Modelling Water Flow in Unsaturated Porous Media

This book examines two issues in mathematical and numerical modelling of flow in unsaturated porous media, discussing spatial discretization of highly nonlinear permeability coefficient, and large scale flow in heterogeneous porous media of binary stucture.

The book focuses on two issues related to mathematical and numerical modelling of flow in unsaturated porous media. In the first part numerical solution of the governing equations is discussed, with particular emphasis on the spatial discretization of highly nonlinear permeability coefficient. The second part deals with large scale flow in heterogeneous porous media of binary structure. Upscaled models are developed and it is shown that the presence of material heterogeneities may give rise to additional non-equilibrium terms in the governing equations or to hysteresis in the averaged constitutive relationships.

Provides consistent presentation of two approaches to modelling water flow in unsaturated porous media Presents in-depth discussion of the numerical solution algorithm with improved method for averaging of the permeability coefficient Analyzes the applicability of the Richards' model for heterogeneous media Includes supplementary material: sn.pub/extras

Contenu
Introduction.- Mathematical Models of Flow in Porous Media.- Numerical Solution of Flow Equations.- Computation of Inter-Nodal Permeabilities for Richards Equation.- Upscaling from Darcy Scale to Field Scale.- Flow in Binary Media with Heterogenous Hydraulic Diffusivity.- Flow in Binary Media with Heterogenous Air-Entry Pressure.