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论文:2014,Vol:32,Issue(3):346-350 |
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引用本文： |
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郝海兵, 张强, 杨永, 梁益华. 基于LU-SGS迭代的DGM隐式方法研究[J]. 西北工业大学 |
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Hao Haibing, Zhang Qiang, Yang Yong, Liang Yihua. An Implicit Scheme of Discontinuous Galerkin Method(DGM) Based on LU-SGS Iterative Method[J]. Northwestern polytechnical university |
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| 基于LU-SGS迭代的DGM隐式方法研究 |
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| 郝海兵1, 张强2, 杨永2, 梁益华1 |
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1. 中国航空计算技术研究所, 陕西 西安 710068;
2. 西北工业大学 翼型叶栅空气动力学国防科技重点实验室, 陕西 西安 710072 |
| 摘要: |
| 考虑到LU-SGS迭代法已经在基于非结构网格的有限体积法中得到了成功应用,文章借鉴其思想,将其推广到高精度间断Galerkin有限元隐式格式求解中来,并对其性能进行了研究。为了避免隐式算法中对大型稀疏矩阵求逆,采用LU-SGS迭代法,只需要在每步时间推进中沿网格号从前到后和从后到前2次扫描计算即可,并且还能有效降低内存需求。通过对NACA0012翼型和ONERA M6机翼跨声速无粘流动进行数值模拟,计算结果表明:与TVD-RKDG显式时间格式相比,隐式格式所需的迭代步数和CPU时间均得到了很大程度上的减少,并且精度保持不变。 |
| 关键词:
间断Galerkin有限元
LU-SGS
欧拉方程
非结构网格
时间隐式方法
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| An Implicit Scheme of Discontinuous Galerkin Method(DGM) Based on LU-SGS Iterative Method |
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| Hao Haibing1, Zhang Qiang2, Yang Yong2, Liang Yihua1 |
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1. Aeronautical Computing technique Research Institute, Xi'an 710068, China;
2. National Key Laboratory of Aerodynamics Design and Research at Northwestern Polytechnical University, Xi'an 710072, China |
| Abstract: |
| Because the LU-SGS iterative method has been successfully applied to the finite volume method based on unstructured grids, we extend it to the implicit scheme of the high-precision discontinuous Galerkin finite element method and study its properties. To avoid solving the inversion of large sparse matrix in the implicit scheme, we use the LU-SGS iterative method to conduct the forward scan and backward scan computation along the Grid Number at each step of time progression, thus effectively reducing memory requirements. To verify the effectiveness of implicit scheme of the DGM, we simulate the transonic inviscid flow around the NACA0012 airfoil and the ONERA M6 wing and compare the simulation results with the TVD-RKDG computation results. The simulation results, given in Figs. 2, 3 and 5, and their analysis show preliminarily that, compared with the TVD-RKDG computation method, the implicit scheme of the DGM greatly reduces the number of iterations, the CPU time and computational cost, thus increasing the speed of convergence around the flow field and computational efficiency. |
| Key words:
airfoils
computational efficiency
computational fluid dynamics
cost reduction
Euler equations
flow fields
Galerkin methods
finite element method
finite volume method
iterative methods
mesh generation
Ｒunge-Kutta methods
transonic flow
wings
discontinuous Galerkin method
implicit scheme
unstructured grid
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| 收稿日期: 2013-10-22
修回日期:
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| DOI: |
| 基金项目: 国家自然科学基金(50976017);国家“863”计划(2012AA01A304)资助 |
| 通讯作者:
Email： |
| 作者简介: 郝海兵(1981-),中国航空计算技术研究所工程师、博士,主要从事高精度数值算法研究。
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| 相关功能 |
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| 作者相关文章 |
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| 郝海兵 在本刊中的所有文章 |
| 张强 在本刊中的所有文章 |
| 杨永 在本刊中的所有文章 |
| 梁益华 在本刊中的所有文章 |
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参考文献: |
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[1] Reed N H, Hill T R. Triangle Mesh Methods for the Neutron Transport Equation[R]. Los Almos Scientific Laboratory, Report LA-UR-73-479, 1973
[2] Fidkowski K J, Oliver T A, Lu J, Darmofal D L. P-Multigrid Solution of High-Order Discontinuous Galerkin Discretizations of the Compressible Navier-Stokes Equations[J]. J Comp Phys, 2005, 207: 92-113
[3] Qiu J, Shu C W. Hermite WENO Schemes and Their Application as Limiters for Runge-Kutta Discontinuous Galerkin Method: One Dimensional Case [J]. J Comp Phys, 2004, 193: 115-135
[4] Zhang L P, Liu W, He L X, Deng X G. A New Class of DG /FV Hybrid Schemes for One-Dimensional Conservation Law[C]//The 8th Asian Conference on Computational Fluid Dynamics, Hong Kong, 2010: 10-14
[5] 郝海兵, 杨永. 非结构网格上 P 型多重网格法流场数值模拟[J]. 计算力学学报, 2011, 28(3): 360-365 Hao Haibing, Yang Yong. The Research of P-Multigrid Solution for Discontinuous Galerkin Method [J]. Chinese Journal of Computational Mechanics, 2011, 28(3): 360-365 (in Chinese)
[6] Bassi F, Rebay S. GMRES for Discontinuous Galerkin Solution of the Compressible Navier-Stokes Equations//Cockburn B, Karniadakis G E, Shu C W, Discontinuous Galerkin Method: Theory, Computations and Applications [M ], SpringerVerlag, 2000
[7] Hartmann R, Houston P. Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations I: Method Formulation[J]. Internatimal Journal of Numerical Analysis and Modeling, 2006(3): 1-20 |
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