圆外区域Stokes流混合边值问题的自然边界元法  

Natural Boundary Element Method for Mixed Problems of Stokes Flow in Exterior Circular Region

作　　者：彭维红[1] 董正筑[2] 曹国华[1] 

机构地区：[1]中国矿业大学机电工程学院,江苏徐州221116 [2]中国矿业大学理学院,江苏徐州221116

出　　处：《四川大学学报（工程科学版）》2010年第2期107-112,共6页Journal of Sichuan University (Engineering Science Edition)

基　　金：青年科学基金资助项目(50909093);中国矿业大学青年科研基金(2008A012)

摘　　要：针对圆外区域Stokes流的速度-压力混合边值问题,基于自然边界元原理及复变函数性质并运用Fourier级数展开法推导了圆外区域Stokes方程的Poisson积分公式及自然积分方程,通过分段线性单元将自然积分方程的近似变分问题离散化,求解出压力边界上的速度分布,从而将速度-压力混合边值问题转化成纯粹的速度边值问题,最后利用Poisson积分公式即可给出相应问题的速度分布表达式。计算结果表明:理论计算得到的速度场与CFD软件的计算结果一致;基于自然边界元法的Stokes流混合边值问题的求解,能够降低维数,同时所需求解的矩阵是对称正定的,尤其是边界为圆周时,矩阵还具有循环特性,从而有助于计算量的减小。Aiming at the velocity-pressure mixed boundary problems of Stokes flow in exterior circular region,based on the character of the function of complex variable,the natural boundary element theory and series expanded method,the Poisson integral formula and the natural integral equation were deduced.The subsection linearity element was utilized to discretize the differential problems of the natural integral equation,and then the velocity value on the pressure boundary was computed,the velocity-pressure mixed problem was transferred into velocity boundary value problem.The velocity distribution was calculated by the Poisson integral formulae.The results showed that the velocity distribution by the natural boundary element method was according to the CFD software;the dimensionality of the problem could be reduced by the natural boundary element method,and the matrices of this approach were symmetrical positive ones.When the boundary was a circle especially,the matrices would be circulant,accordingly,the calculating volume was decreased greatly.

关 键 词：STOKES流 混合边值问题 自然边界元 自然积分方程 

分 类 号：O352[理学—流体力学]