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An Adaptive Finite Difference Scheme for The One-Dimensional Water Flow Equation¹

ABSTRACT

The pressure bead form of the general flow equation for water in a porous medium was numerically solved using a scheme that allowed both the time step (t) and the space increment (z) to be changed during the flow process. The mass balance equation was used as a check for the accuracy of the simulation. A fixed number of grid points in the space direction was continuously redistributed to allow for small z values in regions of large changes in pressure head gradients while allowing large z values in regions of small changes. The method, which is unconditionally stable, is demonstrated for an infiltration and an evaporation process.

¹ Contribution from the Auburn University Agric. Exp. Stn., Auburn University, AL 36849.

² Assistant Professor of Soil Physics, Dep. of Agron. and Soils, and Assistant Professor of Math., Dep. of Math., respectively, Auburn University, AL 36849.

Received for publication September 17, 1980. Accepted for publication July 16, 1981.

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