Discontinuous Galerkin finite element method with anisotropic local grid refinement for inviscid compressible flows

A new discretization method for the three-dimensional Euler equations of gas dynamics is presented, which is based on the discontinuous Galerkin finite element method. Special attention is paid to an efficient implementation of the discontinuous Galerkin method that minimizes the number of flux calculations, which is generally the most expensive part of the algorithm. In addition a detailed discussion of the truncation error of the presented algorithm is given. The discretization of the Euler equations is combined with anisotropic grid refinement of an unstructured, hexahedron-type grid to achieve optimal resolution in areas with shocks, vortices, and other localized flow phenomena. The data structure and searching algorithms necessary for efficient calculation on highly irregular grids obtained with local grid refinement are discussed in detail. The method is demonstrated with calculations of the supersonic flow over a 10? ramp and the ONERA M6 wing under transsonic flow conditions