Hi

Are there other validation cases for 1D compressible code other than the shock tube and nozzle problem? Are these the only ones with exact solutions? What about validation of 2D codes?

Cheers, Shuo

Shock tube problem is also called the Riemann problem. So it is a typical problem setup in 1D. In 2D, there is also a 2D Riemann problem. The definition of the Riemann problem is identical to initial conditions in a shock tube problem. I could not see any other 1D compressible problem which is useful for validation and verification. Good luck. If you see any, let me know .

For 1D, I believe the shock tube problem stands a good test case. I would suggest you to do the benchmarking pertaining to the errors you look at. If it is time integration, a simple advection equation will do. If it is with the Riemann solvers, you can test it with shock tube, or, problems with spatial discontinuities.

Coming to 2D, there are numerous validation cases. Of those, the one that interests me is the convection of a smooth vortex. Also, for a good validation, I recommend you to do a spatial accuracy test first with some trial functions, and then go for the overall accuracy.

If it is the boundary conditions, then, you might consider other cases that involve smooth convection of a flow structure without reflections.

If you are talking about an inviscid case I would recommend you the "vortex evolution" case also. This case handles a vortex that is convected through a 2-D domain. Exact solution of Euler equations should only give the passive convection of vortex, thus, using a periodic domain will help you to test your code. In addition, you can test your scheme's numerical diffusion by using high period numbers.

Regards,

Saygin