Element Free Galerkin Method for the Numerical Solution of the Pure Convection Problems

In this paper, the Meshless method is introduced to the hydraulics. An element free Galerkin (EFG)method for simulation of two-dimensional shallow water flows is presented and its implementation is described. In this method only the nodal data which may be the same as those used in the finite elementmethods (FEMs) and a description of the domain boundary geometry are necessary; no element or grid connectivity is needed. In the EFG method the moving least squares (MLS) interpolations is used to construct the trial functions. The modelled domain is represented thorough the nodal points. A Galerkinmethod is applied to discretize the governing differential equations, resulting in a simultaneous equationsystem. An underlying cell structure for calculation of the integrals is used. The sensitivity analysis is proposed to determine the influence of the different parameters of the EFG method with solving moving cone problem. To verify the efficiency of the proposed method the shoaling problem is analyzed.

Keywords:

meshless method , shallow water problems , sensitivity analysis , moving cone problem , shoaling