Numerical boundary layers for hyperbolic systems in 1-D

Claire Chainais-Hillairet; Emmanuel Grenier

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 35, Issue: 1, page 91-106
  • ISSN: 0764-583X

Abstract

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The aim of this paper is to investigate the stability of boundary layers which appear in numerical solutions of hyperbolic systems of conservation laws in one space dimension on regular meshes. We prove stability under a size condition for Lax Friedrichs type schemes and inconditionnal stability in the scalar case. Examples of unstable boundary layers are also given.

How to cite

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Chainais-Hillairet, Claire, and Grenier, Emmanuel. "Numerical boundary layers for hyperbolic systems in 1-D." ESAIM: Mathematical Modelling and Numerical Analysis 35.1 (2010): 91-106. <http://eudml.org/doc/197550>.

@article{Chainais2010,
abstract = { The aim of this paper is to investigate the stability of boundary layers which appear in numerical solutions of hyperbolic systems of conservation laws in one space dimension on regular meshes. We prove stability under a size condition for Lax Friedrichs type schemes and inconditionnal stability in the scalar case. Examples of unstable boundary layers are also given. },
author = {Chainais-Hillairet, Claire, Grenier, Emmanuel},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Boundary layers stability.; boundary layers stability; hyperbolic systems of conservation laws; Lax-Friedrichs scheme; numerical examples},
language = {eng},
month = {3},
number = {1},
pages = {91-106},
publisher = {EDP Sciences},
title = {Numerical boundary layers for hyperbolic systems in 1-D},
url = {http://eudml.org/doc/197550},
volume = {35},
year = {2010},
}

TY - JOUR
AU - Chainais-Hillairet, Claire
AU - Grenier, Emmanuel
TI - Numerical boundary layers for hyperbolic systems in 1-D
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 35
IS - 1
SP - 91
EP - 106
AB - The aim of this paper is to investigate the stability of boundary layers which appear in numerical solutions of hyperbolic systems of conservation laws in one space dimension on regular meshes. We prove stability under a size condition for Lax Friedrichs type schemes and inconditionnal stability in the scalar case. Examples of unstable boundary layers are also given.
LA - eng
KW - Boundary layers stability.; boundary layers stability; hyperbolic systems of conservation laws; Lax-Friedrichs scheme; numerical examples
UR - http://eudml.org/doc/197550
ER -

References

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  10. T.T. Li and W.C. Yu, Boundary value problems for quasilinear hyperbolic systems. Math. series V. Duke Univ., Durham (1985).  Zbl0627.35001
  11. T.P. Liu, Nonlinear stability of shock waves for viscous conservation laws. Mem. Amer. Math. Soc.56 (1985) 108 p.  Zbl0576.35077
  12. J.B. Rauch and F.J. Massey, III, Differentiability of solutions to hyperbolic initial boundary value problems. Trans. Amer. Math. Soc.189 (1974) 303-318.  Zbl0282.35014
  13. D. Serre, Sur la stabilité des couches limites de viscosité, preprint.  Zbl0963.35009
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