隐式超松弛LU-SGS间断Galerkin算法

doi:10.13190/j.jbupt.2019-023

北京邮电大学学报 ›› 2019, Vol. 42 ›› Issue (5): 8-14.doi: 10.13190/j.jbupt.2019-023

隐式超松弛LU-SGS间断Galerkin算法

段治健^1,2, 谢公南³, 张迎春¹

1. 西北工业大学机电学院, 西安 710072;
2. 咸阳师范学院数学与信息科学学院, 陕西咸阳 712000;
3. 西北工业大学航海学院, 西安 710072

收稿日期:2019-03-01 出版日期:2019-10-28 发布日期:2019-11-25
通讯作者: 谢公南(1980-),男,教授,博士生导师,E-mail:xgn@nwpu.edu.cn. E-mail:xgn@nwpu.edu.cn
作者简介:段治健(1980-),男,副教授.
基金资助:
航空科学基金项目（2017ZA53001）；国家自然科学基金项目（6373174）

Implicit Overrelaxation LU-SGS Discontinuous Galerkin Finite Element Algorithm

DUAN Zhi-jian^1,2, XIE Gong-nan³, ZHANG Ying-chun¹

1. School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an 710072, China;
2. School of Mathematics and Information Science, Xianyang Normal University, Xianyang 712000, China;
3. School of Marine Science and Technology, Northwestern Polytechnical University, Xi'an 710072, China

Received:2019-03-01 Online:2019-10-28 Published:2019-11-25

摘要/Abstract

摘要： 为了提高求解欧拉（Euler）方程和纳维-斯托克斯（NS）方程的计算效率，结合隐式时间离散格式研究了间断伽辽金有限元方法（DGM）.通过改进上下三角分解对称高斯赛德尔（LU-SGS）格式，引入舍入误差项，构造了超松弛内迭代LU-SGS离散格式，实现了非定常可压缩绕流流场的计算.通过Sod激波管问题、二维管道问题验证了算法的可靠性和准确性.数值计算了RAE2822翼型、ONERA M6机翼跨声速可压缩绕流问题，并与多步龙格库塔（RK）算法、LU-SGS算法和广义极小残余（GMRES）算法的计算结果进行了比较.结果表明，超松弛内迭代LU-SGS算法具有良好的稳定性和高效性，计算效率是LU-SGS格式的2.35~3.1倍，是RK格式的5.4倍.

关键词: 隐式时间离散算法, Euler方程, LU-SGS格式, 间断有限元方法

Abstract: In order to improve the computational efficiency of solving Euler equation and Navier-Stokes equation, the discontinuous Galerkin finite element method was investigated by combining with the implicit time discrete scheme. The lower upper-symmetric Gauss-Seidel(LU-SGS) scheme was improved through retaining the round-off error item, and an overrelaxation interior iteration LU-SGS discrete scheme was constructed to realize the calculation of unsteady compressible flow fields. The reliability and accuracy of the algorithm were verified by solving the Sod shock tube problem and the two-dimensional pipeline problem. The transonic compressible flows around RAE2822 airfoil and ONERA M6 wing were numerically calculated, and the results were compared with that of the multistep Runge-Kutta(RK) algorithm, LU-SGS algorithm and generalized minimal residual algorithms(GMRES). The results show that the presented algorithm has good stability and efficiency, and its computational efficiency is 2.35~3.1 times that of LU-SGS scheme and 5.4 times that of RK scheme.

Key words: implicit time discrete algorithm, Euler equation, lower upper-symmetric Gauss-Seidel scheme, discontinuous Galerkin finite element method

中图分类号:

TP399

段治健, 谢公南, 张迎春. 隐式超松弛LU-SGS间断Galerkin算法[J]. 北京邮电大学学报, 2019, 42(5): 8-14.

DUAN Zhi-jian, XIE Gong-nan, ZHANG Ying-chun. Implicit Overrelaxation LU-SGS Discontinuous Galerkin Finite Element Algorithm[J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2019, 42(5): 8-14.

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隐式超松弛LU-SGS间断Galerkin算法

Implicit Overrelaxation LU-SGS Discontinuous Galerkin Finite Element Algorithm

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