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

MA Xin-rong; DUAN Zhi-jian; XIE Gong-nan; LIU San-yang

doi:10.21656/1000-0887.380077

Volume 38 Issue 12

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Article Navigation > Applied Mathematics and Mechanics > 2017 > 38(12): 1377-1388

MA Xin-rong, DUAN Zhi-jian, XIE Gong-nan, LIU San-yang. A Parallel Discontinuous Galerkin FEM for Solving Compressible Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2017, 38(12): 1377-1388. doi: 10.21656/1000-0887.380077

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

doi: 10.21656/1000-0887.380077

¹College of Mathematics and Information Science, Xianyang Normal University, Xianyang, Shaanxi 712000, P.R.China;²School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, P.R.China;³School of Mathematics and Statistics, Xidian University, Xi’an 710071, P.R.China

Funds: The National Natural Science Foundation of China(61401383)

Received Date: 2017-04-05
Rev Recd Date: 2017-05-03
Publish Date: 2017-12-15

Abstract

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.
- discontinuous Galerkin FEM,
- Navier-Stokes equations,
- parallel algorithm,
- domain decomposition algorithm

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References

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