Simulation of Unconfined Aquifer Flow Based on Parallel Adaptive Mesh Refinement

Abstract

The density of a numerical mesh is a key component for the quality of the numerical solution. Common methods in groundwater simulations rely on meshes generated prior to simulation, which lead to unnecessary or insufficient degrees of freedom (dofs). In this study we use Adaptive Mesh Refinement (AMR) to substitute the subjective mesh generation process with a more rigorous approach where new dofs are iteratively added to the solution of an initial coarse mesh based on a solution error estimation. The simulation is solved on a succession of meshes through which the mesh density is increased in areas of steep gradients in the solution variable. Here, we apply the approach to unconfined aquifer flow which is a non‐linear problem commonly encountered in groundwater modeling. By taking advantage of the iterative nature of AMR we arrive at an efficient solver approach. We treat the position of the unconfined boundary as an additional unknown which is estimated iteratively. The first iterations are executed rapidly as the mesh is rather coarse, while the free boundary adapts to the computed water table position as close as the mesh density allows. In this study we demonstrate the viability of the proposed unconfined aquifer simulation method to a series of 2D hypothetical examples under several conditions and stresses as well as a 3D test case. In all cases the AMR was able to automatically resolve the solution in areas with steep hydraulic head gradient, using appropriately higher density to achieve high localized refinement and accuracy.