Groundwater Management: The Use of Numerical Models

Heijde, Paul van der; Bachmat, Yahuda; Bredehoeft, John; Andrews, Barbara; Holtz, David; Sebastian, Scott

doi:10.1029/wm005

Cited by 30 publications

(14 citation statements)

References 207 publications

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“…A large number of modeling programs have been compared and assessed by PANDIT et al (1993) and VAN DER HEIJDE et al (1985). Therefore, the comments in this section are focused on the following commonly used programs:…”

Section: Programsmentioning

confidence: 99%

Interpretation of Geological, Hydrogeological, and Geochemical Results

Jenn

Kofahl

Müller³

et al. 2007

Environmental Geology

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Section: Programsmentioning

confidence: 99%

Interpretation of Geological, Hydrogeological, and Geochemical Results

Jenn

Kofahl

Müller³

et al. 2007

Environmental Geology

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“…Assume that in each triangular prism element ( Fig. 1) we have 6 C (x,y,z,t) = , Cj(t)4I(x,y,z) (45) 1=1 are basis functions given in Eq. (27).…”

Section: Multiple Cell Balance Methods (Mcbm)mentioning

confidence: 99%

“…During the last two decades, a variety of numerical approaches were presented, such as the finite difference methods (FDM), the finite element methods (FEM), and other alternative methods (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14). However, at least three important problems have not been solved perfectly:…”

Section: Introductionmentioning

confidence: 99%

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Applications of Numerical Methods to Simulate the Movement of Contaminants in Groundwater

Sun¹

1989

Environmental Health Perspectives

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This paper reviews mathematical models and numerical methods that have been extensively used to simulate the movement of contaminants through the subsurface. The major emphasis is placed on the numerical methods of advection-dominated transport problems and inverse problems. Several mathematical models that are commonly used in field problems are listed. A variety of numerical solutions for threedimensional models are introduced, including the multiple cell balance method that can be considered a variation of the finite element method. The multiple cell balance method is easy to understand and convenient for solving field problems. When the advection transport dominates the dispersion transport, two kinds of numerical difficulties, overshoot and numerical dispersion, are always involved in solving standard, finite difference methods and finite element methods. To overcome these numerical difficulties, various numerical techniques are developed, such as upstream weighting methods and moving point methods. A complete review of these methods is given and we also mention the problems of parameter identification, reliability analysis, and optimal-experiment design that are absolutely necessary for constructing a practical model.

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“…Smith (1983a) reviewed research in the U.S.A. on unsaturated soil water flow published in the 1979-1982 quadrennium, and a new progress report on unsaturated flow modeling for 1983-1986 was given by van Genuchten and Jury (1987). Van der Heijde et al (1985) include the unsaturated zone in their survey of numerical models available for subsurface flows.…”

Section: Introductionmentioning

confidence: 99%

Advances in modeling of water in the unsaturated zone

Milly

1988

Transp Porous Med

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This paper reviews recent advances in analytical and numerical solution of problems of water flow through rigid soils in the unsaturated zone. The Richards model remains the most widely accepted and fertile framework for water flow analyses. More general formulations are reserved for the analysis of problems involving macroporosity, thermal effects, and air pressure effects. Many exact and approximate solutions have been derived for particular boundary value problems of homogeneous soils using methods such as quasi-linear analysis, Green-Ampt analysis, perturbation, and the kinematic wave approximation. Numerical simulators have become bigger and more accurate due to improvements in the areas of nonlinear solution procedures, mass conservation, computational efficiency, and computer hardware. Problems of natural heterogeneity have been addressed primarily through application of various stochastic methods to the Richards model. The stochastic formulations generally refute the concept of simple 'equivalent' homogeneous properties, but do themselves offer a certain limited potential for a predictive capability.

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Groundwater Management: The Use of Numerical Models

Cited by 30 publications

References 207 publications

Interpretation of Geological, Hydrogeological, and Geochemical Results

Interpretation of Geological, Hydrogeological, and Geochemical Results

Applications of Numerical Methods to Simulate the Movement of Contaminants in Groundwater

Advances in modeling of water in the unsaturated zone

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