On numerical errors associated with the iterative alternating direction implicit (Iadi) finite difference solution of the two dimensional transient saturated‐unsaturated flow (Richards) equation

Abstract

AbstractNumerical models for simulation of multidimensional unsaturated flow are becoming increasingly available, but relatively little has been reported on the detailed analysis of numerical errors associated with such schemes. For unsaturated‐saturated flow, further complexity is introduced to the highly non‐linear unsaturated problem as the form of governing equation changes within the flow field. In this paper, two‐dimensional simulation of infiltration to a water table is considered. Numerical errors associated with selection of time step, grid geometry, convergence criteria, and the representation of internodal hydraulic conductivity are discussed with respect to moisture content profiles and mass balance error. Although solution sensitivity to numerical parameters is problem specific, the results presented indicate the nature and magnitude of numerical effects which should not be overlooked in model applications.