About gas-water two-phase Riemann problem

Ma, Dong-Jun

There is a gas-water two-phase compressible multifluid Riemann problem, governed by the stiffened gas equation of state:

p(\rho,e)=(\gamma-1)\rho e - \gamma p_\infty

For gas, \gamma=1.4, p_\infty=0; For water, \gamma=4.4, p_infty=6.E+8

And the initial conditions are For gas, \rho=1.2 Kg/m^3, p=1.E+5 Pa, velocity=0; For water,\rho=1000 Kg/m^3, p=1.E+9 Pa, velocity=0.

I have used a simple mixture-type Eulerian numerical method proposed by Saurel/Abgrall(SIAM 1998) or Shyue(JCP 1999) to simulate this problem, but the result is very poor because the pressure curve is very different from the exact solution. It is very obvious in the pressure plot for using log curve.

I think this problem is very stiff and the density ratio and pressure ratio is very high(1000/1.2 and 10000/1).

Has someone done some work in this problem and to tell me how to solve this problem?

Ma, Dong-Jun