A low numerical dissipation immersed interface method for the compressible Navier-Stokes equations
Journal of Computational Physics
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This paper concerns the numerical approximation of the Euler equations for multicomponent flows. A numerical method is proposed to reduce spurious oscillations that classically occur around material interfaces. It is based on the explicit simplified interface method (ESIM), previously developed in the linear case of acoustics with stationary interfaces [J. Piraux and B. Lombard, J. Comput. Phys., 168 (2001), pp. 227--248]. This technique amounts to a higher-order extension of the ghost fluid method introduced in Euler multicomponent flows [R. P. Fedkiw, T. Aslam, B. Merriman, and S. Osher, J. Comput. Phys., 152 (1999), pp. 457--492]. The ESIM is coupled to sophisticated shock-capturing schemes for time-marching, and to level-sets for tracking material interfaces. Jump conditions satisfied by the exact solution and by its spatial derivative are incorporated in numerical schemes, ensuring a subcell resolution of material interfaces inside the meshing. Numerical experiments show the efficiency of the method for rich-structured flows.