Three Iterative Finite Element Methods for the Stationary Smagorinsky Model

Abstract

Three iterative stabilised finite element methods based on local Gauss integration are proposed in order to solve the steady two-dimensional Smagorinsky model numerically. The Stokes iterative scheme, the Newton iterative scheme and the Oseen iterative scheme are adopted successively to deal with the nonlinear terms involved. Numerical experiments are carried out to demonstrate their effectiveness. Furthermore, the effect of the parameters $Re$ (the Reynolds number) and $δ$ (the spatial filter radius) on the performance of the iterative numerical results is discussed.