计算力学学报Issue(2)：205-211,7.DOI:10.7511/jslx201402011
矩形空腔内Stokes流的状态空间有限元法
The state space finite element method for Stokes flow in rectangular cavity
摘要
Abstract
Based on the Hellinger-Reissner variational principle ,the Hamilton canonical equation of the plane incompressible Stokes flow was derived from the equilibrium equations ,continuity conditions and the force boundary conditions .By the separation of variables ,the general finite element method was em-ployed in x direction and was derived by the state space control method .In addition ,the precise integra-tion method for the exponential matrix was employed in the calculation .The effectiveness of the state space finite element method is demonstrated by analyzing and comparing the simulation example in case of a single-lid driven cavity with free surface side walls .The study of this paper is to introduce the idea of the semi-analytical method into the low Reynolds number flow problems ,and lay a foundation of further study on the Stokes flow with complex boundary in the Hamiltonian system .关键词
Hellinger-Reissner变分原理/Stokes流/正则方程/状态空间法/精细积分Key words
Hellinger-Reissner variational principle/Stokes flow/Hamilton canonical equation/state space finite element method/precise integration method分类
数理科学引用本文复制引用
孟俊苗,邓子辰,王艳..矩形空腔内Stokes流的状态空间有限元法[J].计算力学学报,2014,(2):205-211,7.基金项目
国家自然科学基金（10972182，11172239，10902089）；国家基础研究计划973项目（2011CB610300）；国家111引智计划（B07050）；高校博士点基金（20106102110019）；大连理工大学工业装备结构分析国家重点实验室开放基金（GZ0802）资助项目． （）
