微分求积模拟二维流体中流函数约束的施加方法研究  

Methods on applying stream-function restraints in differential quadrature modelling of two-dimensional flow

作　　者：王通[1] 何涛[1,3] 曹曙阳[2] 

机构地区：[1]上海师范大学建筑工程学院,上海201418 [2]同济大学土木工程防灾国家重点实验室,上海200092 [3]伯明翰大学工学院,英国伯明翰B152TT

出　　处：《振动与冲击》2017年第8期173-178,共6页Journal of Vibration and Shock

基　　金：国家自然科学基金青年基金项目(51508333)

摘　　要：采用微分求积法数值求解流函数-涡度方程来模拟二维流体时会遇到流函数的超约束问题,即虽然流函数方程为二阶偏微分方程,但在每个固体边界上都存在两个约束条件:一个Dirichlet条件和一个Neumann条件。以二维驱动方腔流动为例,对该问题进行深入分析,进而提出一种新的超约束处理方法,即在边界涡度的计算中考虑Neumann条件,而仅将Dirichlet条件施加于流函数方程。数值结果显示该方法可行,且计算效率较高。同时给出前人提出的单层法和双层法进行比较。试算表明单层法对于网格数的奇偶性很敏感,不适于处理该问题。与双层法对比后发现:该方法计算精度较高,且由于回避了超约束问题而更加方便于使用。The 2D lid-driven cavity flow was simulated by applying the differential quadrature method to solve the stream function-vorticity equations. There were two boundary conditions, one Dirichlet and one Neumann, for the stream function equation at each solid boundary though the stream function equation was just second order. Analysis on this over- specified problem was carried out, based on which a new applying method was proposed: the Neumann condition was considered in calculating the vorticity at the boundary while only the Dirichlet condition was applied in the stream function equation. Validity of this method was verified by comparing its numerical results with benchmark data. Two other existing methods, the one-layer approach and the two-layer approach were shown as contrasts. Trial calculations indicate that the one-layer approach is sensitive to the parity of grid numbers and is not suitable for the present problem. Comparisons between the new method and the two-layer approach show that the former is not only more accurate but also more convenient to be used in practice for avoiding the over-specified problem. © 2017, Editorial Office of Journal of Vibration and Shock. All right reserved.

关 键 词：微分求积 流函数-涡度方程 方腔流 边界条件 超约束 

分 类 号：TV131[水利工程—水力学及河流动力学] O302[理学—力学]