并行间断有限元算法求解Navier-Stokes方程

间断Galerkin有限元方法非常适合在非结构网格上高精度求解Navier-Stokes方程，然而其十分耗费计算资源.为了提高计算效率，提出了高效的MIMD并行算法.采用隐式时间离散GMRES+LU SGS格式，结合多重网格方法，当地时间步长加速算法收敛.为了保证各处理器间负载平衡，采用区域分解二级图方法划分网格，实现内存合理分配，数据只在相邻处理器间传递.数值模拟了RAE2822翼型和M6黏性绕流，加速比基本呈线性变化且接近理想值.结果表明了该算法能有效减少计算时间、合理分配内存，具有较高的加速比和并行效率，适合于MIMD粗粒度科学计算.

A Parallel Discontinuous Galerkin FEM for Solving Compressible Navier-Stokes Equations

Based on unstructured grids, discontinuous Galerkin finite element methods (DGFEM) 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 distributed-memory multicomputers 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 time significantly and allocates memory reasonably with advantages of high acceleration and efficiency, and is very suited for coarse-grained scientific computation of MIMD models.