A parallel discontinuous galerkin fem for solving compressible navier-stokes equations

Based on unstructured grids, discontinuous Galerkin finite element methods (DG-FEM) are very suited to realize high-order approximations of Navier-Stokes equations, but are rather demanding in computing resources. In order to improve the computational efficiency of the DGFEM, an efficient parallel algorithm on distrihuted-memory multicomputer coupled with the multigrid strategy based on the GMRES+LU-SGS procedure was presented here. The domain decomposition method was employed to handle meshes properly and make each processor maintain load balancing. Moreover, the LU-SGS and the local time stepping techniques were used to accelerate the convergence of the solution of Navier-Stokes equations. Numerical tests were conducted for viscid turbulence flow problems around the RAE2822 airfoil and over the M6 wing. The parallel acceleration is near to a linear convergence and up to the ideal solutions. The results indicate that the proposed parallel algorithm reduces computation rime significantly and allocates memory reasonably with advantages of high acceleration and efficiency, and is very suited for coarse-grained scientific computation of MI.MI) models.