Numerical methods for conjunctive two-dimensional surface and three-dimensional sub-surface flows

Sophisticated catchment runoff problems necessitate conjunctive modeling of overland flow and subsurface flow. In this paper, finite difference numeri cal methods are studied for simulation of catchment runoff of two-dimension al surface flow interacting with three-dimensional unsaturated and saturate d sub-surface flows. The equations representing the flows are mathematicall y classified as a type of heat diffusion equation. Therefore, two- and thre e-dimensional numerical methods for heat diffusion equations were investiga ted for applications to the surface and sub-surface flow sub-models in term s of accuracy, stability, and calculation time. The methods are the purely explicit method, Saul'yev's methods, the alternating direction explicit (AD E) methods, and the alternating direction implicit (ADI) methods. The metho ds are first examined on surface and sub-surface flows separately; subseque ntly, 12 selected combinations of methods were investigated for modeling th e conjunctive flows. Saul'yev's downstream (S-d) method was found to be the preferred method for two-dimensional surface flow modeling, whereas the AD E method of Barakat and Clark is a less accurate, stable alternative. For t he three-dimensional sub-surface flow model, the ADE method of Larkin (ADE- L) and Brian's ADI method are unconditionally stable and more accurate than the other methods. The calculations of the conjunctive models utilizing th e S-d surface flow sub-model give excellent results and confirm the expecta tion that the errors of the surface and sub-surface sub-models interact. Th e surface sub-model dominates the accuracy and stability of the conjunctive model, whereas the sub-surface sub-model dominates the calculation time, s uggesting the desirability of using a smaller time increment for the surfac e sub-model. Copyright (C) 2000 John Wiley & Sons, Ltd.