应用数学和力学2017，Vol.38Issue(12)：1377-1388,12.DOI:10.21656/1000-0887.380077
并行间断有限元算法求解Navier-Stokes方程
A Parallel Discontinuous Galerkin FEM for Solving Compressible Navier-Stokes Equations
摘要
Abstract
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.关键词
间断Galerkin有限元方法/Navier-Stokes方程/并行算法/区域分解算法Key words
discontinuous Galerkin FEM/Navier-Stokes equations/parallel algorithm/domain decomposition algorithm分类
数理科学引用本文复制引用
马欣荣,段治健,谢公南,刘三阳..并行间断有限元算法求解Navier-Stokes方程[J].应用数学和力学,2017,38(12):1377-1388,12.基金项目
国家自然科学基金(61401383) （61401383）
陕西省教育厅自然科学基金(17JK0831)本文作者衷心感谢咸阳师范学院科研基金(15XSYK032) （17JK0831）
咸阳师范学院大学生创新创业训练项目(2015050)对本文的资助.The National Natural Science Foundation of China(61401383) （2015050）
