I am solving a strong gas-water shock tube problem. Due to the strong shock, shock and contact discontinuity are close together. They are separated by only about 5 cells or less. Due to these, I can't capture the shock and contact discontinuity appropriately. In fact, ahead of contact discontinuity(right to it), the solution goes to a unphysical things... For the left to the contact discontinuity(left star region), the numerical solution seems right...

Does anyone know how to treat this case which the shock and contact discontinuity are close together?

Thanks in advance.

Refine the grid in that region. Thats the only way to capture all those features.