Entropy-TVD Scheme for Nonlinear Scalar Conservation Laws

Authors:
Rongsan Chen;De-Kang Mao
Affiliations:
School of Mathematics and Physics, China University of Geosciences, Wuhan, P.R. China 430074;Department of Mathematics, Shanghai University, Shanghai, P.R. China 200444
Venue:
Journal of Scientific Computing
Year:
2011

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Abstract

In this paper, we develop a so-called Entropy-TVD scheme for the non-linear scalar conservation laws. The scheme simultaneously simulates the solution and one of its entropy, and in doing so the numerical dissipation is reduced by carefully computing the entropy decrease. We prove that the scheme is feasible and TVD and satisfies the entropy condition. We also prove that the local truncation error of the scheme is of first-order. However, numerical tests show that the scheme has a second-order convergence rate, an order higher than its truncation error, in computing smooth solution, and in many cases is better than a second-order ENO scheme in resolving shocks and corners of rarefaction waves.