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

  • Adimurthi (a1), Rajib Dutta (a1), G. D. Veerappa Gowda (a1) and Jérôme Jaffré (a2)

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.

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Keywords

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

  • Adimurthi (a1), Rajib Dutta (a1), G. D. Veerappa Gowda (a1) and Jérôme Jaffré (a2)

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