哈密顿体系下求解矩形域Stokes流的端部效应研究  

End Effects for Stokes Flow in Rectangular Cavity in Hamiltonian System

作　　者：何士华[1] 张立翔[2] 胡吉敏[1] 邹进[1] 

机构地区：[1]昆明理工大学电力工程学院,云南昆明650500 [2]昆明理工大学建筑工程学院,云南昆明650500

出　　处：《昆明理工大学学报（自然科学版）》2013年第4期95-101,共7页Journal of Kunming University of Science and Technology(Natural Science)

基　　金：国家自然科学基金项目(项目编号:51149013;41061053);昆明理工大学自然科学基金项目(项目编号:KKZ3201304016)

摘　　要：对哈密顿体系下求解矩形域Stokes流的端部效应进行了研究.建立了Stokes流哈密顿对偶方程,获得了反对称问题的非零本征值及其本征解.将对偶方程的解由非零本征值本征解展开,在由端部边界条件导出展开式求解系数的基础上,计算分析了端部效应的衰减规律及其相互作用机理,全面考察了端部边界的误差大小.端部切向驱动所导致的矩形域内流动速度的变化呈逐步衰减趋势;展开式叠加项数越多,满足速度边界的精度越高;深宽比越小,上、下端部的互相干扰越大,端部速度误差也越大;同向驱动时的端部误差大于反向驱动时的误差.The end effects for Stokes flow in a rectangular cavity are investigated with Hamiltonian analytical method. By establishing the dual equations for Stokes flow in Hamihonian system, the non-zero eigenvalues and their eigensolutions are obtained for an anti-symmetric problem. Expanding the solutions of dual equations by non-zero eigensolutions and determining the expansion coefficients by the end boundary conditions, the decay tendency and interaction mechanism of end effects are analyzed and the end boundary error is investigated. The velocity caused by tangent driving end is gradually decayed along the longitudinal direction of cavity. The more number of items the expansions are superposed, the more accurate the solutions are. The smaller the depth-to-width ratios are, the stronger the interference between the top and bottom driving velocity is. The error of ends moving in the same directions is greater than in opposite directions.

关 键 词：哈密顿体系 STOKES流 矩形域 端部效应 

分 类 号：O368[理学—流体力学]