流体力学问题基于核重构思想的最小二乘配点法  

LEAST-SQUARE POINT COLLOCATED MESHLESS METHOD BASED ON KERNEL REPRODUCING FOR HYDRODYNAMIC PROBLEMS

作　　者：史宝军[1] 袁明武[2] 宋世军[1] 

机构地区：[1]山东建筑工程学院机电工程学院,济南250014 [2]北京大学力学与工程科学系,北京100871

出　　处：《工程力学》2006年第4期17-21,38,共6页Engineering Mechanics

基　　金：山东省自然科学基金(Y2002A04)资助项目

摘　　要：将基于核重构思想的最小二乘配点法应用于流体力学问题,给出了离散二维不可压缩粘性流体非线性偏微分方程的最小二乘配点格式。为了检验该方法的有效性,以二维Stokes问题——Couette流动为典型算例,分别研究了正压与负压两种工况作用下Couette流动的速度分布。数值模拟结果表明,无论离散点是均匀分布还是随机分布,均给出了较准确的数值结果。A least-square point collocation meshless formula based on kernel reproducing is proposed to discretize nonlinear partial differential equations for two-dimensional incompressible viscous hydrodynamic problems. A two-dimensional Stokes problem, Couette flow, is taken as a typical example to verify the validity of this meshless approach. The distributions of velocity for the Couette flow are investigated for positive and negative gradient pressures, respectively. The Couette flows with these types of pressure gradients are significant in the lubrication theory. The viscous fluid flow film formed in the journal bearing has similar flow property as that of the Couette flow. The numerical example shows that results obtained in this meshless approach are highly accurate for both uniform and random distribution of discretized points.

关 键 词：流体力学 无网格方法 重构核点法 最小二乘配点法 COUETTE流动 

分 类 号：O241.82[理学—计算数学]