Modeling groundwater flow by the element-free Galerkin (EFG) method

The element-free Galerkin (EFG) method is one of meshless methods, which is a very powerful, efficient and accurate method of modeling problems of fluid or solid mechanics with complex boundary shapes and large changes in boundary conditions. This paper reports the theory and the first-known application of the EFG method to groundwater flow modeling. The EFG method constructs shape functions based on moving least square (MLS) approximations, which do not require any element but only a set of nodes. Thus, the EFG method eliminates time-consuming mesh generation procedure with irregular shaped boundaries. The coupled EFG-FEM technique was used to treat Dirichlet boundary conditions. A computer code EFGGW was developed for the problems of steady-state and transient groundwater flow in homogeneous or heterogeneous aquifers. Solutions by the EFG method were similar in accuracy to that by the FEM. The main advantages of the method are the convenience of node generation and the enforced implementation of boundary conditions.