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无穷域势流问题的有限元/差分线法混合求解
引用本文:吴泽艳,王立峰,武哲.无穷域势流问题的有限元/差分线法混合求解[J].计算力学学报,2011,28(5):754-759.
作者姓名:吴泽艳  王立峰  武哲
作者单位:清华大学 航天航空学院,北京 100084;北京航空航天大学 航空科学与工程学院,北京 100191;清华大学 航天航空学院,北京 100084;北京航空航天大学 航空科学与工程学院,北京 100191
摘    要:提出了一种将有限元和差分线法相结合求解无穷域势流问题的算法。用两同心圆将求解域划分为存在重叠的有限和无限两个区域,在有限和无限域上分别用有限元和差分线法求解Laplace方程边值问题。用差分线法推导出的关系式修正有限元方程,求解该方程组从而得到原问题的解。本算法将求解无穷域问题转化为代数特征值问题和有限域内线性方程组的...

关 键 词:无穷域  势流  有限元  差分线法
收稿时间:2010/6/17 0:00:00
修稿时间:2010/12/20 0:00:00

Calculation of potential flow problems over an infinite domain based on finite element methods and finite difference method of lines
WU Ze-yan,WANG Li-feng and WU Zhe.Calculation of potential flow problems over an infinite domain based on finite element methods and finite difference method of lines[J].Chinese Journal of Computational Mechanics,2011,28(5):754-759.
Authors:WU Ze-yan  WANG Li-feng and WU Zhe
Institution:School of Aerospace, Tsinghua University, Beijing 100084,China;School of Aeronautic Science and Technology, Beijing University of Aeronautics and Astronautics, Beijing 100191,China;School of Aerospace, Tsinghua University, Beijing 100084,China;School of Aeronautic Science and Technology, Beijing University of Aeronautics and Astronautics, Beijing 100191,China
Abstract:An algorithm combining finite element method and finite difference method of lines for potential flow problem over an infinite domain is presented. The solution domain is divided into two overlapping regions by two concentric circles, finite domain and infinite domain, and boundary value problems for Laplace Equation is solved by finite element method and finite difference method of lines respectively. The finite element equations amended by a relationship educed by finite difference method of lines are solved, and the numerical solutions of the original problem are obtained. By this algorithm, the potential flow problems over an infinite domain is converted into two problems, algebraic eigenvalue problem on a circle and linear equations problems on the limited domain, and the computation has been reduced. It is found that with the decrease of overlapping regions the calculation errors increases slightly. Although the algorithm is based on overlapping domain decomposition, repeated iteration is not needed, and the computing time was saved. Numerical example shows the correctness and convergence of the algorithm.
Keywords:unbounded domain  potential flow  finite element methods  finite difference method of lines
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