Efficient water table evolution discretization using domain transformation

Abstract

Domain transformation methods are useful techniques for solving problems on non-stationary domains. In this work, we consider the evolution of the water table in an unconfined aquifer. This nonlinear, time-dependent problem is greatly simplified by using a mapping from the physical domain to a reference domain and is then further reduced to a single, (nonlinear) partial differential equation. We show well-posedness of the approach and propose a stable and convergent discretization scheme. Numerical results are presented supporting the theory.

A 3-D numerical model of the influence of meanders on groundwater discharge to a gaining stream in an unconfined sandy aquifer

“…In the coordinate transformation method (Boon et al, 2016), the groundwater flow equation for 246 saturated conditions is solved in a transformed domain Ω: 247…”

“…To address these aims, the 3-D numerical model employed a novel coordinate transformation 112 method developed by Boon et al (2016). This method solves the equation for groundwater flow in a 113 transformed domain, which is constant in time, while the coordinate system changes depending on 114 the groundwater free surface variations.…”

“…The application of the linear transformation allows the 115 transformed domain geometry to be simpler than the original problem; thus, the method is 116 computationally efficient and can be applied to complex geometries. Boon et al (2016) employs the 117 method to simulate groundwater flow to wells, but it has not been applied to other relevant 118 groundwater systems. Since the application of the coordinate transform method to 119 groundwater/surface water interaction is new, it was first tested and compared to existing approaches 120 (the moving mesh and the saturated-unsaturated groundwater flow method).…”

“…A numerical modeling study analyzing the effect of meander bends on the spatial variability of 540 the groundwater flow in an unconfined and homogenous sandy aquifer to a gaining stream at the 541 reach scale is presented. Results were obtained by applying the coordinate transformation method of 542 Boon et al (2016) to a new problem: the groundwater flow to streams. 543…”