ABGRALL, Remi; PERRIER, Vincent

doi:10.1137/050623851

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ABGRALL, Remi
Institut de Mathématiques de Bordeaux [IMB]
Algorithms and high performance computing for grand challenge applications [SCALAPPLIX]

PERRIER, Vincent
Centre d'Etudes Lasers Intenses et Applications [CELIA]
Institut de Mathématiques de Bordeaux [IMB]
Algorithms and high performance computing for grand challenge applications [SCALAPPLIX]

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Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal. 2006-01-01, vol. 5, n° 1, p. 84-115

Society for Industrial and Applied Mathematics

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The simulation of compressible multiphase problems is a difficult task for modelization and mathematical reasons. Here, thanks to a probabilistic multiscale interpretation of multiphase flows, we construct a numerical scheme that provides a solution to these difficulties. Three types of terms can be identified in the scheme in addition to the temporal term. One is a conservative term, the second one plays the role of a nonconservative term that is related to interfacial quantities, and the last one is a relaxation term that is associated with acoustic phenomena. The key feature of the scheme is that it is {\em locally\/} conservative, contrarily to many other schemes devoted to compressible multiphase problems. In many physical situations, it is reasonable to assume that the relaxation is instantaneous. We present an asymptotic expansion of the scheme that keeps the local conservation properties of the original scheme. The asymptotic expansion relies on the understanding of an equilibrium variety. Its structure depends, in principle, on the Riemann solver. We show that it is not the case for several standard solvers, and hence this variety is characterized by the local pressure and velocity of the flow. Several numerical test cases are presented in order to demonstrate the potential of this technique.< Réduire

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Riemann solvers

compressible multiphase flows

asymptotic expansion

Riemann solvers

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Asymptotic Expansion of a Multiscale Numerical Scheme for Compressible Multiphase Flow

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