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A multiphase Godunov method for compressible multifluid and multiphase flows. (English) Zbl 0937.76053
Summary: We propose a new model and a solution method for two-phase compressible flows. The model involves six equations obtained from conservation principles applied to each phase, completed by a seventh equation for the evolution of the volume fraction. The model is valid for fluid mixtures, as well as for pure fluids. The system of partial differential equations is hyperbolic. Hyperbolicity is obtained because each phase is considered to be compressible. Two difficulties arise for the solution: 1) one of the equations is written in non-conservative form; 2) non-conservative terms exist in the momentum and energy equations. We propose a robust and accurate discretisation of these terms. The method solves the same system at each mesh point with the same algorithm. Several test cases provide reliable results. The method is also able to compute strong shock waves and deal with complex equations of state. \(\copyright\) Academic Press.

76M20 Finite difference methods applied to problems in fluid mechanics
76T99 Multiphase and multicomponent flows
80A22 Stefan problems, phase changes, etc.
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