Numerical Comparison of WENO Finite Volume and Runge–Kutta Discontinuous Galerkin Methods

Abstract

High order WENO (weighted essentially non-oscillatory) schemes and discontinuous Galerkin methods are two classes of high order, high resolution methods suitable for convection dominated simulations with possible discontinuous or sharp gradient solutions. In this paper we first review these two classes of methods, pointing out their similarities and differences in algorithm formulation, theoretical properties, implementation issues, applicability, and relative advantages. We then present some quantitative comparisons of the third order finite volume WENO methods and discontinuous Galerkin methods for a series of test problems to assess their relative merits in accuracy and CPU timing.