Numerical modeling of transient water table in shallow unconfined aquifers: A hyperbolic theory and well-balanced finite volume scheme
Journal
Advances in Water Resources
Journal Volume
193
Start Page
104820
ISSN
03091708
Date Issued
2024
Author(s)
Nakakita, Eiichi
Abstract
We present a new methodology capable of modeling transient motion of shallow phreatic surface of groundwater in unconfined aquifers. This methodology is founded on a new and comprehensive theory for water table motion and a corresponding efficient numerical scheme. In the theoretical aspect, we derived a new set of governing equations constituted by a depth-averaged continuity equation and momentum equations based on unsteady Darcy's law. The derived governing equations are of the hyperbolic type and possess stiff terms in the momentum equations due to the inertia motion in a characteristic time scale that is relatively shorter than the time scale of seepage motion. To effectively solve the derived hyperbolic system with stiff terms, in the numerical aspect, we utilize f-wave propagation algorithm, an explicit finite volume method, that can ensure numerical convergence and well-balancing solutions when momentum is rapidly relaxing to an equilibrium of steady state. Verification is successfully performed by comparing the results with analytic solutions to the classic problem of multidimensional spreading of a groundwater mound. This study demonstrates that the proposed methodology can accurately and satisfactorily simulate the spatiotemporal distribution of shallow water table and its wetting front in unconfined aquifers. © 2024 The Author(s)
Subjects
Finite volume method
Groundwater hydraulics
Shallow water table
Unsteady Darcy's law
Well-balanced scheme
Publisher
Elsevier Ltd
Type
journal article