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| The state space finite element method for Stokes flow in rectangular cavity |
| Received:July 16, 2012 Revised:December 25, 2012 |
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| DOI：10.7511/jslx201402011 |
| KeyWord:Hellinger-Reissner variational principle Stokes flow Hamilton canonical equation state space finite element method precise integration method |
| Author | Institution |
| 孟俊苗 |
西北工业大学 工程力学系, 西安 |
| 邓子辰 |
西北工业大学 工程力学系, 西安 ;大连理工大学 工业装备结构分析国家重点实验室, 大连 |
| 王艳 |
西北工业大学 工程力学系, 西安 |
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| 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 employed in x direction and was derived by the state space control method.In addition,the precise integration 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. |