Soil Water Modeling II: On Sensitivity to Finite Difference Grid Spacing

Abstract

ABSTRACT THE influence of finite difference grid size on soil water flow model accuracy was studied using two cases. One case was of steady, two-dimensional infiltra-tion using the successive overrelaxation (SOR) method of solving finite difference equations. The other was of transient, two-dimensional infiltration using the alter-nating direction implicit (ADI) method. We formulated finite difference expressions for both cases using central differencing techniques. In the transient case, a very small grid size in both time and space dimensions was necessary at the initiation of infiltration. Furthermore, the ADI method for this nonlinear case was only condi-tionally stableat least at the initiation of infiltration. As infiltration proceeded, however, both the time and space grid sizes could be made larger. Indicators of a grid size that was obviously too coarse were a fluctuating infiltration rate in the transient case and irregularly shaped equipotential lines in the steady-state case. Although the models were nonlinear, they both con-verged; i.e., successively smaller grid sizes yielded solu-tions that asymptotically approached a limit. For a given regular grid size, considerable computational saving could be effected without appreciable loss of accuracy by using an irregular grid in which the regular grid size was dup-licated in the part of the section exhibiting the greatest curvature of equipotential lines, while larger grid sizes could be used in other parts of the section. Smaller grid sizes were also needed in regions where hydraulic gradi-ent changed rapidly. Accuracy of estimation varied approximately with the inverse of grid size rather than with the square of the inverse, as is generally claimed for central differencing on a square grid.