# The numerical interface coupling of nonlinear hyperbolic systems of conservation laws: II. The case of systems

Edwige Godlewski; Kim-Claire Le Thanh; Pierre-Arnaud Raviart

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 39, Issue: 4, page 649-692
- ISSN: 0764-583X

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topGodlewski, Edwige, Le Thanh, Kim-Claire, and Raviart, Pierre-Arnaud. "The numerical interface coupling of nonlinear hyperbolic systems of conservation laws: II. The case of systems." ESAIM: Mathematical Modelling and Numerical Analysis 39.4 (2010): 649-692. <http://eudml.org/doc/194281>.

@article{Godlewski2010,

abstract = {
We study
the theoretical and numerical
coupling of two hyperbolic systems of conservation laws at a fixed interface. As already proven in the scalar case, the coupling
preserves in a weak sense the continuity of the solution at the interface
without imposing the overall conservativity of the coupled model. We develop a detailed analysis of the coupling in
the linear case. In the nonlinear case, we either use a linearized approach or a coupling method based on the solution of a Riemann problem. We discuss both approaches in the case of the coupling of two fluid models at a material contact discontinuity, the models being the usual gas dynamics equations with different equations of
state. We also study the coupling of two-temperature plasma fluid models and illustrate the approach by numerical
simulations.
},

author = {Godlewski, Edwige, Le Thanh, Kim-Claire, Raviart, Pierre-Arnaud},

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

keywords = {Conservation laws; Riemann problem; boundary value problems; interface coupling; finite volume schemes.; conservation laws; finite volume schemes; numerical examples; nonlinear hyperbolic systems; fluid models; gas dynamic; plasma},

language = {eng},

month = {3},

number = {4},

pages = {649-692},

publisher = {EDP Sciences},

title = {The numerical interface coupling of nonlinear hyperbolic systems of conservation laws: II. The case of systems},

url = {http://eudml.org/doc/194281},

volume = {39},

year = {2010},

}

TY - JOUR

AU - Godlewski, Edwige

AU - Le Thanh, Kim-Claire

AU - Raviart, Pierre-Arnaud

TI - The numerical interface coupling of nonlinear hyperbolic systems of conservation laws: II. The case of systems

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 39

IS - 4

SP - 649

EP - 692

AB -
We study
the theoretical and numerical
coupling of two hyperbolic systems of conservation laws at a fixed interface. As already proven in the scalar case, the coupling
preserves in a weak sense the continuity of the solution at the interface
without imposing the overall conservativity of the coupled model. We develop a detailed analysis of the coupling in
the linear case. In the nonlinear case, we either use a linearized approach or a coupling method based on the solution of a Riemann problem. We discuss both approaches in the case of the coupling of two fluid models at a material contact discontinuity, the models being the usual gas dynamics equations with different equations of
state. We also study the coupling of two-temperature plasma fluid models and illustrate the approach by numerical
simulations.

LA - eng

KW - Conservation laws; Riemann problem; boundary value problems; interface coupling; finite volume schemes.; conservation laws; finite volume schemes; numerical examples; nonlinear hyperbolic systems; fluid models; gas dynamic; plasma

UR - http://eudml.org/doc/194281

ER -

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