High-order entropy stable schemes based on a local adaptive WENO viscosity for degenerate convection-diffusion equations

Abstract

In this work, high-order entropy stable finite difference methods are constructed to solve systems of degenerate convection-diffusion partial differential equations. The approximation of the convective term is based on high-order entropy stable fluxes under a TeCNO scheme formulation and for the diffusive term high-order entropy conservative fluxes are computed by considering linear combinations of second-order approximations. Numerical simulations show that the proposed high-order entropy conservative schemes provide a convergence rate better than conventional WENO methods. To obtain entropy stability, a local adaptive artificial viscosity is included using weighted essentially nonoscillatory reconstructions satisfying a local sign property at discontinuities. Different WENO interpolations for the local artificial viscosity are numerically analyzed being the fast and optimal WENO interpolation (FOWENO), the one that introduces less spurious oscillations with a lower computational cost.