Radial Basis Functions Alternative Solutions to Shallow Water Equations

Abstract. In this paper, shallow water equations (SWE) are solved through a variety of meshless methods known as radial basis functions (RBF) methods. RBF based Meshless methods have gained much attention in recent years for both the mathematics as well as the engineering community. They have been extensively popularized owing to their flexibility, power and simplicity in solving partial differential equations. The technique is of quasi-analytical type and based on the collocation formulation and does not require the generation of a grid or integrals evaluation. A bundle of techniques such as MQRBF, IMQRBF, GSSRBF, CSRBF are formulated for the specific case of shallow water equations (SWE), with adequate parameters, these techniques show robustness and low computational costs. For validation purposes, two applications are presented. One deals with Burger’s equation (2D), and the second with a linear two-dimensional hydrodynamics model of rectangular channel shape. Finally a third application concerning a real case study of the hydrodynamic of the Ourika valley in Morocco is investigated aiming at rebuilding the 1995 historical flood wave propagation, therefore delineate inundated areas, estimate velocities and wave time arrivals. For illustration purposes, some results are presented in both graphical forms as well in animated movies to show the high speed potential outputs of RBF.