Fully discrete IPDG–HMM for multiscale Richards equation of unsaturated flow in porous media

Gradient schemes for two-phase flow in heterogeneous porous media and Richards equation

The gradient scheme family, which includes the conforming and mixed finite elements as well as the mimetic mixed hybrid family, is used for the approximation of Richards equation and the two-phase flow problem in heterogeneous porous media. We prove the convergence of the approximate saturation and of the approximate pressures and approximate pressure gradients thanks to monotony and compactnes...

Fluid flow in porous media using image-based modelling to parametrize Richards' equation

The parameters in Richards' equation are usually calculated from experimentally measured values of the soil-water characteristic curve and saturated hydraulic conductivity. The complex pore structures that often occur in porous media complicate such parametrization due to hysteresis between wetting and drying and the effects of tortuosity. Rather than estimate the parameters in Richards' equati...

Multiscale Flow and Transport in Porous Media

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...

Algebraic multiscale method for flow in heterogeneous porous media with embedded discrete fractures (F-AMS)

This paper introduces an Algebraic MultiScale method for simulation of flow in heterogeneous porous media with embedded discrete Fractures (F-AMS). First, multiscale coarse grids are independently constructed for both porous matrix and fracture networks. Then, a map between coarseand fine-scale is obtained by algebraically computing basis functions with local support. In order to extend the loc...