> What would you suggest for appropriate boundary-conditions where wave
: phenomena show themselves?

Perhaps the simplest reasonable ones are those of Thompson (J. Comp. Phys. late 80s) but the subject has received a lot of attention during the 90s as CAA and general purpose compressible flow developed.

> Do commercial solvers allow such boundary-conditions?

I do not have direct experience but several of the fruitful areas like unsteady flow in compressor/turbine blading will require it and so I expect the answer is yes.

Hello again! I overcame this problem that I had and everything is going perfectly. Thank you very much for your advice. I implemented my code for moving walls also and for pressure boundary conditions and it converges and the results are fine (without any scock-like regions). The problem was at the differencing scheme that I am using (hybrid).I did not include the temp div(u) in the Ap coefficient.What a silly thing to do... Nevermind...

Well done... Good luck with your future research...

diaw...