Quasi-3D Finite Element Shallow-Water Flow with $k- epsilon$ Turbolence Model
Thursday 11th November 2004
Leupi, Celestin; Miglio, Edie; Altinakar, A.; Quarteroni, Alfio; Deville, M.O.
An extension of a three-dimensional (3D) finite element method is proposed for shallow-water equations (SWE). The method is based on the Raviart-Thomas finite element approximation. A numerical solution for shallow-water flows is developed based on the unsteady Reynolds-averaged Navier-Stokes (RANS) equations. In this work the assumption of hydrostatic pressure is applied. The SWE equations are solved in a given multilayered system (which consist of an a priori subdivision of the vertical direction of the domain into layers of fixed thickness), with a semi-implicit time stepping method. The eddy viscosity is calculated using the standard $k- epsilon$ turbolence model. The boundary conditions at the bed are based on the equilibrium assumption of the production terms with vertical diffusione terms using wall functions. To test the validity of the new algorithm the model is applied to three-dimensional flows for which experimental data and other numerical results are available for comparison.