Three Dimensional Discontinuous Galerkin Methods for Euler Equations on the Adaptive Consistent Meshes

In the numerical simulation of three dimensional fluid dynamical equations, the huge computational quantity is a main challenge problem. Based on the three dimensional consistent unstructured tetrahedron meshes, we study the discontinuous Galerkin (DG) finite element method [1] combined with the adaptive mesh refinement (AMR) [2, 3] for solving Euler equations in this paper. 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, we adopt the local time stepping (LTS) technique [4] and the arbitrary high order of accuracy (ADER) scheme [5] in time and space. The numerical examples show the validity of our methods.