对Taylor-Galerkin有限元法的一点改进和它的应用
A Modification of Taylor-Galerkin Finite Element Method and its Application
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摘要: 本文针对Taylor-Galerkin有限元法的两个基本假设进行讨论.改进了原假设,仅以一个假设作为出发点,得到了广义的有限元离散公式.对具体流函数—涡量方程的求解进行了改进的Taylor-Galerkin有限元分析.提出了组合式的求解方法,使求解过程更为合理.算例计算表明,该方法的效果是很好的.Abstract: Two basic hypothesises of Taylor-Galerkin Finite Element Method are studied in this paper. One of them which is unreasonable is redefined. The only hypothesis becomes the standpoint of Generalized Finite Element. We use this idea to analysis stream function-vorticity equations with Modified Taylor-Galerkin Finite Element Method, and give the two-step solving method, which makes the solving process more reasonable than ever before. Several computational examples reveal that the results of this new method are satisfied.
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Key words:
- hypothesis /
- finite element method /
- stream function iteration /
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[1] Donea,J.,S.Giuliani and H.Laval,Time-accurate solution of advection-diffusion problems by finite elements,Computer Methods in Applied Mechanics and Engineering,45(1984). [2] Hughes,T.J.R.,and M.Mallet,A new finite element formulation for computational fluid dynamics:Ⅳ,Mechanical Engineering,58(1986). [3] 章本照,《流体力学中的有限元方法》,械机工业出版社(1986). [4] 朱刚,陈农、景思睿、胡庆康,各向异性张力有限单元的构造及应用,西安交通大学学报(待发表). -
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