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

2009 ◽  
Vol 2009 ◽  
pp. 1-20 ◽  
Author(s):  
Yan Zhang ◽  
Yinnian He
Keyword(s):  
Finite Element ◽  
Stokes Equations ◽  
Mixed Finite Element ◽  
Fluid Flows ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Viscous Term ◽  
Subgrid Model ◽  
High Reynolds ◽  
Large Flow

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 L2-projection. The fluctuation operator can be implemented by the L2-projection from high-order interpolation finite-element spaces to the low-order interpolation finite-element spaces. In this paper, P2/P1 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.

An Oseen-Type Post-Processed Finite Element Method Based on a Subgrid Model for the Time-Dependent Navier–Stokes Equations

2019 ◽  
Vol 17 (04) ◽  
pp. 1950002
Author(s):  
Qihui Zhang ◽  
Yueqiang Shang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stokes Equations ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Time Dependent ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Subgrid Model ◽  
Element Method

An Oseen-type post-processed mixed finite element method based on a subgrid model is presented for the simulation of time-dependent incompressible Navier–Stokes equations. This method first solves a subgrid stabilized nonlinear Navier–Stokes system on a mesh of size [Formula: see text] to obtain an approximate solution pair [Formula: see text] at the given final time [Formula: see text], and then post-processes the solution [Formula: see text] by solving a stabilized Oseen problem on a finer mesh or in higher-order finite element spaces. We prove stability of the stabilized method, derive error estimates for the post-processed solutions, give some numerical results to verify the theoretical predictions and demonstrate the effectiveness of the proposed method.

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