A second-order γ-model BGK scheme for multimaterial compressible flows

We present a second-order γ-model BGK scheme for compressible multimaterial flows, which extends the authors' earlier work on a first-order scheme [S. Jiang, G. Ni, A γ-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 γ-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.