A numerical model for steady flow in a partially saturated porous medium is presented. The model uses the multigrid solution algorithm for solving the system of equations resulting from the discrete approximation to the partial differential equation. The model solutions checked favorably with an existing analytical solution. Used for a hypothetical problem with realistic soil characteristics the model has been shown to be very efficient for problems with the number of unknowns on the order of 10,000 and more. Specifically, the multigrid scheme was shown to be 22 times faster in terms of CPU time than the line successive overtaxation method for the particular problem chosen. In addition, the required CPU time is shown to be a linear function of the number of unknowns within the solution domain. This indicates that the convergence rate of the multigrid solution algorithm is independent of the grid resolution. Because of the significant improvement in computational efficiency, the multigrid model can be used to simulate field scale partially saturated flow problems with very fine grid resolution as is often required by highly nonlinear soil characteristics. Further studies and application of the multigrid solution technique are suggested.
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