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Volume 7, Issue 4
Subgrid Model for the Stationary Incompressible Navier-Stokes Equations Based on the High Order Polynomial Interpolation

Y. Zhang, M. Feng & Y. He

Int. J. Numer. Anal. Mod., 7 (2010), pp. 734-748.

Published online: 2010-07

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  • Abstract

In this paper, we propose a subgrid finite element method for the two-dimensional (2D) stationary incompressible Navier-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 reduced-order 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.

  • Keywords

Navier-Stokes equation, subgrid method, eddy viscosity, error analysis and numerical tests.

  • AMS Subject Headings

35R35, 49J40, 60G40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-7-734, author = {Zhang , Y.Feng , M. and He , Y.}, title = {Subgrid Model for the Stationary Incompressible Navier-Stokes Equations Based on the High Order Polynomial Interpolation}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2010}, volume = {7}, number = {4}, pages = {734--748}, abstract = {

In this paper, we propose a subgrid finite element method for the two-dimensional (2D) stationary incompressible Navier-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 reduced-order 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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/749.html} }
TY - JOUR T1 - Subgrid Model for the Stationary Incompressible Navier-Stokes Equations Based on the High Order Polynomial Interpolation AU - Zhang , Y. AU - Feng , M. AU - He , Y. JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 734 EP - 748 PY - 2010 DA - 2010/07 SN - 7 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/749.html KW - Navier-Stokes equation, subgrid method, eddy viscosity, error analysis and numerical tests. AB -

In this paper, we propose a subgrid finite element method for the two-dimensional (2D) stationary incompressible Navier-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 reduced-order 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.

Zhang , Y.Feng , M. and He , Y.. (2010). Subgrid Model for the Stationary Incompressible Navier-Stokes Equations Based on the High Order Polynomial Interpolation. International Journal of Numerical Analysis and Modeling. 7 (4). 734-748. doi:
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