Analysis of Shallow Water Problems Using Element-Free Galerkin Method

Abstract

A numerical meshless method is proposed to investigate the solution to shallow water equations. The numerical solution to pure convection equations, such as shallow water equations, is an important component of many problems. An element-free Galerkin (EFG) method has been developed and implemented to solve these equations. In this method, there is no need for nodal connectivity; it simply uses nodal data that are similar to those used in the finite element method. The essential boundary condition is enforced by the penalty method and the moving least squares approximation is used for the interpolation scheme. The numerical efficiency of the proposed method is demonstrated by solving several benchmark examples. Sensitivity analysis on the parameters of the EFG method was carried out and the results confirm its ability to solve shallow water equations and reveal that increasing the number of field nodes and Gauss quadrature points can improve the accuracy of the proposed method. It can be concluded that the average distance of the Gauss points should be less than one-third of the average distance of the nodal points. To produce the best results, the radius of influence domain should be three times the distance of the nodal points.