Numerical Evaluation on the Accuracy of Soil Water Movement Simulation, Oriented to Water Table Recharge Problem

Abstract

Finite difference method was applied to analyze one-dimensional unsaturated-saturated water movement in soil. Because it is difficult to obtain the exact solution analytically on usual physical phenomena in soil-water system, it follows that numerical analysis can be checked on only two ideal cases, namely, vertical infiltration into uniform soil column from its surface, and water table recharge above impermeable boundary. Then both stability and accuracy of numerical scheme were evaluated by comparing numerical solutions with exact ones, for various sets of grid sizes (A t , Az). Two iterative methods, the linear method and the Newton method were adopted to solve the system of non-linear algebraic equations derived from partial differential equation. In case of vertical infiltration,both methods were found to give sufficient stability, when satisfying von Neumann* s criteria. Their numerical errors could be minimized below 5%, by letting both grids sizes approach zero. However, too small sizes of finite differences caused the serious accumulation of round-off errors, when used to simulate water table recharge. It proved that the Newton iterative method was more accurate than the linear one, and was applicable to a wide variety of problems in soil-water system.