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In this paper, we propose approximate solvers for two-phase fluids with general equations of state (EOS) in high dimension. The standard finite volume scheme is used for each fluid away from material interface. The two-phase interfaces are captured by the level set method coupled with a multi-resolution algorithm. For the Riemann solver of two-phase fluids with general equations of state, we construct an iterative approximation method by the solver for binomial equations of state. The velocity of the interface and the interface exchange fluxes are obtained precisely. With the help of the adaptive multi-resolution algorithms, we extend the method to three space dimensions conveniently. Numerical examples are carried out to demonstrate the strength and robustness of this method.

We present a second-order @c-model BGK scheme for compressible multimaterial flows, which extends the authors' earlier work on a first-order scheme [S. Jiang, G. Ni, A @c-model BGK scheme for compressible multifluids, Internat. J. Numer. Methods Fluids 46 (2004) 163-182]. The scheme is based on the incorporation of a conservative @c-model scheme given in [R. Abgrall, How to prevent pressure oscillations in multicomponent flow calculations: A quasi conservative approach, J. Comput. Phys. 125 (1996) 150-160] into the gas kinetic BGK scheme [K.H. Prendergast, K. Xu, Numerical hydrodynamics from gas-kinetic theory, J. Comput. Phys. 109 (1993) 53-66; K. Xu, K.H. Prendergast, Numerical Navier-Stokes solutions from gas kinetic theory, J. Comput. Phys. 114 (1994) 9-17]. Several numerical examples presented in this paper validate the scheme in numerical simulations of compressible multifluids.