Modelling Water Flow in Unsaturated Porous Media: Accounting for Nonlinear Permeability and Material Heterogeneity
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.
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2 Mathematical Models of Flow in Porous Media
3 Numerical Solution of Flow Equations
4 Computation of InterNodal Permeabilities for Richards Equation
5 Upscaling from Darcy Scale to Field Scale
6 Flow in Binary Media with Heterogeneous Hydraulic Diffusivity
7 Flow in Binary Media with Heterogeneous AirEntry Pressure
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Modelling Water Flow in Unsaturated Porous Media: Accounting for Nonlinear ...
No preview available - 2014
Adv Water Resour air entry pressure air-entry approach approximation arithmetic mean assumed averaging schemes background material boundary conditions capillary function capillary pressure coefficient computed control volume corresponding Darcian Darcy scale Darcy-scale defined diffusivity domain drainage effective permeability equivalent permeability field-scale finite element finite element method finite volume finite volume method flow equation flow in porous fluid phase flux formula fractured Genuchten governing equations gradient gravity grid heterogeneous medium homogeneous hydraulic conductivity infiltration inter-nodal permeability intrinsic permeability iterative kfmw large-scale layered matrix block nodal nodes nonlinear numerical diffusion numerical simulations numerical solution obtained one-dimensional parameters peffw periodic cell permeability tensor pore porous media pressure head relative permeability functions Richards equation soil spatial discretization Szymkiewicz two-phase flow unsaturated flow upscaled model upstream Vadose Zone variable vertical volumetric water content water flow water pressure water pressure head Water Resour Res water saturation x(ij x(jk