RBF Applications to Selected Water Resources Problems

Abstract. Many numerical solution alternatives based on Navier Stokes equations or Reynolds equations with single or double phase closure turbulence model were proposed. These have the drawback of : i) High computational cost, ii) The detailed complexity of the flow are partially accounted for, iii) Parameters estimation is still an open problem. In this paper, we proceeded by depth averaging of the Navier Stokes equations, so called shallow water equations (SWE). This reduces the dimensionality of the problem by one and therefore will allow more faster simulation to understand the ongoing mechanics. Shallow water equations are usually dealt with quite conventional methods grid based discretisation such as finite difference, finite element or finite volume methods. In this paper we use meshless method known as radial basis functions (RBF) method. RBF based Meshless methods have gained much attention in recent years, not only in the mathematics but also in the engineering community. It has been extensively popularized owing to their flexibility in solving PDE problem. The technique is of quasi-analytical and based on the collocation formulation and does not require the generation of a grid and any integral evaluation. Three applications are presented. The first one deals with Burger’s equation (1-D, 2-D), the seconde one concern a linear two-dimensional hydrodynamic model of rectangular channel for validation purposes. Finaly the third is a real case concerning the hydrodynamic of Ourika valley in Morocco aiming at predicting inundated areas.