并行间断有限元算法求解Navier-Stokes方程

马欣荣; 段治健; 谢公南; 刘三阳

doi:10.21656/1000-0887.380077

并行间断有限元算法求解Navier-Stokes方程

doi: 10.21656/1000-0887.380077

¹咸阳师范学院数学与信息科学学院, 陕西咸阳 712000;²西北工业大学航海学院, 西安 710072;³西安电子科技大学数学与统计学院, 西安 710071

基金项目: 国家自然科学基金(61401383); 陕西省教育厅自然科学基金(17JK0831)

详细信息

作者简介:
马欣荣(1980—), 女, 博士(通讯作者. E-mail: mxryx1021@163.com)；段治健(1980—), 男, 副教授, 博士(E-mail: zhijian_duan@126.com);谢公南(1980—), 男, 教授, 博士(E-mail: xgn@nwpu.edu.cn);刘三阳(1959—), 男, 教授(E-mail: liusanyang@126.com).

中图分类号: O246
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出版历程
- 收稿日期: 2017-04-05
- 修回日期: 2017-05-03
- 刊出日期: 2017-12-15

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

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)

摘要

摘要: 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.
- 间断Galerkin有限元方法 /
- NavierStokes方程 /
- 并行算法 /
- 区域分解算法
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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参考文献(18)

[1]	Bassi F, Crivellini A, Rebay S, et al. Discontinuous Galerkin solution of the Reynolds-averaged Navier-Stokes and k-ω turbulence model equations[J]. Computers & Fluids,2005,34(4/5): 507-540.
[2]	贺立新, 张来平, 张涵信. 间断Galerkin有限元和有限体积混合计算方法研究[J]. 力学学报, 2007,39(1): 15-22.(HE Li-xin, ZHANG Lai-ping, ZHANG Han-xin. A finite element/finite volume mixed solver on hybrid grids[J]. Chinese Journal of Theoretical and Applied Mechanics,2007,39(1): 15-22.(in Chinese))
[3]	张来平, 贺立新, 刘伟, 等. 基于非结构/混合网格的高阶精度格式研究进展[J]. 力学进展, 2013,43(2): 202-236.(ZHANG Lai-ping, HE Li-xin, LIU Wei, et al. Reviews of high-order methods on unstructured and hybrid grid[J]. Advances in Mechanics,2013,43(2): 202-236.(in Chinese))
[4]	Brandt A. Multi-level adaptive solutions to boundary-value problems[J]. Mathematics of Computation,1977,31(138): 333-390.
[5]	李宗哲, 王正华, 姚路, 等. 非结构网格的并行多重网格解算器[J]. 软件学报, 2013,24(2): 391-404.(LI Zong-zhe, WANG Zheng-hua, YAO Lu, et al. Parallel multigrid solver for unstructured grid[J]. Journal of Software,2013,24(2): 391-404.(in Chinese))
[6]	Carré G, Fournier L, Lanteri S. Parallel linear multigrid algorithms for the acceleration of compressible flow calculations[J]. Computer Methods in Applied Mechanics and Engineering,2000,184(2/4): 427-448.
[7]	Lambropoulos N K, Koubogiannis D G, Giannakoglou K C. Acceleration of a Navier-Stokes equation solver for unstructured grids using agglomeration multigrid and parallel processing[J]. Computer Methods in Applied Mechanics and Engineering,2004,193(9/11): 781-803.
[8]	Dolean V, Lanteri S. Parallel multigrid methods for the calculation of unsteady flows on unstructured grids: algorithmic aspects and parallel performances on clusters of PCs[J]. Parallel Computing,2004,30(4): 503-525.
[9]	LUO Hong, LUO Lu-qing, Ali A, et al. A parallel, reconstructed discontinuous Galerkin method for the compressible flows on arbitrary grids[J]. Communications in Computational Physics,2011,9(2): 363-389.
[10]	XIA Yi-dong, LUO Hong, Frisbey M, et al. A set of parallel, implicit methods for a reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids[J]. Computers & Fluids,2014,98: 134-151.
[11]	Beck A, Bolemann T, Frank H, et al. Discontinuous Galerkin for high performance computational fluid dynamics[C]// High Performance Computing in Science and Engineering . Berlin, Heidelberg: Springer, 2013: 281-294.
[12]	司海青, 王同光. 多块并行计算中负载平衡策略及时间成本估算方法[J]. 航空学报, 2007,28(S): 57-61.(SI Hai-qing, WANG Tong-guang. Load balancing strategy for parallel calculation and time cost estimation[J]. Acta Aeronautica et Astronautica Sinica,2007,28(S): 57-61.(in Chinese))
[13]	Kameda H, Fathy E Z S, Ryu I, et al. A performance comparison of dynamic vs. static load balancing policies in a mainframe-personal computer network model[C]// Proceedmgs of the 〖STBX〗39th IEEE Conference on Decision and Control . Sydney, Australia, 2000: 1415-1420.
[14]	马欣荣, 刘三阳. 非结构网格上双曲守恒律的并行算法研究[J]. 四川大学学报(工程科学版), 2015,47(2): 123-128.(MA Xin-rong, LIU San-yang. Parallel algorithm for conservation laws with unstructured grids[J]. Journal of Sichuan University (Engineering Science Edition),2015,47(2): 123-128.(in Chinese))
[15]	Roe P L. Approximate Riemann solvers, parameter vectors, and difference schemes[J]. Journal of Computational Physics,1981,43(2): 357-372.
[16]	LUO Hong, Sharov D, Baum J D, et al. Parallel unstructured grid GMRES+LU-SGS method for turbulent flows[C]//41st Aerospace Sciences Meeting and Exhibit.Reno, Nevada, 2003: AIAA 2003-273.
[17]	Dongarra J J, Duff I S, Danny C, et al. Numerical Linear Algebra on High-Performance Computers[M]. Society for Industrial and Applied Mathematics, 1998.
[18]	李晓梅, 吴建平. 数值并行算法与软件[M]. 北京: 科学出版社, 2007.(LI Xiao-mei, WU Jian-ping. Numerical Parallel Algorithms and Software [M]. Beijing: Science Press, 2007.(in Chinese))

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并行间断有限元算法求解Navier-Stokes方程

doi: 10.21656/1000-0887.380077

作者简介:
马欣荣(1980—), 女, 博士(通讯作者. E-mail: mxryx1021@163.com)；段治健(1980—), 男, 副教授, 博士(E-mail: zhijian_duan@126.com);谢公南(1980—), 男, 教授, 博士(E-mail: xgn@nwpu.edu.cn);刘三阳(1959—), 男, 教授(E-mail: liusanyang@126.com).

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

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留言板

并行间断有限元算法求解Navier-Stokes方程

doi: 10.21656/1000-0887.380077

作者简介: 马欣荣(1980—), 女, 博士(通讯作者. E-mail: mxryx1021@163.com)；段治健(1980—), 男, 副教授, 博士(E-mail: zhijian_duan@126.com);谢公南(1980—), 男, 教授, 博士(E-mail: xgn@nwpu.edu.cn);刘三阳(1959—), 男, 教授(E-mail: liusanyang@126.com).

计量

出版历程

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

计量

出版历程

目录

作者简介:
马欣荣(1980—), 女, 博士(通讯作者. E-mail: mxryx1021@163.com)；段治健(1980—), 男, 副教授, 博士(E-mail: zhijian_duan@126.com);谢公南(1980—), 男, 教授, 博士(E-mail: xgn@nwpu.edu.cn);刘三阳(1959—), 男, 教授(E-mail: liusanyang@126.com).