A Deforming Mixed-Hybrid Finite Element Model for Robust Groundwater Flow Simulation in 3D Unconfined Aquifers with Unstructured Layered Grids

Abstract

Determining the water table shape and position in unconfined aquifers is fundamental to many groundwater flow assessment studies. The commonly used industry-standard fixed mesh models, contrary to popular belief, do not provide an accurate description of the phreatic surface. When using such models, the water table position is post-processed from the simulated groundwater heads, leading to an approximation error. This error becomes larger for coarse vertical grids. This paper introduces a novel moving mesh technique to simulate the groundwater table in three-dimensional unconfined aquifers under steady-state or transient conditions. We adopt the face-based mixed-hybrid finite element discretization approach in space, leading to a more accurate approximation of the specific discharge field. The model uses an adaptive unstructured but layered mesh which is iteratively adjusted until its top fits the phreatic surface. The developed algorithm accounts for a linearized form of the kinematic boundary condition prescribed on the moving boundary and also supports usual boundary conditions as well. The model was compared to the existing analytical, fixed mesh, and previously published solutions. The obtained results show that the developed model is superior in terms of its numerical stability, convergence behavior, and accuracy. Furthermore, the simulated phreatic surface is free from a cellwise interpolation error and independent of the vertical grid size as used in fixed mesh methods. We also found that the robustness of the moving mesh method cannot be surpassed by a fixed mesh alternative. The model’s efficiency is supported by an almost quadratic rate of convergence of the outer iteration loop.