help:gas-water shocktube problem
 

I am working on gas-water shocktube problem ,and I want a preference "exact" solution to check my numerical results, but I don't know how to make it. I have seen the exact solution figure in some paper, but I don't know how they get it, who can help me?

my example is like this: Sod model (rho, u, p, gama)-----------

Wl= (1, 0, 2.5, 1.2) Wr= (0.125, 0, 0.1, 1.4)