f)
+ ###########################################################################
+ ###########################################################################
+ traj_index = 3
+ for neighbours, smoothness in neighbours_smoothness_list:
+ interp_name = 'I{0}O{1}'.format(2*neighbours+2, 2*smoothness+1)
+ cc = DNS(simname = 'nsvep_base_' + interp_name)
+ cc.compute_statistics()
+ xx_base = read_trajectory(cc, traj_index, iter0 = 0, dset_name = 'velocity')
+ iter0 = 16
+ tt_base = np.array(range(iter0, iter0 + xx_base.shape[0]))*cc.parameters['dt']
+ f = plt.figure()
+ ax_counter = 1
+ for factor in [1, 2, 4]:
+ a = f.add_subplot(310 + ax_counter)
+ ax_counter += 1
+ a.plot(tt_base,
+ xx_base[:, 2],
+ label = 'base_' + interp_name,
+ marker = '+',
+ linewidth = 0.5,
+ alpha = 0.2)
+ cc = DNS(simname = 'nsvep_{0}x_'.format(factor) + interp_name)
+ cc.compute_statistics(iter0 = 8*factor)
+ xx = read_trajectory(cc, traj_index, iter0 = 8*factor, dset_name = 'velocity')
+ tt = np.array(range(8*factor, xx.shape[0]+8*factor))*cc.parameters['dt']
+ a.plot(tt,
+ xx[:, 2],
+ label = interp_name + '$f = {0}$'.format(factor),
+ marker = 'x',
+ dashes = (4/factor, 3, 4/factor),
+ alpha = 0.2)
+ df = h5py.File(cc.simname + '_checkpoint_0.h5', 'r')
+ xx = df['tracers0/rhs/{0}'.format(8*factor)][()]
+ for rhs_index in [1, 2, 3]:
+ a.scatter((8*factor - rhs_index)*cc.parameters['dt'],
+ xx[rhs_index, traj_index, 2],
+ marker = '*',
+ zorder = -10,
+ alpha = 0.5,
+ color = 'black')
+ df.close()
+ a.legend(loc = 'best', fontsize = 7)
+ a.set_xlabel('$t$ [code units]')
+ a.set_ylabel('$v_y$ [code units]')
+ f.tight_layout()
+ f.savefig('velocities_{0}.pdf'.format(interp_name))
+ plt.close(f)
+ ###########################################################################
return None
- def read_trajectory(cc, traj_index, iter0):
+ def read_trajectory(
+ cc,
+ traj_index,
+ iter0,
+ dset_name = 'position'):
cc.parameters['niter_part'] = cc.get_data_file()['parameters/niter_part'][()]
df = cc.get_particle_file()
xx = []
- for ii in range(iter0, cc.get_data_file()['iteration'][()], cc.parameters['niter_part']):
- xx.append(df['tracers0/position/{0}'.format(ii)][traj_index])
+ for ii in range(iter0, cc.get_data_file()['iteration'][()]+1, cc.parameters['niter_part']):
+ xx.append(df['tracers0/' + dset_name + '/{0}'.format(ii)][traj_index])
df.close()
return np.array(xx)
diff --git a/documentation/sphinx_static/trajectories.svg b/documentation/sphinx_static/trajectories.svg
index fd6796fa..5c6ec9a6 100644
--- a/documentation/sphinx_static/trajectories.svg
+++ b/documentation/sphinx_static/trajectories.svg
@@ -7,7 +7,7 @@
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<cc:Work>
<dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
- <dc:date>2022-01-07T21:18:20.267358</dc:date>
+ <dc:date>2022-01-20T07:20:04.265273</dc:date>
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+ <use transform="translate(290.136719 0.015625)" xlink:href="#DejaVuSans-61"/>
+ <use transform="translate(393.408203 0.015625)" xlink:href="#DejaVuSans-49"/>
+ </g>
+ </g>
+ <g id="line2d_25">
+ <path d="M 392.04 61.067656
+L 406.04 61.067656
+" style="fill:none;stroke:#9467bd;stroke-dasharray:3,4.5,3;stroke-dashoffset:0;stroke-opacity:0.2;stroke-width:1.5;"/>
+ </g>
+ <g id="line2d_26">
+ <g>
+ <use style="fill:#9467bd;fill-opacity:0.2;stroke:#9467bd;stroke-opacity:0.2;" x="399.04" xlink:href="#me6acc25a23" y="61.067656"/>
+ </g>
+ </g>
+ <g id="text_17">
+ <!-- I8O5$f = 2$ -->
+ <g transform="translate(411.64 63.517656)scale(0.07 -0.07)">
+ <use transform="translate(0 0.015625)" xlink:href="#DejaVuSans-73"/>
+ <use transform="translate(29.492188 0.015625)" xlink:href="#DejaVuSans-56"/>
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+ <use transform="translate(393.408203 0.015625)" xlink:href="#DejaVuSans-50"/>
+ </g>
+ </g>
+ <g id="line2d_27">
+ <path d="M 392.04 71.342344
+L 406.04 71.342344
+" style="fill:none;stroke:#8c564b;stroke-dasharray:1.5,4.5,1.5;stroke-dashoffset:0;stroke-opacity:0.2;stroke-width:1.5;"/>
+ </g>
+ <g id="line2d_28">
+ <g>
