Python Software Foundation - SfePy : GSoC 2013 : Week 3

Hi Pythonistas,

This week kicked off with the hunt for a robust Navier-Stokes solver for SfePy.
I went through huge amount of resources.

To summarise the journey:

For our Navier-Stokes currently we use the Newton method with backtracking line-search. in OpenFoam and most of the CFD code the linearization approach is based on Patankar's SIMPLE algorithm.[1][2]
I talked to my professor who told me that SIMPLE is used in commercial softwares like FLUENT too.

I found few papers which tells us some other approaches:

• http://www.google.co.in/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&ved=0CC0QFjAA&url=http%3A%2F%2Fwww.wias-berlin.de%2Fpeople%2Fjohn%2FPP99_13.ps&ei=mW3VUZqzOMmzrgeKuYD4DA&usg=AFQjCNEp9_rShrLSjkYdax6bOimSrkD-KQ&sig2=8S654V-zz2vd4mFZOilZCw&bvm=bv.48705608,d.bmk
• http://numerik.iwr.uni-heidelberg.de/Oberwolfach-Seminar/CFD-Course.pdf
• http://dspace.uta.edu/bitstream/handle/10106/5144/JIAJAN_uta_2502M_10764.pdf
• http://www.reaction-eng.com/downloads/nksolver_pernice.pdf
• http://aero-comlab.stanford.edu/Papers/birkenjamesonproceedings09.pdf
• https://cs.uwaterloo.ca/research/tr/1993/02/CS-93-02.pdf
• http://www.cs.sandia.gov/~rstumin/backtrack.pdf
• http://repository.cmu.edu/cgi/viewcontent.cgi?article=1032&context=math
• http://www8.cs.umu.se/kurser/5DA001/HT07/lectures/newton-handouts.pdf

[1]: http://www.cfd-online.com/Forums/openfoam-solving/60167-how-nonlinear-discretised-equations-linearised-openfoam.html
[2]: http://web.cecs.pdx.edu/~gerry/class/ME448/notes/pdf/SIMPLEslides.pdf


I did some more digging from the implementation point of view and came across some interesting things:

This tutorial demonstrates the solution of Incompressible Navier-Stokes Equations using Fenics. it uses Chlorin's method[3] to solve the problem.
http://fenicsproject.org/documentation/dolfin/1.2.0/python/demo/pde/navier-stokes/python/documentation.html

Other Implementations:

• Parallel Spectral Numerical Methods/The Two- and Three-Dimensional Navier-Stokes Equations - http://en.wikibooks.org/wiki/Parallel_Spectral_Numerical_Methods/The_Two-_and_Three-Dimensional_Navier-Stokes_Equations
• 2D Navier-Stokes solver implemented as a Python package with Python modules and C++ extension modules. It uses the finite difference method on a uniform, rectangular grid. It handles single- and two-phase incompressible, Newtonian, laminar flow with obstacles. -https://code.google.com/p/kmkns/
• Finite Volume Based - http://www.ctcms.nist.gov/fipy/

Here is a list of Open Source CFD codes. Maybe we can fork a repo and use it or learn from it:
http://www.cfd-online.com/Wiki/Codes

According to people iNavier and dolphyn are promising:
http://www.cfd-online.com/Forums/main/13529-colver-code-c-c.html

Someone was using PyAMG to develop Jacobian-Free Newton-Krylov code to solve the Navier Stokes equations : https://groups.google.com/forum/#!topic/pyamg-user/HXrXTyvXPpw

[3] http://en.wikipedia.org/wiki/Projection_method_%28fluid_dynamics%29

This is everything I could harness this week. There is a lot of things to take care to lock the final solver to be used which I would do the current week. Also I am currently narrowing down and rigorously searching a way to implementing SIMPLE in the FE context.

On a side note I have also been working on a SfePy version for Python 3 and benchmarking the simulation results.

This journey is surely turning out to be awesome!

Cheers!