SOLUTION OF EQUATION FOR TWO-DIMENSIONAL INFILTRATION PROBLEMS

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Abstract
A finite element, weighted residual, successive substitution algorithm has been used to solve two-dimensional infiltration problems whose governing partial differential equation and boundary conditions are highly nonlinear. The results compared favorably with other published numerical solutions to similar examples. The soil water diffusivity, as well as the capillary conductivity, were approximated within a finite element in terms of shape functions and discretized values of these functions calculated using guessed values or previously calculated values at a certain time level of the water content at the nodes. This successive substitution scheme converged rapidly within each time step. The method is general and can be extended to three-dimensional flows and the use of higher order approximations. A finite element, weighted residual, successive substitution algorithm has been used to solve two-dimensional infiltration problems whose governing partial differential equation and boundary conditions are highly nonlinear. The results compared favorably with other published numerical solutions to similar examples. The soil water diffusivity, as well as the capillary conductivity, were approximated within a finite element in terms of shape functions and discretized values of these functions calculated using guessed values or previously calculated values at a certain time level of the water content at the nodes. This successive substitution scheme converged rapidly within each time step. The method is general and can be extended to three-dimensional flows and the use of higher order approximations. © Williams & Wilkins 1976. All Rights Reserved.

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