Nonlinear Galerkin Method for the Exterior Nonstationary Navier-Stokes Equations
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摘要: 提出了求解外部非定常Navier-stokes方程的有限元边界元耦合的非线性Galerkin算法,证明了相应变分问题的正则性和数值解的收敛速度。收敛性分析表明如果选取粗网格尺度H是细网格尺度h的开平方数量级,则该算法提供了与古典Galerkin算法同阶的收敛速度。然而非线性Galerkin算法仅仅需要在粗网格解非线性问题,在细网格上解线性问题。因此,该算法可以节省计算工作量。
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关键词:
- Navier-Stokes方程 /
- 有限元 /
- 边界元 /
- 外部 /
- 非线性 /
- Galerkin算法
Abstract: A new algorithm combining nonlinear Galerkin method and coupling method of finite element and boundary element is introduced to solve the exterior nonstationary Navier-Stokes equations. The regularity of the coupling variational formulation and the convergence of the approximate solution corresponding to the algorithm are proved.If the fine meshh is choosed as coarse mesh H-sgure, the nonlinear Galerkin method,nonlineatity is only treated on the coarse grid and linearity is treated on the fine grid.Hence,the new algorithm can save a large amount of computational time.-
Key words:
- Navier-Stokes equation /
- finite element /
- boundary element /
- exterior /
- nonlinear /
- galerkin merhod
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