Numerical method of the Riemann problem for two-dimensional multi-fluid flows with general equation of state

Based on the classical Roe method, we develop an interface capture method according to the general equation of state, and extend the single-fluid Roe method to the two-dimensional (2D) multi-fluid flows, as well as construct the continuous Roe matrix for the whole flow field. The interface capture equations and fluid dynamic conservative equations are coupled together and solved by using any high-resolution schemes that usually suit for the single-fluid flows. Some numerical examples are given to illustrate the solution of 1D and 2D multi-fluid Riemann problems.