Numerical Methods for Gasdynamic Systems on Unstructured Meshes

摘要: This article considers stabilized finite element and volume discretization techniques for systems of conservation laws. Using newly developed in entropy symmetrization theory, simplified forms the Galerkin least-squares (GLS) discontinuous (DG) method are analyzed. The use variables yields numerical schemes which inherit global stability properties PDE system. Detailed consideration is given to Euler, Navier-Stokes, magneto-hydrodynamic (MHD) equations. Numerous calculations presented evaluate spatial accuracy feature resolution capability DG GLS discretizations. Next, upwind methods reviewed. Specifically considered generalizations Godunov’s high order unstructured meshes. An important component accurate Godunov reconstruction operator. A number operators reviewed based on Green-Gauss formulas as well approximation. Several theoretical results using maximum principle analysis method. To assess performance technique, various computational fluid dynamics provided.