Numerical Modeling of One-Dimensional Saint Venant equations Based on a Finite Element Approach

In this article, a finite element numerical model is presented for solving one dimensional shallow water (Saint Venant) equations. For variable approximations, one-dimensional elements with 3 nodes along with quadratic interpolating functions are used. The standard weighted Residual Galerkin method is applied to discretize the spatial terms while combination of forward finite difference and semi-implicit (method) has been used to discretize the temporal terms of the governing equations. In order to validate the accuracy of the suggested code, two common tests of dam break and solitary wave propagation are presented. Computational results of the current code have been compared against the analytical solution as well as the results of TELEMAC software and good agreements have been achieved.