A new approach to simulating lake-groundwater interactions

Lakes have significant hydraulic connections with their surrounding groundwater, thus the coupled simulation of lake and groundwater interactions is an important component of the numerical modelling of groundwater flow. This paper proposes a new approach for simulating lake-groundwater interactions (Sloping Lakebed Method, short for SLM) based on the block-centered finite difference method. In this approach, a discretization of the lakebed elevation in the vertical direction is conducted independently of the spatial discretization of the aquifer system, greatly simplifying the subdivision of the aquifer system. The lakebed is generalized by a slope across each lake cell, and the lake grid cells are classified as fully submerged, partially submerged, and unsubmerged to simulate the interactions between the lake and the aquifer according to the relative elevations of the lake surface and lake bed. Transitions between different states ensure the continuity of the boundary conditions, improving the convergence of the calculation process. The proposed method accounts for all source and sink terms for the lake, establishing a governing equation for lake water balance. The lake stage can then be obtained by solving this equation. A series of tests were run verifying the rationality and superiority of the SLM, suggesting that it provides similar results to those of the well-established MODFLOW LAK3 Package developed by the United States Geological Survey. However, the SLM has significant advantages over LAK3 in its ease of use and calculation stability.