Entropy-TVD Scheme for Nonlinear Scalar Conservation Laws
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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.
KeywordsEntropy decrease Numerical entropy Step-reconstruction Truncation error
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- 2.Cui, Y.F., Mao, D.-K.: Error self-canceling of a difference scheme maintaining two conservation laws for linear advection equation. Math. Comput. (submitted) Google Scholar
- 7.Lagoutière, F.: Non-dissipative entropic discontinuous reconstruction schemes for hyperbolic conservation laws. Pub Labo JL Lions, R06017 (2006) Google Scholar
- 8.LeVeque, R.J.: Numerical Methods for Conservation Lws. Birkhäuser, Basel (1990) Google Scholar
- 10.Li, H.X.: Second-order entropy dissipation scheme for scalar conservation laws in one space dimension. Master’s thesis, No. 11903-99118086, Shanghai University (in Chinese) (1999) Google Scholar