The Biot–Darcy–Brinkman model of flow in deformable double porous media; homogenization and numerical modelling

Numerical Model for Saturated-Unsaturated Flow in Deformable Porous Media

An integrated finite difference algorithm is presented for numerically solving the governing equation of saturated-unsaturated flow in deformable porous media. In recognition that stability of the explicit equation is a local phenomenon a mixed explicit-implicit procedure is used for marching in the time domain. In this scheme the explicit changes in potential are first computed for all element...

Numerical homogenization of two-phase flow in porous media

Homogenization has proved its effectiveness as a method of upscaling for linear problems, as they occur in single-phase porous media flow for arbitrary heterogeneous rocks. Here we extend the classical homogenization approach to nonlinear problems by considering incompressible, immiscible two-phase porous media flow. The extensions have been based on the principle of preservation of form, stati...

Numerical Modelling of Multiphase Flow in Porous Media

Numerical Homogenization of Well Singularities in the Flow Transport through Heterogeneous Porous Media: Fully Discrete Scheme

Motivated by well-driven flow transport in porous media, Chen and Yue proposed a numerical homogenization method for Green function [Multiscale Model. Simul. 1 (2003) 260–303]. In that paper, the authors focused on the well pore pressure, so the local error analysis in maximum norm was presented. As a continuation, we will consider a fully discrete scheme and its multiscale error analysis on th...

Numerical Homogenization of Well Singularities in the Flow Transport through Heterogeneous Porous Media