Free surface flow modelling on a complex topographyby Mohamed Naaim, Div Nivologie - CEMAGREF, Saint Martin d'Heres, France,
Gerard Brugnot, Div Nivologie - CEMAGREF, Saint Martin d'Heres, France,
Abstract: The aim of this paper is to describe the different construction stages and the validation of a free surface flow model on a complex topography. This model is based on the two dimensional shallow water equations. In order to treat the complex topography a finite element space description is used. It allows us to follow the domain boundary and to use a reduced cell number. To solve these equations two numerical methods are used. The first one is based on a finite elements formulation. The Galerkin formulation is modified to add two new terms called stream line diffusion and shock capturing. These two terms make the method steady for the hyperbolic non-linear system. The second one is based on a finite volumes formulation. It consists in integrating the system on each cell and in applying a Riemann solver to obtain the numerical flux at the cell interface. The speed and the accuracy of the two methods are compared in the case of a dam break on an initially dry bottom. The accuracy obtained through the two methods is the same. Concerning the speed, the finite volumes method is more effective, therefore it was adopted. The model developed in this way was tested comparing it to experimental results obtained in the cases of a two dimensional dam break and a wave propagation in a lake with a complex topography. The obtained results show a good agreement between the numerical simulation and the experimental results.
Subject Headings: Finite volume method | Topography | Hydrologic models | Finite element method | Free flow | Two-dimensional models | Numerical models
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