Numerical Modeling of Two-Phase Fluid Flow in non- Deforming Porous Media using Element Free Galerkin EFG Method

Over the past few decades, subsurface contamination by organic compounds, water-air phase movement in unsaturated soils, and oil reservoir exploitation have motivated researchers in various fields of engineering to study and simulate the complicated two-phase flow systems in soils and rocks. This paperpresents the application of a type of mesh-less method, called Element-Free Galerkin (EFG), to simulate the water and air flow in variably saturated porous media. The numerical algorithm is based on Galerkin’s weighted residual approach and utilizes the penalty method to enforce the essential boundary conditions.The resulting constrained Galerkin weak forms of governing equations are discretized in space using thesame EFG shape functions and a fully implicit scheme is employed for the temporal discretization. The accuracy and efficiency of the developed EFG code are evaluated by solving a number of benchmark examples. Comparing the obtained numerical results with the experimental observations and/or solutions of other numerical algorithms demonstrates the good performance of the proposed mesh-free model insimulating the complexities involved in the behavior of two-phase flow systems in soils and rocks.