+ <use style="fill:#8c564b;fill-opacity:0.2;stroke:#8c564b;stroke-opacity:0.2;" x="399.04" xlink:href="#m4f5604d9a2" y="71.342344"/>
+ </g>
+ </g>
+ <g id="text_18">
+ <!-- I8O5$f = 4$ -->
+ <g transform="translate(411.64 73.792344)scale(0.07 -0.07)">
+ <use transform="translate(0 0.015625)" xlink:href="#DejaVuSans-73"/>
+ <use transform="translate(29.492188 0.015625)" xlink:href="#DejaVuSans-56"/>
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<defs>
- <clipPath id="pa8c46be0ca">
- <rect height="291.1975" width="386.53" x="63.47" y="10.8"/>
+ <clipPath id="p444e95376c">
+ <rect height="291.1975" width="399.31" x="50.69" y="10.8"/>
</clipPath>
</defs>
</svg>
diff --git a/examples/convergence/particles_temporal.py b/examples/convergence/particles_temporal.py
index 054a2538..53697edd 100644
--- a/examples/convergence/particles_temporal.py
+++ b/examples/convergence/particles_temporal.py
@@ -63,12 +63,12 @@ def run_simulations_particles():
# 1. Run NSVEparticles for a few iterations, to build up rhs values, consistent
# with the relevant velocity field.
- # create dns object
- # launch simulation
factor = 1
for neighbours, smoothness in neighbours_smoothness_list:
interp_name = 'I{0}O{1}'.format(2*neighbours+2, 2*smoothness+1)
+ # create dns object
cc = DNS()
+ # launch simulation
cc.launch([
'NSVEparticles',
'-n', '{0}'.format(factor*32),
@@ -157,7 +157,7 @@ def run_simulations_particles():
'--tracers0_neighbours', '{0}'.format(neighbours),
'--tracers0_smoothness', '{0}'.format(smoothness),
'--tracers0_integration_steps', '4',
- '--cpp_random_particles', '0'], # turn off cpp particle initialization
+ '--cpp_random_particles', '0'], # turn off C++ particle initialization
iter0 = 8*factor)
source_file.close()
return None
--
GitLab
From 5162d638224e251c8d1b68cc6dab6a5a31e5fd98 Mon Sep 17 00:00:00 2001
From: Cristian C Lalescu <Cristian.Lalescu@mpcdf.mpg.de>
Date: Thu, 27 Jan 2022 17:30:40 +0100
Subject: [PATCH 23/24] fixes typo, adds explanation
---
.../sphinx_static/convergence_fields.rst | 4 +--
.../sphinx_static/convergence_particles.rst | 25 ++++++++++++++++---
examples/convergence/fields_temporal.py | 4 +--
examples/convergence/particles_temporal.py | 4 +--
4 files changed, 27 insertions(+), 10 deletions(-)
diff --git a/documentation/sphinx_static/convergence_fields.rst b/documentation/sphinx_static/convergence_fields.rst
index 45b3aa25..5830e4e7 100644
--- a/documentation/sphinx_static/convergence_fields.rst
+++ b/documentation/sphinx_static/convergence_fields.rst
@@ -72,7 +72,7 @@ The full function is given below:
.. code:: python
def generate_initial_conditions():
- # change these two values as neded.
+ # change these two values as needed.
# number of MPI processes to use
nprocesses = 8
# number of OpenMP threads per MPI process to use
@@ -121,7 +121,7 @@ NSVE solvers):
.. code:: python
def run_simulations_field(err_vs_t = False):
- # change these two values as neded.
+ # change these two values as needed.
# number of MPI processes to use
nprocesses = 8
# number of OpenMP threads per MPI process to use
diff --git a/documentation/sphinx_static/convergence_particles.rst b/documentation/sphinx_static/convergence_particles.rst
index 35e04080..170033f7 100644
--- a/documentation/sphinx_static/convergence_particles.rst
+++ b/documentation/sphinx_static/convergence_particles.rst
@@ -63,7 +63,7 @@ run:
.. code:: python
def generate_initial_conditions():
- # change these two values as neded.
+ # change these two values as needed.
# number of MPI processes to use
nprocesses = 8
# number of OpenMP threads per MPI process to use
@@ -110,11 +110,26 @@ To put it simply, for the simulation "nsvep_base" the dataset
However, the "tracers0/rhs/8" dataset for simulation "nsvep_1x" contains
meaningful values (that **are** used because we request that `iter0` is
different from 0).
+In order to generate consistent values of the "rhs" datasets, we first
+run a simulation at the highest resolution (smallest time-step), and
+then we extract the appropriate snapshots --- see also the second part
+of the trajectory plot function.
