By a porous medium we mean a material consisting of a solid matrix with an interconnected
void. We suppose that the solid matrix is either rigid (the usual situation) or it undergoes …

Large linear systems of saddle point type arise in a wide variety of applications throughout
computational science and engineering. Due to their indefiniteness and often poor spectral …

The main purpose of this chapter is to give a derivation, which is mathematically precise,
physically natural, and conceptually simple, of the quasilinear system of partial differential …

Integrated, process‐based numerical models in hydrology are rapidly evolving, spurred by
novel theories in mathematical physics, advances in computational methods, insights from …

The transport of substances back and forth between surface water and groundwater is a very
serious problem. We study herein the mathematical model of this setting consisting of the …

This book presents an account of theories of? ow in porous media which have proved
tractable to analysis and computation. In particular, the t-ories of Darcy, Brinkman, and …

In this work, we couple the incompressible steady Navier–Stokes equations with the Darcy
equations, by means of the Beaver–Joseph–Saffman's condition on the interface. Under …

This paper is an overview of known and new results about the coupling of Navier-Stokes
and Darcy equations to model the filtration of incompressible fluids through porous media …

We study numerical methods for solving a coupled Stokes–Darcy problem in porous media
flow applications. A two-grid method is proposed for decoupling the mixed model by a …

A locally conservative numerical method for solving the coupled Stokes and Darcy flows
problem is formulated and analyzed. The approach employs the mixed finite element …