Numerical solutions for unsteady flow in unconfined aquifers

Guvanasen, V.; Volker, R. E.

doi:10.1002/nme.1620151107

Cited by 15 publications

(3 citation statements)

References 7 publications

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“…For free surface seepage no suitable analytical solutions are available and so other comparisons have to be resorted to. Amar (1975) and Guvanasen & Volker (1980) used sand tank tests to check the accuracy of their programs but obviously experimental results are subject to errors. Todsen (1971) compared his results with those obtained by Herbert (1968) from electrical resistance analogues.…”

Section: Comparison Of Methodsmentioning

confidence: 99%

“…Subsequent work by Amar (1975) followed the work of Todsen but Singh (1976) used similar techniques to those of Verma & Brutsaert but without the moving mesh. Guvanasen & Volker (1980) whilst mainly concentrating on finite elements did look in detail at the work of Todsen and briefly at that of Verma & Brutsaert and Singh. In this paper the work of Guvanasen & Volker is extended to fully consider both methods and the various problems which occur with regard to stability are discussed.…”

Section: Introductionmentioning

confidence: 99%

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The representation of time variant free surface seepage using finite difference methods: a review

Miles¹

1986

EGSP

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Several numerical techniques are available for the representation of time variant free surface seepage, notably finite elements, boundary elements and finite difference methods. This work concentrates on the latter. Over the last twenty years several papers have been published on the representation of free surface seepage using finite differences but unfortunately each paper advocates the use of different approximations and stability criteria. The choice of which variation to use is therefore a problem. In this paper the various methods are reviewed and tested against a variety of solutions and recommendations are made as to which method is the most stable and accurate.

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Section: Comparison Of Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The representation of time variant free surface seepage using finite difference methods: a review

Miles¹

1986

EGSP

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“…Real aquifer problems are complex in nature due to heterogeneities and geometrical irregularities, and typically require numerical discretization of the underlying equations. In many studies, mesh-based methods such as the Finite Difference Methods (FDM) and Finite Element Methods (FEM) have successfully proven their potential for dealing with field problems (Guvanasen and Volker 1980;Rastogi 1989;Chu and Willis 1984). However, mesh generation is a fundamental and time-consuming step that must often be repeated several times until an accurate solution is obtained.…”

Section: Introductionmentioning

confidence: 99%

Simulation of Groundwater Flow in an Unconfined Sloping Aquifer Using the Element-Free Galerkin Method

Pathania

Bottacin‐Busolin

Rastogi

et al. 2019

Water Resour Manage

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Numerical simulation of groundwater flows in real aquifers has been commonly based on Finite Difference (FDM) and Finite Element Methods (FEM). These mesh-based methods require a computational grid, which can be costly to generate in case of complex geometries and can significantly increase the computational cost when adaptive remeshing is required. This work presents the Element-Free Galerkin Method (EFGM) for solution of the groundwater equation and demonstrates its application to a real unconfined sloping aquifer. EFGM uses the Moving Least Square (MLS) method for approximating the unknown head and computing the EFGM shape function, leading to increased accuracy, stability in function approximation and higher convergence rate than mesh-based methods. In the present study, EFGM is initially applied to one-and two-dimensional hypothetical problems, and validated with analytical solutions. Subsequently, EFGM is applied to the simulation of groundwater flow in the Blue Lake Aquifer (BLA) in North California, and the simulation results are compared with those obtained using MODFLOW. The results demonstrate the potential of EFGM for analyzing real aquifer problems.

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Numerical solutions for solute transport in unconfined aquifers

Guvanasen

Volker

1983

Numerical Methods in Fluids

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SUMMARYTwo numerical methods for solving the problem of solute transport in unsteady flow in unconfined aquifers are studied. They are the method of characteristics (MOC) based on the finite difference method (FDM), and the finite element method (FEM). The FEM is further subdivided into four schemes: moving mesh, pseudo-Lagrangian (FEM1); stationary mesh, pseudo-Lagrangian (FEM2); pseudo saturated-unsaturated, Eulerian (FEM3); and non-stationary element, Eulerian (FEM4).Experiments on a one-dimensional flow case are performed to illustrate the schemes and to determine the effect of discretization on accuracy. In two-dimensional flow the above methods are compared with experimental results from a sand box model. Results indicate that for a similar degree of accuracy, the FEM requires less computational effort than the MOC. Among the four FEM schemes, FEM4 appears to be most attractive as it is the most efficient and most convenient to apply.

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Numerical solutions for unsteady flow in unconfined aquifers

Cited by 15 publications

References 7 publications

The representation of time variant free surface seepage using finite difference methods: a review

The representation of time variant free surface seepage using finite difference methods: a review

Simulation of Groundwater Flow in an Unconfined Sloping Aquifer Using the Element-Free Galerkin Method

Numerical solutions for solute transport in unconfined aquifers

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