Is there any one knowing the exact solution method using Rankine-Hugoniot condition in the compressible flow? I am solving two-phase compressible flow but I had oscillation at the material interface. Someone recommended me that the exact solution only at the material interface is able to remove the oscillation by the interpolating method with the adjacent two cells(e.g. left and right)

interface

|

| |---o---|---o-|-|---o---|

i-1 i | i+1

|

The approach is that the contact discontinuity at the material interface has two wave pattern moving left and right. Values at i-1 and i+1 have pure material properties(e.g. water and gas) while value at i has a mixed material properties so that the oscillation used to be arisen across few cells.

If someone know how to compute the Riemann problem or where good references are available, please help me. Thanks in advance.

interface

| |------o-------|------o---|--|------o-------|

i-1 i | i+1

Main reference was that "treatment of interface problem with Godunov-type schemes" written by J.P. Cocchi, R. Saurel, 1996

Please help me

Maybe you can find what you are looking for in

Generalized Riemann Problems in Computational Fluid Dynamics, by Matania Ben-Artzi and Joseph Falcovitz

http://www.cfd-online.com/Books/show...hp?book_id=498