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Hyperbolic relaxation models for granular flows

Published online by Cambridge University Press:  27 January 2010

Thierry Gallouët ,
Philippe Helluy ,
Jean-Marc Hérard  and
Julien Nussbaum
Thierry Gallouët
Affiliation:
IRMA, 7 rue Descartes, 67084 Strasbourg Cedex, France. helluy@math.u-strasbg.fr
Philippe Helluy
Affiliation:
IRMA, 7 rue Descartes, 67084 Strasbourg Cedex, France. helluy@math.u-strasbg.fr
Jean-Marc Hérard
Affiliation:
IRMA, 7 rue Descartes, 67084 Strasbourg Cedex, France. helluy@math.u-strasbg.fr
Julien Nussbaum
Affiliation:
IRMA, 7 rue Descartes, 67084 Strasbourg Cedex, France. helluy@math.u-strasbg.fr
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Abstract

In this work we describe an efficient model for the simulation of atwo-phase flow made of a gas and a granular solid. The starting point is the two-velocitytwo-pressure model of Baer and Nunziato [Int. J. Multiph. Flow16 (1986) 861–889]. The model is supplemented bya relaxation source term in orderto take into account the pressure equilibrium between the two phases andthe granular stress in the solid phase. We show that the relaxationprocess can be made thermodynamically coherent with an adequate choice of the granular stress. We then propose a numerical scheme based on a splitting approach. Each step of the time marchingalgorithm is made of two stages. In the first stage, the homogeneous convection equations are solved by a standard finite volume Rusanov scheme. In the second stage, the volume fractionis updated in order to take into account the equilibrium source term.The whole procedure is entropy dissipative.For simplified pressure laws (stiffened gas laws) we are able to prove that the approximated volumefraction stays within its natural bounds.

Keywords

Two-phase flowhyperbolicityrelaxationfinite volumeentropy
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 44 , Issue 2 , March 2010 , pp. 371 - 400
Copyright
© EDP Sciences, SMAI, 2010

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References

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