Finite-Element Grid Configurations for Drains

Abstract

Several different finite-element grid configurations were evaluated for use in the numerical approximation of steady and transient flow to a single drain. By comparing the numerically simulated drain flow rates and head distributions with analytic values, a nested configuration was found to be appropriate for an effective drain radius of 0.01 m, and a square configuration was suitable for an effective drain radius of 0.05 m. Using an analytic solution, a method was developed to determine the distance of influence of a drain as a function of its effective radius and the geometry of its flow domain. The distance of influence was found to be independent of material type. An appropriate between-drain grid spacing was selected for the numerical simulation of multiple drains by increasing the grid mesh spacing outside the distance of influence. The position of the water table and drain flow rate with time were used to evaluate the between-drain grid spacing for transient variably saturated flow. Grid Péclet and Courant numbers, together with the shape of the solute advance front, were used to evaluate the suitability of the selected single drain configuration and between-drain grid spacing for solute transport. The resulting finite-element grid configuration for single and multiple drains ensures a stable efficient numerical solution, and it has applicability to numerical modeling of multiple subsurface drains.