Correction of the Vimoke–Taylor Concept Representing Drains in a Numerical Simulation Model

Proper prediction of drain discharge using the single node Vimoke and Taylor approach in a numerical simulation model requires an additional correction factor. This correction factor was calibrated and dependent on node size, drain radius and the way of averaging the hydraulic conductivity. For a transient situation the additional correction factor resulted in higher groundwater levels and lower drain discharges. Drains are special internal or boundary conditions in numerical simulation models. Instead of approximating them by a hole surrounded by a very dense grid of finite elements, the single node or single element approach based on the theory of Vimoke and Taylor proposed in 1962 offers a good alternative. Several authors have suggested that the Vimoke and Taylor constant to adapt the hydraulic conductivity of the element representing the drain should be changed by a certain factor. However, different correction factors have been given. Here this correction factor is derived for a control volume finite element numerical simulation model for different ratios of the size of the control volume representing the drain and the effective drain radius. It is shown that this relationship is dependent on the way the hydraulic conductivity is averaged at the interfaces between the neighboring control volumes. The relationships were obtained by optimization against an analytical solution for a steady-state, saturated situation. By applying the additional correction to a hypothetical transient situation for four soil types it was shown that the application of the additional correction factor resulted in 3 to 13% lower drain discharges compared to uncorrected simulations. Consequently, higher groundwater levels of on average 2 to 4 cm were obtained when applying the additional correction. For situations where exact predictions of drain discharge are needed, typically when solute transport is considered, it is advised to make use of the additional correction. Model specific correction factors may be required.