I am solving two-phase shock tube. By an initial condition, the final state of profiles shows the contact discontinuity and the shock front are very close together. Due to such close placement of both of them, the numerical simulation fail to get the reasonable result. I am thinking the reasons.

First, I am using local Lax-Friderich numerical scheme which is least simple but most diffusive one. Thus, due to the relatively large diffusion, the numerical simulation lead to fail Second, I am using minmod limiter which is also least simple but most diffusive one. Thus, it also leads to a relatively large diffusion across the region where the contact discontinuity and shock front closely are located.

How do you think my guesses?

You are right in your guesses. You can try to use characteristic variables. Perform both limiting and flux computation in characteristic variables. This is very common in DG methods. You can consult some DGFEM papers for the details.

I found something after then. Minmod and moment limiter can't give me a reasonable profile even though they worked very well for the common shock tube problem describing by gamma=1.4.

After many reviewing papers, I found another approach named 'maxmod coupled with minmod' can capture the desirable profiles in a challenging example but it still contains wrong features due to some mis-implementation. Have you hear about that?

I found it in the paper, 'A problem-independent limiter for high-order runge-kutta discontinuous galerkin methods',A.Burbeau, Journal of computational physics 169, 111-150(2001).

Due to complex notations, I couldn't fully understand his approach. I am still doing it.

If you experienced it before, please advice me.

Thanks in advance.