Modeling groundwater flow with a free and moving boundary using the element-free Galerkin (EFG) method

Abstract

This paper presents the results of the first-time application of the element-free Galerkin (EFG) method for simulations of groundwater flow with free and moving boundaries. The EFG method does not require any element or grid, therefore it eliminates time-consuming remeshing procedures in modeling of moving boundary problems. The EFG method employs time dependent shape functions based on the moving least square (MLS) approximations. A coupled EFG-FEM technique was used to treat Dirichlet boundary conditions that are difficult in the EFG method. The EFG method was verified by comparing numerical results with analytical solutions for a steady-state seepage problem. In order to demonstrate applicability of the EFG method dealing with flow problems with moving boundaries, a transient free-surface and seepage problem in an unconfined aquifer was simulated. Difficulties associated with modeling a free and moving irregular boundary have been successfully overcome by employing the EFG method.