Numerical approximations based on different forms of the governing partial differential equation can lead to significantly different results for unsaturated flow problems. Numerical solution based on the standard h-based form of Richards equation generally yields poor results, characterized by large mass balance errors and erroneous estimates of infiltration depth. Conversely, numerical solutions based on the mixed form of Richards equation can be shown to possess the conservative property, so that mass is perfectly conserved. This leads to significant improvement in numerical solution performance, while requiring no additional computational effort. However, use of the mass-conservative method does not guarantee good solutions. Accurate solution of the unsaturated flow equation also requires use of a diagonal time (or mass) matrix. Only when diagonal time matrices are used can the solution be shown to obey a maximum principle, which guarantees smooth, nonoscillatory infiltration profiles. This highlights the fact that proper treatment of the time derivative is critical in the numerical solution of unsaturated flow.

A General Mass-Conservative Numerical Solution for the Unsaturated Flow Equation

A one-dimensional dual-porosity model has been developed for the purpose of studying variably saturated water flow and solute transport in structured soils or fractured rocks. The model involves two overlaying continua at the macroscopic level: a macropore or fracture pore system and a less permeable matrix pore system. Water in both pore systems is assumed to be mobile. Variably saturated water flow in the matrix as well as in the fracture pore system is described with the Richards' equation, and solute transport is described with the convection-dispersion equation. Transfer of water and solutes between the two pore regions is simulated by means of first-order rate equations. The mass transfer term for solute transport includes both convective and diffusive components. The formulation leads to two coupled systems of nonlinear partial differential equations which were solved numerically using the Galerkin finite element method. Simulation results demonstrate the complicated nature of solute leaching in structured, unsaturated porous media during transient water flow. Sensitivity studies show the importance of having accurate estimates of the hydraulic conductivity near the surface of soil aggregates or rock matrix blocks. The proposed model is capable of simulating preferential flow situations using parameters which can be related to physical and chemical properties of the medium.

A dual-porosity model for simulating the preferential movement of water and solutes in structured porous media

http://www.pc-progress.com/Documents/Jirka/Simunek_et_al_MacroFl_2002.pdf

Review and comparison of models for describing non-equilibrium and preferential flow and transport in the vadose zone

Three-dimensional analysis of variably-saturated flow and solute transport in discretely-fractured porous media

Water flow in soils can be characterized, in principle, for many boundary and initial conditions by solving the proper governing differential equations. There are several reasons why this state-of-the-art technology is not yet fully utilized. One reason may be complexity and expense of computer based numerical solutions. However, a more important reason is the difficulty of obtaining the primary input which is the relationship between matrix potential and hydraulic conductivity as a function of soil water content. Approximate water flow models based on physical principles or empirical results may simplify the computational requirements; however, soil property inputs are still required.

Estimation of Soil Water Retention and Hydraulic Properties

This paper gives a review of our current conceptual understanding of the basic processes of water flow and chemical transport in the untsaturated (vadose) zone and of various deterministic mathematical models that are being used to describe these processes. During the past few decades, tremendous effort has been directed toward unravelling the complexities of various interactive physical, chemical, and microbiological mechanisms affecting unsaturated flow and transport, with contributions being made by soil scientists, geochemists, hydrologists, soil microbiologists, and others. Unfortunately, segmented, disciplinary research has contributed to a lack of experimental and theoretical understanding of the vadose zone, which, in turn, has precluded the accurate prediction and management of flow and contaminant transport through it. Thus a more unified and interdisciplinary approach is needed that considers the most pertinent physical, chemical, and biological processes operative in the unsaturated zone. Challenges for both fundamental and applied researchers to reveal the intricacies of the zone and to integrate these with currently known concepts are numerous, as is the urgency for progress inasmuch as our soil and ground water resources are increasingly subjected to the dangers of long-term pollution. Specific research areas in need of future investigation are outlined.

D. R. Nielsen

Papers

Water flow and solute transport processes in the unsaturated zone