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论文:2016,Vol:34,Issue(5):754-760 |
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引用本文： |
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马明生, 龚小权, 邓有奇, 赵辉. 一种适用于非结构网格的间断Galerkin有限元LU-SGS隐式方法[J]. 西北工业大学学报 |
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Ma Mingsheng, Gong Xiaoquan, Deng Youqi, Zhao Hui. An Implicit LU-SGS Scheme for the Discontinuous Galerkin Method on Unstructured Grids[J]. Northwestern polytechnical university |
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| 一种适用于非结构网格的间断Galerkin有限元LU-SGS隐式方法 |
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| 马明生1,2, 龚小权1, 邓有奇1, 赵辉1 |
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1. 西北工业大学 航空学院, 陕西 西安 710072;
2. 中国空气动力研究与发展中心计算空气动力研究所, 四川 绵阳 621000 |
| 摘要: |
| 具有TVD性质的显式Runge-Kutta间断Galerkin（RKDG）格式在CFD领域得到广泛应用，但是显式计算稳定性差、计算效率低。为改善时间推进效率，基于高阶间断Galerkin有限元方法，采用欧拉一阶后差（BDF1），发展了一套高效的隐式LU-SGS（lower upper-symmetric Gauss-Seidel）求解方法，方法基于MPI并行实现，适合于不同计算精度。针对非线性系统左端项矩阵，对比了简化前后LU-SGS的计算效率。建立的间断Galerkin有限元方法基于非结构网格，采用Taylor基函数，计算精度最高达到四阶精度。通过NACA0012翼型以及M6机翼算例对发展的LU-SGS方法进行了考察，与显式算法相比，隐式格式的迭代步数和CPU时间均较大程度减小，效率能够提高1个量级以上。最后将隐式算法用于复杂外形翼身组合体F4的流场计算，结果表明所发展的隐式方法具有较好的鲁棒性，能够用于复杂外形计算。 |
| 关键词:
间断Galerkin有限元
欧拉方程
Taylor基函数
LU-SGS
计算效率
非结构网格
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| An Implicit LU-SGS Scheme for the Discontinuous Galerkin Method on Unstructured Grids |
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| Ma Mingsheng1,2, Gong Xiaoquan1, Deng Youqi1, Zhao Hui1 |
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1. School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China;
2. China Aerodynamics Research and Development Center, Mianyang 621000, China |
| Abstract: |
| The TVD explicit Runge-Kutta discontinuous Galerkin(TVD-RKDG) are widely used in CFD, but it has poor stability property and low computational efficiency. To improve the time advancing efficiency, an efficient implicit lower-upper symmetric Gauss-Seidel (LU-SGS) scheme based on backwards differencing methods (BDF1) has been applied to the high-order discontinuous Galerkin method. The method is implemented parallelly through MPI library and is suit for different computational orders. The left matrix of nonlinear system is simplified and computational efficiency is compared. The DGM is based on the Taylor basis functions on unstructured grid and the accuracy is up to forth order. The developed LU-SGS scheme is verified through NACA0012 airfoil and ONERA M6 wing. Compared to the traditional explicit Runge-Kutta scheme, the implicit scheme can greatly reduce the iteration number and CPU time. The computational efficiency can be accelerated evidently with more than one order of magnitude speed. At last the flow field of DLR-F4 is simulated to verify the robustness of the developed implicit scheme. The result proves that the developed LU-SGS scheme can be applied to complex configuration simulation. |
| Key words:
discontinuous Galerkin method
Euler equations
Taylor basis
LU-SGS
computational efficiency
unstructured grid
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| 收稿日期: 2016-03-20
修回日期:
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| DOI: |
| 通讯作者:
Email： |
| 作者简介: 马明生(1962-),西北工业大学兼职教授,主要从事飞行器设计与计算流体力学研究。
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相关文献: |
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1．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]. 西北工业大学学报, 2014,32(3): 346-350 |
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