Monotone embedded discrete fractures method for flows in porous media

Abstract

We propose a new method for modeling of flows in fractured media which preserves non-negativity of the solution or satisfies the discrete maximum principle. The method consists in coupling of the embedded discrete fracture method (EDFM) with two nonlinear schemes: monotone two-point flux approximation and compact multi-point flux approximation with the discrete maximum principle. The resulting monotone EDFM (mEDFM) combines effectiveness and simplicity of standard EDFM approach with accuracy and physical relevance of the nonlinear FV schemes on non-orthogonal grids and anisotropic media.