Research paper
A physically based, two-dimensional, finite-difference algorithm for modeling variably saturated flow

https://doi.org/10.1016/0022-1694(94)90121-XGet rights and content

Abstract

A computationally simple, numerical algorithm capable of solving a wide variety of two-dimensional, variably saturated flow problems is developed. Recent advances in modeling variably saturated flow are incorporated into the algorithm. A physically based form of the general, variably saturated flow equation is solved using finite differences (centered in space, fully implicit in time) employing the modified Picard iteration scheme to determine the temporal derivative of the water content. The algorithm avoids mass-balance errors in unsaturated regions and is numerically stable. The resulting system of linear equations is solved by a preconditioned conjugate gradient method, which is known to be computationally efficient for the type of equation set obtained. The algorithm is presented in sufficient detail to allow others to implement it easily, and is verified using four published, illustrative sets of experimental data.

References (39)

  • J.H. Dane et al.

    An adaptive finite difference scheme for the one-dimensional water flow equation

    Soil Sci. Soc. Am. J.

    (1981)
  • P.R. Day et al.

    A numerical solution of the differential equation of flow for a vertical drainage problem

  • F.A.L. Dullien

    Porous Media Fluid Transport and Pore Structure

  • R.A. Freeze

    The mechanism of natural groundwater recharge and discharge 1. One-dimensional, vertical, unsteady, unsaturated flow above a recharging and discharging groundwater flow system

    Water Resour. Res.

    (1969)
  • R.A. Freeze

    Three dimensional transient, saturated-unsaturated flow in a groundwater basin

    Water Resour. Res.

    (1971)
  • R.A. Freeze

    Influence of the unsaturated flow domain on seepage through earth dams

    Water Resour. Res.

    (1971)
  • G.H. Golub et al.

    Matrix Computations

  • H.P. Hall

    An investigation of steady state flow toward a gravity well

    Houille Blanche

    (1955)
  • R. Haverkamp et al.

    A comparative study of three forms of the Richards' equation used for predicting one-dimensional infiltration in unsaturated soil

    Soil Sci. Soc. Am. J.

    (1981)
  • Cited by (0)

    1

    Present address: Battelle, Pacific Northwest Laboratories, Battelle Boulevard, P.O. Box 999, Richland, WA 99352, USA.

    View full text