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

Published online by Cambridge University Press:  26 September 2014

Adimurthi ,
Rajib Dutta ,
G. D. Veerappa Gowda  and
Jérôme Jaffré
Adimurthi
Affiliation:
TIFR-CAM, PB 6503, Sharadanagar, 560065 Bangalore, India.. aditi@math.tifrbng.res.in; rajib@math.tifrbng.res.in; gowda@math.tifrbng.res.in
Rajib Dutta
Affiliation:
TIFR-CAM, PB 6503, Sharadanagar, 560065 Bangalore, India.. aditi@math.tifrbng.res.in; rajib@math.tifrbng.res.in; gowda@math.tifrbng.res.in
G. D. Veerappa Gowda
Affiliation:
TIFR-CAM, PB 6503, Sharadanagar, 560065 Bangalore, India.. aditi@math.tifrbng.res.in; rajib@math.tifrbng.res.in; gowda@math.tifrbng.res.in
Jérôme Jaffré
Affiliation:
INRIA, BP 105, 78153 Le Chesnay Cedex, France.; jerome.jaffre@inria.fr
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Abstract

For scalar conservation laws in one space dimension with a flux function discontinuous inspace, 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. Forsolutions corresponding to a connection (A,B), there exists convergent numerical schemesbased 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., usedwidely 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 fromthe singular mapping technique of Temple and chain estimate of Adimurthi and Gowda, weprove the convergence of the schemes.

Keywords

Conservation lawsdiscontinuous fluxLax−Friedrichs schemesingular mappinginterface entropy condition(A,B)connection
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 48 , Issue 6 , November 2014 , pp. 1725 - 1755
Copyright
© EDP Sciences, SMAI, 2014

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