Abstract

Seepage boundary conditions are commonly used in groundwater simulations to allow groundwater to discharge at the upper surface of the model when groundwater head exceeds atmospheric pressure. However, the extent and transient behavior of the seepage zone is often unknown a priori and is difficult to predict. A mathematical description of the boundary condition is straightforward, such that head is equivalent to elevation only when groundwater flow indicates a seepage condition, which is a mixed conditional Dirichlet and Neumann boundary condition. This standard representation of the boundary condition has been successfully implemented and applied in a real-world context by most groundwater models. However, it is rarely reported that convergence is only guaranteed when both the efflux and zero pressure conditions are simultaneously satisfied, often requiring unnecessarily small timestep sizes, which results in low computational efficiency. This study suggests a continuous differentiable equation as an alternative to model the seepage boundary. The new formulation is derived by analogy to the first-order exchange equation, which is commonly used to represent the interactions between surface water and groundwater flow in integrated hydrologic simulations. The results of this study suggest that mixed Dirichlet and Neumann boundary conditions can be effectively converted into a Robin boundary condition, which is a head-dependent flux condition that incorporates appropriate physical considerations. This new approach has the potential to significantly improve the accuracy and efficiency of groundwater flow simulations and can help to advance the understanding of subsurface hydrology.