A Reduced Model for Flow and Transport in Fractured Porous Media with Non-matching Grids

Abstract

In this work we focus on a model reduction approach for the treatment of fractures in a porous medium, represented as interfaces embedded in a n-dimensional domain, in the form of a (n- 1)-dimensional manifold, to describe fluid flow and transport in both domains. We employ a method that allows for non-matching grids, thus very advantageous if the position of the fractures is uncertain and multiple simulations are required. To this purpose we adopt an XFEM approach to represent discontinuities of the variables at the interfaces, which can arbitrarily cut the elements of the grid. The method is applied to the numerical solution of the Darcy problem, and advection-diffusion problems in porous media.