Author(s): Ilhan Ozgen-Xian; Adrian Navas-Montilla

Linked Author(s): Ilhan Özgen-Xian

Keywords: Groundwater; Finite volume; Hyperbolic; Boussinesq

Abstract: The Boussinesq flow equation describes depth-averaged saturated groundwater flow in nearly horizontal aquifers. In this contribution, Cattaneo's relaxation approach is applied to reformulate the parabolic Boussinesq equation as a first-order hyperbolic system. The reformulation allows to compute discharges as primary variables with the same accuracy as the piezometric head. Further, the time step constraint is relaxed to the classical Courant-Friedrichs-Lewy stability criterion. The hyperbolization enables a unified computation of the primary variable and its gradients, for example piezometric head and unit discharge in the Boussinesq equation. This contribution presents an augmented finite-volume solver that preserves moving equilibrium solutions to machine accuracy. Computational test cases confirm that the hyperbolised Boussinesq equation converges to the original formulation, and that the augmented solver is accurate for transient and steady cases.

DOI: https://doi.org/10.3850/IAHR-39WC252171192022296

Year: 2022