Mesh design for numerical solution of Richards' Equation

Abstract

Richards' equation is difficult to solve numerically because water flow in the unsaturated zone is complicated by the fact that the soil's permeability depends on its water saturation. The accuracy and computational efficiency of numerical solution are affected by the form of the governing equation, the estimation of the internodal hydraulic conductivity and the time-stepping scheme. In order to save computational time and improve efficiency of numerical techniques, two classical dimensionless numbers, Peclet and Courant numbers, and their combinations, Fourier and Advective Peclet numbers, are used as the criteria for estimating the spatial and temporal increments needed for the numerical solution of the linear Richards' equation (for example expo_nential hydraulic functions) and two new dimensi_onless numbers, Modified Peclet and Courant numbers for the non-linear Richards' equation (van Genuchten's hydraulic functions). In this way, we can get numerical solutions of Richards' equation not only with no oscillation and mass conservation, but also with adequate convergency speed and accuracy. These numbers are only related to the soil-hydraulic properties and grid size.