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

Abstract

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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.

How to cite

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Godlewski, 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 -

References

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