不可压缩流基于块预处理的并行有限元计算

doi:10.19596/j.cnki.1001-246x.7627

计算物理 ›› 2018, Vol. 35 ›› Issue (2): 151-160.DOI: 10.19596/j.cnki.1001-246x.7627

不可压缩流基于块预处理的并行有限元计算

李凌霄

中国科学院计算数学与科学工程计算研究所, 北京 100190

收稿日期:2017-01-17 修回日期:2017-05-23 出版日期:2018-03-25 发布日期:2018-03-25
作者简介:李凌霄(1991-),男,博士研究生,从事不可压流体动力学的有限元数值模拟,E-mail:lilingxiao@lsec.cc.ac.cn

Parallel Finite Element Computation of Incompressible Viscous Flows Based on Block Preconditioning Strategy

LI Lingxiao

Institute of Computational Mathematics and Scientific/Engineering Computing of Chinese Academy of Sciences, Beijing 100190, China

Received:2017-01-17 Revised:2017-05-23 Online:2018-03-25 Published:2018-03-25

摘要/Abstract

摘要： 发展了一个模拟非定常不可压缩粘性流的并行有限元求解器，时间离散使用具有二阶精度的隐式中点格式，基于三维非结构四面体网格剖分，使用高阶混合有限元离散速度场（P2）和压力场（P1）.全离散格式产生的代数方程组是大型、稀疏、非对称和病态的，基于修正的压力对流扩散预处理（PCD）和精心设计的子问题迭代执行策略，采用预处理的GMRES迭代法来高效求解线性方程组.利用相同的子问题迭代策略，同时给出基于最小二乘交换子（LSC）预处理的并行效率对比.大量数值算例验证了算法的精度、可扩展性和可靠性.三维驱动方腔流模拟结果（Re=3200.0）清晰地显示了方腔流中主涡（PE）、下游二次涡（DSE）、上游二次涡（USE）、侧壁涡（EWV）和TGL涡的存在.

关键词: 不可压缩Navier-Stokes, 块预处理, GMRES迭代, 混合有限元, 并行计算

Abstract: A parallel finite element solver is developed for simulation of the unsteady incompressible viscous flows. Implicit mid-point scheme is used to discretize time variable. Based on unstructured grid, velocity and pressure are discretized by classical P2-P1 Taylor-Hood mixed finite element. Resulting linear algebraic systems are large-scale, sparse, non-symmetric and ill-conditioned. Using a specially designed iterative strategy, it is solved by preconditioned GMRES method with modified pressure-convection-diffusion(PCD) preconditioner. A number of numerical experiments verify scability and validity of the solver. Especially, driven cavity flow simulation in 3D (Re=3200.0) clearly shows existence of primary eddy, downstream secondary eddy, upstream secondary eddy, end-wall vortices and T-G-like vortices. A parallel efficiency comparison with least-squares commutator(LSC) preconditioner is also given.

Key words: incompressible Navier-Stokes, block preconditioning, GMRES iteration, mixed finite element, parallel computation

中图分类号:

O241.82

李凌霄. 不可压缩流基于块预处理的并行有限元计算[J]. 计算物理, 2018, 35(2): 151-160.

LI Lingxiao. Parallel Finite Element Computation of Incompressible Viscous Flows Based on Block Preconditioning Strategy[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2018, 35(2): 151-160.

参考文献

[1] CHEN R, YAN Z, ZHAO Y, et al. Simulating flows passing a wind turbine with a fully implicit domain decomposition method[M]//Domain Decomposition Methods in Science and Engineering XXⅡ. Springer International Publishing, 2016:453-460.
[2] 孙振旭,郭迪龙,等. 高速列车地面效应数值模拟研究[J]. 计算物理,2013,30(1):61-69.
[3] 李贝贝,王婷婷,等. 方腔内双扩散混合对流非线性格子Boltzmann研究[J]. 计算物理,2016,33(2):156-162.
[4] ELMAN H C, SILVESTER D J, WATHEN A J. Finite elements and fast iterative solvers:With applications in incompressible fluid dynamics[M]. Second edition. New York:Oxford University Press, 2015:413-442.
[5] 胡军,刘婵,等. 磁流体方腔槽道流整体线性稳定性数值方法研究[J]. 计算物理,2016,33(4):379-390.
[6] MORLEY N B, NI M J, MUNIPALLI R, et al. MHD simulations of liquid metal flow through a toroidally oriented manifold[J]. Fusion Engineering and Design, 2008, 83(7):1335-1339.
[7] GUERMOND J L, MINEV P, SHEN J. An overview of projection methods for incompressible flows[J]. Computer Methods in Applied Mechanics and Engineering, 2006, 195(44):6011-6045.
[8] TAYLOR C, HOOD P. A numerical solution of the Navier-Stokes equations using the finite element technique[J]. Computers & Fluids, 1973, 1(1):73-100.
[9] SAAD Y, SCHULTZ M H. GMRES:A generalized minimal residual algorithm for solving nonsymmetric linear systems[J]. SIAM Journal on Scientific and Statistical Computing, 1986, 7(3):856-869.
[10] KAY D, LOGHIN D, WATHEN A. A preconditioner for the steady-state Navier-Stokes equations[J]. SIAM Journal on Scientific Computing, 2002, 24(1):237-256.
[11] 陈荣亮,蔡小川. 高可扩展区域分解算法及其在流体模拟和优化问题中的应用[J]. 中国科学:数学,2016, 46(7):915-928.
[12] 尚月强,何银年. 不可压缩流动的并行数值方法[J]. 中国科学:数学, 2013, 43(6):577-590.
[13] 尚月强,何银年. 非定常Navier-Stokes方程基于完全重叠型区域分解的有限元并行算法[J]. 计算物理,2011,28(2):181-187.
[14] HACHEM E, RIVAUX B, KLOCZKO T, et al. Stabilized finite element method for incompressible flows with high Reynolds number[J]. Journal of Computational Physics, 2010, 229(23):8643-8665.
[15] SMETHURST C, SILVESTER D, MIHAJLOVIC. Unstructured finite element method for the solution of the Boussinesq problem in three dimensions[J]. Int J Numer Meth Fluids, 2013, 73:791-812.
[16] GIRAULT V, RAVIART P A. Finite element methods for Navier-Stokes equations:Theory and algorithms[M]. Berlin:Springer, 1986:78-80.
[17] YANG U M. BoomerAMG:A parallel algebraic multigrid solver and preconditioner[J]. Applied Numerical Mathematics, 2002, 41(1):155-177.
[18] PHG[CP/OL]. http://lsec.cc.ac.cn/phg/.
[19] ZHANG L B. A parallel algorithm for adaptive local refinement of tetrahedral meshes using bisection[J]. Numer Math:Theory, Methods and Applications, 2009, 2(1):65-89.
[20] ZHANG L B, CUI T, LIU H. A set of symmetric quadrature rules on triangles and tetrahedra[J]. Journal of Computational Mathematics, 2009:89-96.
[21] SHANKAR P N, DESHPANDE M D. Fluid mechanics in the driven cavity[J]. Annual Review of Fluid Mechanics, 2000, 32(1):93-136.

不可压缩流基于块预处理的并行有限元计算

Parallel Finite Element Computation of Incompressible Viscous Flows Based on Block Preconditioning Strategy

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