Finite Element Method for Low Froude Number Saint-Venant Equations

Abstract

The flow in shallow water bodies can be described by the Saint-Venant equations, including bottom friction, viscosity and Coriolis- Boussinesq factor. In this work a numerical method is proposed for the solution of the Saint- Venant system, for the case of negligeable Froude number, employing a rigid lid approximation. The problem is discretized employing the Finite Element Method in a triangular mesh. Spatial discretization of the diffusion and pressure terms is made through the Galerkin method. The MINI element is selected, among the Taylor- Hood family of conforming elements that satis- fied the LBB condition. The substantial deriva- tive is discretized through a semi-Lagrangean technique, using a first-order backward Euler im- plicit scheme. The linear system is solved em- ploying the discrete projection method, based on LU decomposition. The code is developed using the object-oriented paradigm. This work is sup- ported by Furnas Centrais Elétricas S.A..