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

Adimurthi, . ; Dutta, Rajib ; Veerappa Gowda, G. D. ; Jaffré, Jérôme (2014) Monotone (A,B) entropy stable numerical scheme for Scalar Conservation Laws with discontinuous flux ESAIM: Mathematical Modelling and Numerical Analysis, 48 (6). pp. 1725-1755. ISSN 0764-583X

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Official URL: https://www.esaim-m2an.org/articles/m2an/abs/2014/...

Related URL: http://dx.doi.org/10.1051/m2an/2014017

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.

Item Type:Article
Source:Copyright of this article belongs to EDP Sciences.
Keywords:Conservation Laws; Discontinuous Flux; Lax−Friedrichs Scheme; Singular Mapping; Interface Entropy Condition; (A,B)Connection
ID Code:112156
Deposited On:31 Jan 2018 04:31
Last Modified:31 Jan 2018 04:31

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