2D riemann solver
 

I am trying to use roe scheme for a converging diverging nozzle. The basic work is from the work of Liu and Vinokur AIAA 89-0201. I first tried the method for a Sod shock tube problem. It forms the desired shape but there is a small jump on the expansion part,right on the middle of the tube where we assume the initial discontinuity. The same thing happens when I tried the code for a nozzle, The shock is formed, but on the throat, there is an unreal big jump downward. I tried to put some extra constant area zone to the beginning of the nozzle to have the throat some place other than imax/2 location , just as a guess of source of problem, but no difference actually.
I'll be thankful even if some body can guide me through any efficient formulations of Roe scheme for two dimensional applications.

Hi moein_joon27,

The best Riemann solver I know of is called GRP (Generalized Riemann Problem) by Joseph Falcowitz & Matania Ben-Artzi, and Sod's problem was their test case to show the GRP superiority over other schemes. It is quite complex, though. If you are not deterred - search for their publications since the mid 80's or so (there is even a book by these authors on the subject).