Adaptive Mesh Refinement for One-Dimensional Three-Phase Flows in Heterogeneous Fractured Porous Media

This article presents an analysis of the implementation of the adaptive mesh refinement (AMR) technique to one-dimensional three-phase flows in heterogeneous fractured media. Variations of matrix permeability and matrix–fracture transfer shape factor cause matrix saturation discontinuities. In order to avoid directly performing refining or coarsening operations on these matrix quantities, we suggest using two separated grid systems for the fracture and matrix equations, respectively. The fracture and matrix equations are decoupled by a special decomposition approach during the Newton-Raphson procedure for solving the resulting nonlinear equations. The numerical examples show that the proposed AMR technique is fast with good accuracy.