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

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.