+
+Finally, the `launch` method is called in an unusual way for TurTLE.
+Firstly, we demand a DNS that starts at an iteration different from 0.
+Secondly, we manually copy the forcing parameters from the source
+simulation; since the source cannot be specified explicitly, the `DNS`
+class cannot search for the source parameters itself.
+Thirdly, I will note that one may in fact break this call by modifying
+the `iter0` and `checkpoints_per_file` values, since we have explicitly
+placed `iter0` in the `checkpoint` 0 file.
+However, a full discussion of the `iter0` and `checkpoint` subtleties is
+beyond the scope of this tutorial.
.. code:: python
def run_simulations_particles():
- # change these two values as neded.
+ # change these two values as needed.
# number of MPI processes to use
nprocesses = 8
# number of OpenMP threads per MPI process to use
@@ -147,7 +162,8 @@ different from 0).
'--tracers0_neighbours', '{0}'.format(neighbours),
'--tracers0_smoothness', '{0}'.format(smoothness),
'--tracers0_integration_steps', '4',
- '--cpp_random_particles', '{0}'.format(particle_random_seed)])
+ '--cpp_random_particles', '{0}'.format(particle_random_seed),
+ '--checkpoints_per_file', '{0}'.format(16)])
# 2. Prepare initial conditions
for neighbours, smoothness in neighbours_smoothness_list:
@@ -216,7 +232,8 @@ different from 0).
'--tracers0_neighbours', '{0}'.format(neighbours),
'--tracers0_smoothness', '{0}'.format(smoothness),
'--tracers0_integration_steps', '4',
- '--cpp_random_particles', '0'], # turn off C++ particle initialization
+ '--cpp_random_particles', '0', # turn off C++ particle initialization
+ '--checkpoints_per_file', '{0}'.format(16)],
iter0 = 8*factor)
source_file.close()
return None
diff --git a/examples/convergence/fields_temporal.py b/examples/convergence/fields_temporal.py
index c7111c68..d5e271be 100644
--- a/examples/convergence/fields_temporal.py
+++ b/examples/convergence/fields_temporal.py
@@ -21,7 +21,7 @@ def main():
return None
def generate_initial_conditions():
- # change these two values as neded.
+ # change these two values as needed.
# number of MPI processes to use
nprocesses = 8
# number of OpenMP threads per MPI process to use
@@ -65,7 +65,7 @@ def generate_initial_conditions():
return None
def run_simulations_field(err_vs_t = False):
- # change these two values as neded.
+ # change these two values as needed.
# number of MPI processes to use
nprocesses = 8
# number of OpenMP threads per MPI process to use
diff --git a/examples/convergence/particles_temporal.py b/examples/convergence/particles_temporal.py
index 53697edd..c7b0ac15 100644
--- a/examples/convergence/particles_temporal.py
+++ b/examples/convergence/particles_temporal.py
@@ -26,7 +26,7 @@ def main():
return None
def generate_initial_conditions():
- # change these two values as neded.
+ # change these two values as needed.
# number of MPI processes to use
nprocesses = 8
# number of OpenMP threads per MPI process to use
@@ -55,7 +55,7 @@ def generate_initial_conditions():
return None
def run_simulations_particles():
- # change these two values as neded.
+ # change these two values as needed.
# number of MPI processes to use
nprocesses = 8
# number of OpenMP threads per MPI process to use
--
GitLab
From 92839865fe676d306b78588b92cecb7aa4735baa Mon Sep 17 00:00:00 2001
From: Cristian C Lalescu <Cristian.Lalescu@mpcdf.mpg.de>
Date: Thu, 27 Jan 2022 17:39:58 +0100
Subject: [PATCH 24/24] adds comment
---
documentation/sphinx_static/convergence_particles.rst | 8 ++++++--
1 file changed, 6 insertions(+), 2 deletions(-)
diff --git a/documentation/sphinx_static/convergence_particles.rst b/documentation/sphinx_static/convergence_particles.rst
index 170033f7..45fd4dab 100644
--- a/documentation/sphinx_static/convergence_particles.rst
+++ b/documentation/sphinx_static/convergence_particles.rst
@@ -123,8 +123,12 @@ class cannot search for the source parameters itself.
Thirdly, I will note that one may in fact break this call by modifying
the `iter0` and `checkpoints_per_file` values, since we have explicitly
placed `iter0` in the `checkpoint` 0 file.
-However, a full discussion of the `iter0` and `checkpoint` subtleties is
-beyond the scope of this tutorial.
+While a full discussion of the `iter0` and `checkpoint` subtleties is
+beyond the scope of this tutorial, I will mention that it was a
+conscious choice to use a simple `iteration` to `checkpoint`
+correspondence, since we don't actually need anything smarter outside of
+extreme scenarios that need to be addressed individually anyway
+due to other complexities.
.. code:: python
--
GitLab