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

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

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 6, pp. 1725-1755.

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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