Entropy-Monotone Scheme for Nonlinear Scalar Conservation Laws

The Entropy-TVD scheme was developed for the non-linear scalar conservation laws in [1]. The scheme with step reconstruction simultaneously compute the two numerical entities, the numerical solution and the numerical entropy, and numerical examples show that the scheme provides a super-convergence rate. In this paper, we present an Entropy-Monotone scheme with linear reconstruction for the non-linear scalar conservation laws. The GRP fluxes are used to compute numerical fluxes. Numerical tests show that the convergent rates of Entropy-Monotone scheme are more stable than Entropy-TVD scheme and Entropy-Monotone scheme has better resolution of shocks and corners of rarefaction waves.