A DG HWENO scheme for hyperbolic equations

Abstract

In an effort to build a higher order discontinuous Galerkin (DG) finite element solver for the nonlinear Euler equations of gas dynamics, we develop a shock capturing scheme for hyperbolic equations. The Hermite Weighted Essentially Non-Oscillatory (HWENO) methodology introduced by Qiu [10, 14] is used as the starting point for the proposed limiter. We present a general approach for building a limiter for Runge-Kutta time marching schemes which reconstructs the higher order moments of troubled cells using only information of neighboring cells. This technique is used to develop a limiter in 1-D for P₂ to P₅ interpolants on non-uniform grids and in 2-D for P₂ interpolants on triangular unstructured grids. Numerical results for this limiter are presented for Burgers equation.