[Vivio]

Hi everyone,

I am doing a simple comparative study for compressible solvers in OpenFOAM v2106 to validate a solver I have written (and for a comparison with overset schemes, which are supposed to be bad at this sort of thing), using a simple 1D shock tube case. The initial conditions are p = 100kPa and T = 348K on one side of the diaphragm and p = 10kPa and T = 278K on the other side. There is a zero gradient boundary condition at each end of the tube (it is open, so that the shock will not reflect) and the other boundaries in the y- and z- directions are empty such that the simulation is 1D

As expected, the density-based rhoCentralFoam gives me better shock definition than the pressure-based rhoPimpleFoam for the same cell sizes, However, when I was checking the grid convergence properties, even on a simple single grid with the standard solvers, the order of convergence of the L2 error with cell size is not even 1st order, even with rhoCentralFoam.

The attached graph shows the L2 error of density over the entire domain compared with an exact solution using an explicit Riemann solver (not OpenFOAM, it is written in Python), at a time of 0.005s, which is before the shock reaches the end of the shock tube. Is this the limit of performance I can expect with OpenFOAM when it comes to capturing shock waves, or am I doing something wrong? Is there a different error metric I should be benchmarking with rather than the L2 norm?

I am not expecting 2nd order convergence but I had expected it would be better than 1st order at least.

Best regards,
Vivio

[arjun]

The major issue is the flux dissipation that is added to keep the solutions stable etc. This has huge impact on the accuracy of the solution.

This I learned during creation of third order model for Wildkatze solver.

To show the impact of flux dissipation, consider Taylor Green Vortex benchmark and for this on a particular fine enough mesh.

These are the error L1 values (This is from my validation cases)

1. Third order solver, normal dissipation 6E-10

2. With recently improved dissipation: 1.0E-10

Just by improving the dissipation error dropped by 5 times.


3. Errors with NO flux dissipation at all, 5E-11.


In my case I have much better convergence order than what you shown (With the mesh refinement) but have to keep the flux dissipation in because without that solver is not stable mostly.

( https://fvus.github.io/wildkatze/art...thirdorderflow)

Note the graph here is 2 years old, i will update it with current values , now that i have noticed it.

In case of Riemann problem, ,the error due to dissipation could be even higher (this is based on my experience with fluxes). Which is probably what is killing the solution there (just a guess).


/Arjun