# Hyperbolic relaxation models for granular flows

Thierry Gallouët; Philippe Helluy; Jean-Marc Hérard; Julien Nussbaum

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 44, Issue: 2, page 371-400
- ISSN: 0764-583X

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topGallouët, Thierry, et al. "Hyperbolic relaxation models for granular flows." ESAIM: Mathematical Modelling and Numerical Analysis 44.2 (2010): 371-400. <http://eudml.org/doc/250711>.

@article{Gallouët2010,

abstract = {
In this work we describe an efficient model for the simulation of a
two-phase flow made of a gas and a granular solid. The starting point is the two-velocity
two-pressure model of Baer and Nunziato
[Int. J. Multiph. Flow16 (1986) 861–889].
The model is supplemented by
a relaxation source term in order
to take into account the pressure equilibrium between the two phases and
the granular stress in the solid phase. We show that the relaxation
process 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 marching
algorithm 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 fraction
is 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 volume
fraction stays within its natural bounds.
},

author = {Gallouët, Thierry, Helluy, Philippe, Hérard, Jean-Marc, Nussbaum, Julien},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Two-phase flow; hyperbolicity; relaxation; finite volume;
entropy; two-phase flow; entropy},

language = {eng},

month = {3},

number = {2},

pages = {371-400},

publisher = {EDP Sciences},

title = {Hyperbolic relaxation models for granular flows},

url = {http://eudml.org/doc/250711},

volume = {44},

year = {2010},

}

TY - JOUR

AU - Gallouët, Thierry

AU - Helluy, Philippe

AU - Hérard, Jean-Marc

AU - Nussbaum, Julien

TI - Hyperbolic relaxation models for granular flows

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 44

IS - 2

SP - 371

EP - 400

AB -
In this work we describe an efficient model for the simulation of a
two-phase flow made of a gas and a granular solid. The starting point is the two-velocity
two-pressure model of Baer and Nunziato
[Int. J. Multiph. Flow16 (1986) 861–889].
The model is supplemented by
a relaxation source term in order
to take into account the pressure equilibrium between the two phases and
the granular stress in the solid phase. We show that the relaxation
process 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 marching
algorithm 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 fraction
is 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 volume
fraction stays within its natural bounds.

LA - eng

KW - Two-phase flow; hyperbolicity; relaxation; finite volume;
entropy; two-phase flow; entropy

UR - http://eudml.org/doc/250711

ER -

## References

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