A Saint-Venant Model for Overland Flows with Precipitation and Recharge
Journal article, 2021

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.

rainfall

shallow water

simulation

water

Saint-Venant

precipitation

friction

recharge

Author

Mehmet Ersoy

University of Toulon

Omar Lakkis

University of Sussex

Philip Townsend

University of Gothenburg

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Mathematical and Computational Applications

1300-686X (ISSN) 2297-8747 (eISSN)

Vol. 26 1 1

Subject Categories

Computational Mathematics

Water Engineering

Probability Theory and Statistics

DOI

10.3390/mca26010001

More information

Latest update

5/11/2021