diff --git a/documentation/_static/overview.rst b/documentation/_static/overview.rst index 83902801ae1205aa2ad8d9d72cc2358a583177d8..b694f002ff03d5072a92cff0f9c61fbaca8433cc 100644 --- a/documentation/_static/overview.rst +++ b/documentation/_static/overview.rst @@ -1,22 +1,27 @@ Overview and Tutorial ===================== -At the moment, this code is meant to run pseudospectral DNS of -Navier-Stokes, using FFTW 3, and to integrate particle trajectories in -the resulting fields. -I'm trying to write it as general as possible, so that it can be -expanded in the future; it remains to be seen how well this will work. - -The Navier-Stokes solver has been extensively tested (tests are included -in the repository), and it is working as expected. Parameters and -statistics are stored in HDF5 format, together with code information, -so simulation data should be "future proof". - -Users of this code are expected to either use `NavierStokes` objects -directly, or construct their own class that inherits this class. -The way I use it is to I inherit and add custom statistics as necessary; I -also have private C++ code that can get added and used when needed. -I plan on adding documentation on the procedure as when other people -show interest in using the code, or when time permits. +Equations +--------- +The code uses a fairly standard pseudo-spectral algorithm to solve fluid +equations. +The incompressible Navier Stokes equations in velocity form are as +follows: + +.. math:: + + \partial_t \mathbf{u} + \mathbf{u} \cdot \nabla \mathbf{u} = + - \nabla p + \nu \Delta \mathbf{u} + \mathbf{f} + +In fact, the code solves the vorticity formulation of these equations: + +.. math:: + \partial_t \mathbf{\omega} + + \mathbf{u} \cdot \nabla \mathbf{\omega} = + \mathbf{\omega} \cdot \nabla \mathbf{u} + + \nu \Delta \mathbf{\omega} + \nabla \times \mathbf{f} + +Tutorial +-------- diff --git a/documentation/index.rst b/documentation/index.rst index 8a028fe90639bbba3bea41d67d9d8f2b0112f107..dc9c5865f2f29f6b0dc8e63f3ea03dc0eb3697c5 100644 --- a/documentation/index.rst +++ b/documentation/index.rst @@ -3,6 +3,7 @@ You can adapt this file completely to your liking, but it should at least contain the root `toctree` directive. + Welcome to bfps's documentation! ================================ @@ -14,7 +15,6 @@ Welcome to bfps's documentation! /_static/development - Indices and tables ==================