无穷域势流问题的有限元/差分线法混合求解  

Calculation of potential flow problems over an infinite domain based on finite element methods and finite difference method of lines

作　　者：吴泽艳[1] 王立峰[2] 武哲[1,2] 

机构地区：[1]清华大学航天航空学院,北京100084 [2]北京航空航天大学航空科学与工程学院,北京100191

出　　处：《计算力学学报》2011年第5期754-759,共6页Chinese Journal of Computational Mechanics

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求解问题,减少了计算量。考察了重叠区域的大小对计算精度的影响,发现随着重叠区域的减小,计算误差小幅度地增大。算法虽然基于重叠型区域分解,但是计算无需反复迭代,节省了计算时间。数值算例验证了算法的正确性。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.

关 键 词：无穷域 势流 有限元 差分线法 

分 类 号：O241[理学—计算数学]