High-Order Space-time Discontinuous Galerkin Cell Vertex Scheme toward Compressible Navier Stokes Equations

Abstract

Abstract : This project continues our previous AFOSR project (Grant No. FA9550-08-1-0122) to extend and verify our high order space-time cell vertex scheme (DG-CVS) toward solving the compressible Navier-Stokes equation. The DG-CVS method integrates the best features of the space-time Conservation Element/Solution Element (CE/SE) method [1] and the discontinuous Galerkin (DG) method [2]. The core idea is to construct a staggered space-time mesh through alternate cell-centered CEs and vertex-centered CEs (cf. Fig. 1 (right)) within each time step. Inside each SE (cf. Fig. 1 (left)), the solution is approximated using high-order space-time DG basis polynomials. The space-time flux conservation is enforced inside each CE using the DG discretization. The solution is updated successively at the cell level and at the vertex level within each physical time step. For this reason and the method s DG ingredient, the method was named as the space-time discontinuous Galerkin cell-vertex scheme (DG-CVS).