A multiscale Darcy–Brinkman model for fluid flow in fractured porous media

Multiscale Model Reduction Methods for Flow in Heterogeneous Porous Media

In this paper we provide a general framework for model reduction methods applied to fluid flow in porous media. Using reduced basis and numerical homogenization techniques we show that the complexity of the numerical approximation of Stokes flow in heterogeneous media can be drastically reduced. The use of such a computational framework is illustrated at several model problems such as two and t...

A Numerical Algorithm for Fluid Flow in 3D Naturally Fractured Porous Media

Fluid ow in three-dimensional (3D) fractured porous media is considered. The governing system of partial di erential equations consists of two subsystems { one describing the ow in the fractures, and the other describing the ow in the matrix blocks. In this paper, we develop an e cient algorithm for the numerical solution of the problem. An operator splitting technique is employed, as a part of...

Cellular Automaton Model for Fluid Flow in Porous Media

A cellular automaton model for the simulation of fluid flow in porous media is presented. A lattice and a set of rules are int roduced, such th at the flow equations in the continuum limit are formally the same as the equations for one-phase liquid flow in porous media. The model is valid in two as well as th ree dimensions. Numerical calculatio ns of some simple problems are presented and comp...

Multiscale Flow and Transport in Porous Media

Benchmarks for single-phase flow in fractured porous media

This paper presents several test cases intended to be benchmarks for numerical schemes for single-phase fluid flow in fractured porous media. A number of solution strategies are compared, including a vertex and a cell-centered finite volume method, a non-conforming embedded discrete fracture model, a primal and a dual extended finite element formulation, and a mortar discrete fracture model. Th...