Professor Yu Xijun Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics, Beijing China

Three Dimenional Discontinuous Galerkin Methods for Euler Equations on the Adaptive Conforming Meshes

Abstract

  In the numerical simulation of three dimensional fluid dynamical equations, the huge computational quantity is a main challenge problem. In this paper, the discontinuous Galerkin (DG) finite element method [1] combined with the adaptive mesh refinement (AMR) [2, 3] is studied to solve the three dimensional Euler equations based on conforming unstructured tetrahedron mesh, that is according the equation solution variation to refine and coarsen grids so as to decrease total mesh number. The four space adaptive strategies are given and analyzed their advantages and disadvantages. Meanwhile, to overcome lower temporal computational efficiency in the explicit time discretization of AMR with a large number of refinement levels, the local time stepping (LTS) technique [4] in time and the arbitrary accuracy derivative Riemann (ADER) scheme [5] in space are adopted. The numerical examples show the validity of our methods.