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Asymptotic expansion of a multiscale numerical scheme for compressible multiphase flow

Remi Abgrall 1, 2 Vincent Perrier 3
1 SCALAPPLIX - Algorithms and high performance computing for grand challenge applications
INRIA Futurs, Université Bordeaux Segalen - Bordeaux 2, Université Sciences et Technologies - Bordeaux 1, École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), CNRS - Centre National de la Recherche Scientifique : UMR5800
3 CONCHA - Complex Flow Simulation Codes based on High-order and Adaptive methods
INRIA Futurs, UPPA - Université de Pau et des Pays de l'Adour, CNRS - Centre National de la Recherche Scientifique : UMR5142
Abstract : 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 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.
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Submitted on : Sunday, July 12, 2009 - 10:45:43 PM
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  • HAL Id : inria-00403703, version 1

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Remi Abgrall, Vincent Perrier. Asymptotic expansion of a multiscale numerical scheme for compressible multiphase flow. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, Society for Industrial and Applied Mathematics, 2006, 5 (1), pp.84-115. ⟨inria-00403703⟩

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