2D Riemann analytic solution.
 

I am solving a two-fluid flow both in 1D and in 2D. In 1D, the constant states across the material interface are aligned normally. But in 2D, the application of the normal-to-interface is not trivial applied. So I am using the level set method to treat it by the normal-to-interface logic. Although it seems the normal-to-interface, the Riemann solution across the material interface was not applicable. Have you ever experienced this kind of case?

Please anyone teach me how to use the Riemann analytic solution in 2D. That is, the condition in the star region was usually taken by the cartesian 1D Riemann analytic solution then I tried to apply these values across the material interface in 2D.