Hi,
I recently started out simulating incompressible flow Navier Stokes equations.
Now, I would like to try performing similar simulations for compressible flow.
I have been looking around for examples of compressible flow implementation in FEniCS, however, I was not successful in finding any.
How do I proceed? Do any of you have any good sources/examples that I can use to get started on this project?
Thank you in advance.
I believe this work used FEniCS, and states the stabilized formulation(s) clearly. I’ve worked with related stabilized methods myself, as written up here, although my experience in compressible flow was all using other Fortran and C/C++ research codes.
The pressure–velocity–temperature formulation of the second linked reference remains suitable even in the incompressible limit, which is useful for some applications, and I believe all the tedious matrices of partial derivatives spelled out in the appendices could be automated using UFL’s diff function. I did some experiments on this for fun a few years ago, which looked promising, but I never completed the implementation. The 5\times 5 matrix square root would be a bit awkward to implement in UFL, but if you look through the cited references by Hauke, there are simpler formulas that are typically effective in practice.
I’ve done it for the steady case with application to aerodynamics. E.g. compressible Navier-Stokes around a NACA0012 airfoil here. Cf. paper here. Extension to transient systems is trivial.
Updated links December 2023:
dolfinx: dolfin_dg/demo/dolfinx/compressible_navier_stokes_naca0012/dg_naca0012_2d.py at master · nate-sime/dolfin_dg · GitHub
legacy dolfin: dolfin_dg/demo/dolfin/compressible_navier_stokes_naca0012/dg_naca0012_2d.py at master · nate-sime/dolfin_dg · GitHub
Thank you very much for your swift response, with help of this example application and the paper I will be able to get started on this matter.
Thank you kamensky for your quick reply and for the examples you provided. I will look into the material and report my progress in the upcoming days.
To solve compressible Navier-Stokes around a NACA0012 airfoil, the Discontinuous Galerkin method was used. Is there a specific reason why you would use discontinuous galerkin methods in this case?
The reason I am asking is because I only used CG methods before and I wonder if DG methods are in some way preferred for compressible NS equations.