On the accuracy of finite volume and discontinuous Galerkin discretizations for compressible flow on unstructured grids

This paper presents a comparison between two high-order methods. The first one is a high-order finite volume (FV) discretization on unstructured grids that uses a meshfree method (moving least squares (MLS)) in order to construct a piecewise polynomial reconstruction and evaluate the viscous fluxes. The second method is a discontinuous Galerkin (DG) scheme. Numerical examples of inviscid and viscous flows are presented and the solutions are compared. The accuracy of both methods, for the same grid resolution, is similar, although the DG scheme requires a larger number of degrees of freedom than the FV-MLS method. Copyright (C) 2009 John Wiley & Sons, Ltd.