INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2000; 00:1–6 Prepared using nmeauth.cls [Version: 2002/09/18 v2.02] On the accuracy of Finite Volume and Discontinuous Galerkin discretizations for compressible flow on unstructured grids X. Nogueira a , L. Cueto-Felgueroso b , I. Colominas a∗ ,H.G´omez a,c , F. Navarrina a , M. Casteleiro a a Group of Numerical Methods in Engineering, GMNI, Dept. of Applied Mathematics Civil Engineering School, Universidade da Coru˜ na Campus de Elvi˜ na, 15071, A Coru˜ na, SPAIN b Aerospace Computational Design Laboratory, Dept. of Aeronautics and Astronautics Massachusetts Institute of Technology 77 Massachusetts Ave., Cambridge, MA 02139, U.S.A c Institute for Computational Engineering and Sciences The University of Texas at Austin 1 University Station, C0200 201 E. 24th Street, Austin, TX 78712 SUMMARY 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 finite volume scheme is consistently more accurate in the present tests. Furthermore, the DG scheme requires a larger number of degrees of freedom than the FV-MLS method. Copyright c  2000 John Wiley & Sons, Ltd. key words: Compressible flow. Finite Volume method. Discontinuous Galerkin method. High- resolution schemes. High-order methods. Moving Least-Squares approximation. Unstructured grids. 1. INTRODUCTION The field of Computational Fluid Dynamics has developed greatly during the last decade. The increase of computer capabilities has allowed the possibility of solving progressively more complex problems, which require numerical methods with the capability for capturing the flow features in a very accurate way. DNS and LES of turbulent flows, or aeroacoustics simulations * Correspondence to: E.T.S. de Ingenieros de Caminos, Canales y Puertos, Universidade da Coru˜ na, Campus de Elvi˜ na, 15071 A Coru˜ na, Spain. Email: icolominas@udc.es Received Yesterday Copyright c  2000 John Wiley & Sons, Ltd. Revised Today