Subgrid scale stabilized finite element for solution of incompressible viscous flows

Started with the concept and fundamental of Subgrid Scalestabilized (SGS) method, an improved SSS finite element formulation isproposed to obtain time independent solutions by solving the unsteadyincompressible Navier-Stokes equations. Based on some rational approximationand simplification, a new stabilization parameter which has relation withthe selective time step size is deduced. As a result, the numericalinstability resulting from high Reynolds and/or small time step size iseliminated. Combined with standard k-\varepsilon turbulence model andwall function method to estimate turbulent viscosity, the improved SGS method is applied to solve incompressible turbulent flows. Thefinite element implementation of wall function along with solution ofturbulence transport equations is discussed in detail and the positivitypreserving limiter for turbulence variables is introduced. A segregatedalgorithm for time stepping to solve incompressible turbulent flows isdeveloped. The numerical examples of laminar and turbulent flows over abackward facing step are presented in order to show the possibility,stability and high accuracy of the proposed approach for simulating steadyincompressible viscous flows.