Abstract
In this paper, we consider a subgrid stabilized Oseen iterative method for the Navier-Stokes equations with nonlinear slip boundary conditions and high Reynolds number. We provide one-level and two-level schemes based on this stability algorithm. The two-level schemes involve solving a subgrid stabilized nonlinear coarse mesh inequality system by applying m Oseen iterations, and a standard one-step Newton linearization problems without stabilization on the fine mesh. We analyze the stability of the proposed algorithm and provide error estimates and parameter scalings. Numerical examples are given to confirm our theoretical findings.
Highlights
We consider the approximations for steady, incompressible Navier-Stokes equations:
A subgrid scale model based on an elliptic projection of the velocity is utilized to stabilize the numerical form of the incompressible Navier-Stokes equations on a coarse grid, and a linear problem that the convection term is fixed by the coarse grid solution which is solved on the fine grid
In this paper, based on the one-level scheme we develop a two-level subgrid stabilized Oseen iterative method for the Navier-Stokes equations with nonlinear slip boundary conditions
Summary
We consider the approximations for steady, incompressible Navier-Stokes equations:. where u is the velocity, p is the pressure, f is the given body force, Ω ⊂ R2 is an open bounded domain with sufficiently smooth boundary ∂Ω, and ν is the viscosity of the fluid. In this method, a subgrid scale model based on an elliptic projection of the velocity is utilized to stabilize the numerical form of the incompressible Navier-Stokes equations on a coarse grid, and a linear problem that the convection term is fixed by the coarse grid solution which is solved on the fine grid. A subgrid scale model based on an elliptic projection of the velocity is utilized to stabilize the numerical form of the incompressible Navier-Stokes equations on a coarse grid, and a linear problem that the convection term is fixed by the coarse grid solution which is solved on the fine grid Both theoretical analysis and numerical examples show that the method can efficiently simulate the high Reynolds number flows.
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