Capacitance and Initial Time Step Effects on Numerical Solutions of Richards Equation

Abstract

The numerical solution of the Richards equation is sensitive to the value of the specific soil moisture capacity or capacitance, C, that is used when the soil is at or near saturation. Near saturation C is zero, but a numerical solution cannot be obtained for C = 0. Therefore some small nonzero value for C must be used. The initial allowable value of C was not dependent upon saturated hydraulic conductivity, but decreased as a (proportional to the inverse of the air entry value of pressure head) decreased. As the value of C is decreased the initial time step for the numerical solution must be decreased to obtain convergence. In most cases the initial time step should be of the same order of magnitude as C. Larger values of C require less computer time but give inaccurate results. Attempting to use too large a time step may actually increase the required computer time because of the extra iterative solutions required to obtain convergence.