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Advances in Numerical Analysis
Volume 2009 (2009), Article ID 494829, 20 pages
http://dx.doi.org/10.1155/2009/494829
Research Article

A Subgrid Model for the Time-Dependent Navier-Stokes Equations

Faculty of Science, Xi'an Jiaotong University, Shanxi 710049, China

Received 22 November 2008; Revised 5 May 2009; Accepted 25 June 2009

Academic Editor: Weimin Han

Copyright © 2009 Yan Zhang and Yinnian He. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We propose a stabilized subgrid finite-element method for the two-dimensional (2D) nonstationary incompressible Naver-Stokes equation (NSE). This method yields a subgrid eddy viscosity which does not act on the large flow structures. The proposed eddy viscous term is constructed by a fluctuation operator based on an -projection. The fluctuation operator can be implemented by the -projection from high-order interpolation finite-element spaces to the low-order interpolation finite-element spaces. In this paper, mixed finite-element spaces are adopted to implement the calculation and the analysis. The error analysis is given based on some regular assumptions. Finally, in the part of numerical tests, the numerical computations show that the numerical results agree with theoretical analysis very well. Meanwhile, the numerical investigations demonstrate that the proposed subgrid is very effective for high Reynolds number fluid flows and superior to other referred subgrid models.