Information about the spreadsheet models:

These finite-difference spreadsheet models require Excel 5.0 or later.

These Excel spreadsheets are designed to help you visualize how simple finite difference solutions to groundwater problems work. In these spreadsheets each cell is a node, and the finite-difference equation for that node can be inspected by clicking on the cell. You can change the boundary conditions along the spreadsheet margins or at the pumping well.

I have protected the spreadsheets so that cells containing formulas cannot be inadvertantly altered.

IMPORTANT NOTE: For these spreadsheets to function properly, you MUST have "iteration" turned on in Excel. In recent versions of Excel, choose "Preferences" from the "Edit" menu (e.g., in Excel 2001) or from the "Tools" menu (e.g., in Excel 98), click on the "Calculation" tab, then click the little box labeled "Iteration", and then click "OK". In old versions of Excel (e.g., Excel 5) choose "Calculation" from the "Options" menu, click the iterations box, and then click "OK".

Models:

Gauss-Seidel Groundwater Examples

Finite-difference expressions of Laplace equation for steady-state pumping in homogeneous isotropic confined aquifer with pumping well at center.

Two small examples: one simple Gauss-Seidel model and one Gauss-Seidel with successive over-relaxation (SOR).

 

Gauss-Seidel Sector GSOR

Finite-difference expression of Laplace equation for steady-state pumping in homogeneous isotropic confined aquifer using Gauss-Seidel method with successive over-relaxation (GSOR)

 

Poisson SOR

Finite-difference model of steady-state discharge well in homogeneous isotropic recharging confined aquifer using Poisson's equation with successive over-relaxation (SOR)

 

Poisson Circular SOR

Finite-difference model of steady-state discharge well in homogeneous isotropic recharging confined aquifer using Poisson's equation with successive over-relaxation (SOR). Circular region of influence as boundary conditions. (See Wang & Anderson p. 48-51.)

 

Poisson-Dupuit

Finite-difference model of steady-state discharge well in homogeneous isotropic unconfined aquifer using Dupuit assumptions and Poisson's equation with successive over-relaxation (SOR).

 

Poisson-Dupuit Inclined Water Table

Finite-difference model of steady-state discharge well in homogeneous isotropic unconfined aquifer with sloping water table using Dupuit assumptions and Poisson's equation with successive over-relaxation (SOR).

 

 

References:

 

Ousey, J.R., 1986, Modeling steady-state groundwater flow using microcomputer spreadsheets, Journal of Geological Education, v. 34, p. 305-311.

Wang, H.F. and M. P. Anderson, 1982, Introduction to Groundwater Modeling, W.H. Freeman, 237 p.

 

Spreadsheets © 1994 by Andre Lehre, Dept. of Geology, Humboldt State University. Models may be freely distributed providing they are not charged for. Author assumes no responsibility for any errors in the models or their use.

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