A novel three-dimensional element free Galerkin (EFG) code for simulating two-phase fluid flow in porous materials

In the past few decades, numerical simulation of multiphase flow systems has received increasing attention because of its importance in various fields of science and engineering. In this paper, a three-dimensional numerical model is developed for the analysis of simultaneous flow of two fluids through porous media. The numerical approach is fairly new based on the element-free Galerkin (EFG) method. The EFG is a type of mesh-less method which has rarely been used in the field of flow in porous media. The weak forms of the governing partial differential equations are derived by applying the weighted residual method and Galerkin technique. The penalty method is utilized for imposition of the essential boundary conditions. To create the discrete equation system, the EFG shape functions are used for spatial discretization of pore fluid pressures and a fully implicit scheme is employed for temporal discretization. The obtained numerical results indicate that the EFG method has the capability to substitute the classical FE and FD approaches from the accuracy point of view, provided that the efficiency of the EFG is improved. The developed EFG code can be used as a robust numerical tool for simulating two-phase flow processes in the subsurface layers in various engineering disciplines.