Interpolated pressure laws in two-fluid simulations and hyperbolicity

Philippe Helluy 1, 2 Jonathan Jung 1
2 TONUS - TOkamaks and NUmerical Simulations
IRMA - Institut de Recherche Mathématique Avancée, Inria Nancy - Grand Est
Abstract : We consider a two-fluid compressible flow. Each fluid obeys a stiffened gas pressure law. The continuous model is well defined without considering mixture regions. However, for numerical applications it is often necessary to consider artificial mixtures, because the two-fluid interface is diffused by the numerical scheme. We show that classic pressure law interpolations lead to a non-convex hyperbolicity domain and failure of well-known numerical schemes. We propose a physically relevant pressure law interpolation construction and show that it leads to a necessary modification of the pure phase pressure laws. We also propose a numerical scheme that permits to approximate the stiffened gas model without artificial mixture.
Type de document :
Chapitre d'ouvrage
Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects, Springer, pp.37-53, 2014
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Philippe Helluy, Jonathan Jung. Interpolated pressure laws in two-fluid simulations and hyperbolicity. Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects, Springer, pp.37-53, 2014. <hal-00957043>

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