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A robust entropy−satisfying finite volume scheme for theisentropic Baer−Nunziato model

Published online by Cambridge University Press:  18 December 2013

Frédéric Coquel ,
Jean-Marc Hérard ,
Khaled Saleh  and
Nicolas Seguin
Frédéric Coquel
Affiliation:
CMAP, École Polytechnique CNRS, UMR 7641, Route de Saclay, 91128 Palaiseau Cedex, France.
Jean-Marc Hérard
Affiliation:
EDF-R&D, Département MFEE, 6 Quai Watier, 78401 Chatou Cedex, France.
Khaled Saleh
Affiliation:
EDF-R&D, Département MFEE, 6 Quai Watier, 78401 Chatou Cedex, France. UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, 75005, Paris, France.. [email protected] CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, 75005, Paris, France.
Nicolas Seguin
Affiliation:
UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, 75005, Paris, France.. [email protected] CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, 75005, Paris, France. Inria Paris-Rocquencourt, BP 105, 78153 Le Chesnay Cedex, France.
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Abstract

We construct an approximate Riemann solver for the isentropic Baer−Nunziato two-phaseflow model, that is able to cope with arbitrarily small values of the statistical phasefractions. The solver relies on a relaxation approximation of the model for which theRiemann problem is exactly solved for subsonic relative speeds. In an original manner, theRiemann solutions to the linearly degenerate relaxation system are allowed to dissipatethe total energy in the vanishing phase regimes, thereby enforcing the robustness andstability of the method in the limits of small phase fractions. The scheme is proved tosatisfy a discrete entropy inequality and to preserve positive values of the statisticalfractions and densities. The numerical simulations show a much higher precision and a morereduced computational cost (for comparable accuracy) than standard numerical schemes usedin the nuclear industry. Finally, two test-cases assess the good behavior of the schemewhen approximating vanishing phase solutions.

Keywords

Two-phase flowsentropy-satisfying methodsrelaxation techniquesRiemann problem
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 48 , Issue 1 , January 2014 , pp. 165 - 206
Copyright
© EDP Sciences, SMAI 2013

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