A Simple Scheme to Solve Saint-Venant Equations by Finite Element Method

Abstract

Solving the Saint-Venant equations by finite element method (FEM) takes a long CPU time (even for a short time). Hence, we can apply the fast numerical methods such as finite difference method. But, these methods are not stable most of the time and moreover verification of the stability for these methods is very hard. The main reason is that the construction of the system needs the (analytical or numerical) integration of many (complicated) nonlinear functions in each time step. In this paper, we present a methodology to solution of these equations. The proposed method stabilizes the Saint-Venant equations, avoiding oscillations around discontinuities. In comparison with current methodology for construction of the system discretized by FEM, our methodology takes much shorter time. In addition, we split the discretized system into two simple systems so that each of them can be solved through direct methods. To demonstrate the performance of the method, some examples are presented.