The fourth order non oscillatory entropy stable scheme for degenerate convection diffusion equation part I

Abstract

In this article, we formulate an entropy stable scheme for nonlinear degenerate convection diffusion equation with viscous terms in non-conservative formulations. Here in we extend the S.Jerez idea of first order entropy stable convection scheme for semi discrete scheme in to fourth order scheme using finite central difference scheme. Major advantage of this work is fourth order accuracy of the solution and fixed numerical diffusion term which can provide the non- oscillatory solution. Finally, few computational analyses are given to shown the accuracy of entropy stable scheme for degenerate parabolic equations.