Comparison of mesh adaptation techniques for high-speed compressible flow problems : the scramjet testcase for the Euler equations

Abstract

Paper presented at the 8th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Mauritius, 11-13 July, 2011.We consider the classical Scramjet test problem for the compressible Euler equations. Our objective is the comparison of different mesh refinement techniques: on the one hand hierarchical refinement of quadrilateral meshes with hanging nodes, on the other hand isotropic and anisotropic triangular meshes. Discretization of the Euler equations written in conservative variables is done by a standard discontinuous finite element (Galerkin) method. In each step of the algorithm, an error indicator is used to guide the mesh modification. Here we implemented as criterion for quadrilateral mesh refinement, indicators based on the physical variables jumps, as they are usually used in practice. Comparison is done with respect to the resolution of certain physical features, and also with respect to CPU-time, which appears to be fair, since the different algorithms are programmed within the same program handling the different ingredients in a uniform manner. For the anisotropic mesh refinement algorithm we use BAMG. All other algorithms have been implemented by the authors in the C++-library Concha.