Subgrid model for the stationary incompressible Navier-Stokes equations based on the high order polynomial interpolation
Y. Zhang 1, N. Feng 2, Y. He 11 Faculty of Science, Xi'an Jiaotong University, Shaanxi, 710049, P. R. China.
2 School of Applied Mathematics, University of Electronic science and Technology of China, Chengdu, Sichuan 610054, P. R. China.
Received by the editors January 1, 2009 and, in revised form, October 22, 2009.
In this paper, we propose a subgrid finite element method for the two-dimensional (2D) stationary incompressible Naver-Stokes equation (NSE) based on high order finite element polynomial interpolations. This method yields a subgrid eddy viscosity which does not act on the large scale flow structures. The proposed eddy viscous term consists of the fluid flow fluctuation stress. The fluctuation stress can be calculated by means of simple reducedorder polynomial projections. Assuming some regular results of NSE, we give a complete error analysis. Finally, in the part of numerical tests, the numerical computations show that the numerical results agree with some benchmark solutions and theoretical analysis very well.AMS subject classifications: 35R35, 49J40, 60G40
Key words: Navier-Stokes equation, subgrid method, eddy viscosity, error analysis and numerical tests.
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