I am solving two-phase flow when the strong shock is existed.

<Air-Water shock tube initial condition>

(Rho_L,u_L,p_L,gamma_L)=1000,0.0,10^9,4.4 (Rho_R,u_R,p_R,gamma_R)= 50,0.0,10^5,1.4

The initial speeds of sound are abt.2000 and 50, respectively.

In my previous simulations, I usually took cfl=0.2~0.5 and it worked well.

But in above set, I couldn't advance the simulation with usual cfl number I used before. Actually, the cfl I am still running is 0.0001. It's unusual. I couldn't make sure in terms of results and stability since it is still running.

Does anyone experience this kind of problem before?

And I am wondering about the importance of the CFL number in the multi-phase simulation.

Compute the local CFL number at each grid point/cell. For unsteady problems, you will have to take the minimum of these local values. So if your grid is clustered in some region or the physics in some region dictates small time steps, then you end up with these problems. Just compute local time steps and see in which regions you get very small time steps. That might tell you something.