Monotone (A,B) entropy stable numerical scheme for Scalar Conservation Laws with discontinuous flux

Adimurthi; Rajib Dutta; G. D. Veerappa Gowda; Jérôme Jaffré

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2014)

  • Volume: 48, Issue: 6, page 1725-1755
  • ISSN: 0764-583X

Abstract

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For scalar conservation laws in one space dimension with a flux function discontinuous in space, there exist infinitely many classes of solutions which are L1 contractive. Each class is characterized by a connection (A,B) which determines the interface entropy. For solutions corresponding to a connection (A,B), there exists convergent numerical schemes based on Godunov or Engquist−Osher schemes. The natural question is how to obtain schemes, corresponding to computationally less expensive monotone schemes like Lax−Friedrichs etc., used widely in applications. In this paper we completely answer this question for more general (A,B) stable monotone schemes using a novel construction of interface flux function. Then from the singular mapping technique of Temple and chain estimate of Adimurthi and Gowda, we prove the convergence of the schemes.

How to cite

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Adimurthi, et al. "Monotone (A,B) entropy stable numerical scheme for Scalar Conservation Laws with discontinuous flux." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 48.6 (2014): 1725-1755. <http://eudml.org/doc/273304>.

@article{Adimurthi2014,
abstract = {For scalar conservation laws in one space dimension with a flux function discontinuous in space, there exist infinitely many classes of solutions which are L1 contractive. Each class is characterized by a connection (A,B) which determines the interface entropy. For solutions corresponding to a connection (A,B), there exists convergent numerical schemes based on Godunov or Engquist−Osher schemes. The natural question is how to obtain schemes, corresponding to computationally less expensive monotone schemes like Lax−Friedrichs etc., used widely in applications. In this paper we completely answer this question for more general (A,B) stable monotone schemes using a novel construction of interface flux function. Then from the singular mapping technique of Temple and chain estimate of Adimurthi and Gowda, we prove the convergence of the schemes.},
author = {Adimurthi, Dutta, Rajib, Veerappa Gowda, G. D., Jaffré, Jérôme},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {conservation laws; discontinuous flux; Lax−Friedrichs scheme; singular mapping; interface entropy condition; (A; b)connection; connection; Lax-Friedrichs scheme; stability; convergece},
language = {eng},
number = {6},
pages = {1725-1755},
publisher = {EDP-Sciences},
title = {Monotone (A,B) entropy stable numerical scheme for Scalar Conservation Laws with discontinuous flux},
url = {http://eudml.org/doc/273304},
volume = {48},
year = {2014},
}

TY - JOUR
AU - Adimurthi
AU - Dutta, Rajib
AU - Veerappa Gowda, G. D.
AU - Jaffré, Jérôme
TI - Monotone (A,B) entropy stable numerical scheme for Scalar Conservation Laws with discontinuous flux
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2014
PB - EDP-Sciences
VL - 48
IS - 6
SP - 1725
EP - 1755
AB - For scalar conservation laws in one space dimension with a flux function discontinuous in space, there exist infinitely many classes of solutions which are L1 contractive. Each class is characterized by a connection (A,B) which determines the interface entropy. For solutions corresponding to a connection (A,B), there exists convergent numerical schemes based on Godunov or Engquist−Osher schemes. The natural question is how to obtain schemes, corresponding to computationally less expensive monotone schemes like Lax−Friedrichs etc., used widely in applications. In this paper we completely answer this question for more general (A,B) stable monotone schemes using a novel construction of interface flux function. Then from the singular mapping technique of Temple and chain estimate of Adimurthi and Gowda, we prove the convergence of the schemes.
LA - eng
KW - conservation laws; discontinuous flux; Lax−Friedrichs scheme; singular mapping; interface entropy condition; (A; b)connection; connection; Lax-Friedrichs scheme; stability; convergece
UR - http://eudml.org/doc/273304
ER -

References

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