Next Article in Journal
A Localized Collocation Solver Based on T-Complete Functions for Anti-Plane Transverse Elastic Wave Propagation Analysis in 2D Phononic Crystals
Previous Article in Journal
The Pareto Tracer for General Inequality Constrained Multi-Objective Optimization Problems
Article

A Saint-Venant Model for Overland Flows with Precipitation and Recharge

1
Institut Mathématiques de Toulon (IMATH), Université de Toulon, 83957 La Garde, France
2
Department of Mathematics, University of Sussex, Brighton BN1 9QH, UK
3
Department of Mathematical Sciences, Chalmers University of Technology, 41296 Gothenburg, Sweden
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2021, 26(1), 1; https://doi.org/10.3390/mca26010001
Received: 9 September 2020 / Revised: 25 November 2020 / Accepted: 10 December 2020 / Published: 29 December 2020
(This article belongs to the Section Natural Sciences)
We propose a one-dimensional Saint-Venant (open-channel) model for overland flows, including a water input–output source term modeling recharge via rainfall and infiltration (or exfiltration). We derive the model via asymptotic reduction from the two-dimensional Navier–Stokes equations under the shallow water assumption, with boundary conditions including recharge via ground infiltration and runoff. This new model recovers existing models as special cases, and adds more scope by adding water-mixing friction terms that depend on the rate of water recharge. We propose a novel entropy function and its flux, which are useful in validating the model’s conservation or dissipation properties. Based on this entropy function, we propose a finite volume scheme extending a class of kinetic schemes and provide numerical comparisons with respect to the newly introduced mixing friction coefficient. We also provide a comparison with experimental data. View Full-Text
Keywords: simulation; shallow water; Saint-Venant; rainfall; recharge; precipitation; friction; water simulation; shallow water; Saint-Venant; rainfall; recharge; precipitation; friction; water
Show Figures

Figure 1

MDPI and ACS Style

Ersoy, M.; Lakkis, O.; Townsend, P. A Saint-Venant Model for Overland Flows with Precipitation and Recharge. Math. Comput. Appl. 2021, 26, 1. https://doi.org/10.3390/mca26010001

AMA Style

Ersoy M, Lakkis O, Townsend P. A Saint-Venant Model for Overland Flows with Precipitation and Recharge. Mathematical and Computational Applications. 2021; 26(1):1. https://doi.org/10.3390/mca26010001

Chicago/Turabian Style

Ersoy, Mehmet, Omar Lakkis, and Philip Townsend. 2021. "A Saint-Venant Model for Overland Flows with Precipitation and Recharge" Mathematical and Computational Applications 26, no. 1: 1. https://doi.org/10.3390/mca26010001

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop