High Order Finite Difference and Finite Volume WENO Schemes and Discontinuous Galerkin Methods for CFD

In recent years high order numerical methods have been widely used in computational fluid dynamics CFD, to effectively resolve complex flow features using meshes which are reasonable for todays computers. In this paper we review and compare three types of high order methods being used in CFD, namely the weighted essentially non-oscillatory WENO finite difference methods, the WENO finite volume methods, and the discontinuous Galerkin DG finite element methods. We summarize the main features of these methods, from a practical users point of view, indicate their applicability and relative strength, and show a few selected numerical examples to demonstrate their performance on illustrative model CFD problems.