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An efficient shock-capturing algorithm for compressible multicomponent problems. (English) Zbl 0934.76062
Summary: A simple shock-capturing approach to multicomponent flow problems is developed for compressible Euler equations with a stiffened gas equation of state in multiple space dimensions. The algorithm uses a quasi-conservative formulation of the equations, that is derived to ensure the correct fluid mixing when approximating the equations numerically with interfaces. A \(\gamma\)-based model and a volume-fraction model are described, and both of them are solved using the standard high-resolution wave propagation method for general hyperbolic systems of partial differential equations. Several calculations are presented with a Roe approximate Riemann solver that show accurate results obtained using the method without any spurious oscillations of pressure near the interfaces. We show the convergence of computed solutions to the correct weak ones for a two-dimensional Richtmyer-Meshkov unstable interface problem, where we perform a mesh-refinement study and also show front-tracking results for comparison. \(\copyright\) Academic Press.

76M20 Finite difference methods applied to problems in fluid mechanics
76L05 Shock waves and blast waves in fluid mechanics
76N15 Gas dynamics (general theory)
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