Numerical modeling of transient water table in shallow unconfined aquifers: A hyperbolic theory and well-balanced finite volume scheme

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.