Subgrid scale stabilized finite element for solution of incompressible viscous flows

Started with the concept and fundamental of Subgrid Scale stabilized (SGS) method, an improved SSS finite element formulation is proposed to obtain time independent solutions by solving the unsteady incompressible Navier-Stokes equations. Based on some rational approximation and simplification, a new stabilization parameter which has relation with the selective time step size is deduced. As a result, the numerical instability resulting from high Reynolds and/or small time step size is eliminated. Combined with standard k-ε turbulence model and wall function method to estimate turbulent viscosity, the improved SGS method is applied to solve incompressible turbulent flows. The finite element implementation of wall function along with solution of turbulence transport equations is discussed in detail and the positivity preserving limiter for turbulence variables is introduced. A segregated algorithm for time stepping to solve incompressible turbulent flows is developed. The numerical examples of laminar and turbulent flows over a backward facing step are presented in order to show the possibility, stability and high accuracy of the proposed approach for simulating steady incompressible viscous flows.