Cristian Lalescu
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+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).
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+        # 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),
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+                '--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')
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+----------------------
+
+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.
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+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.