A Saint-Venant model for overland flows with precipitation and recharge

Ersoy, Mehmet, Lakkis, Omar and Townsend, Philip (2021) A Saint-Venant model for overland flows with precipitation and recharge. Mathematical and Computational Applications, 26 (1). pp. 1-27. ISSN 1300-686X

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Abstract

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.

Item Type: Article
Keywords: simulation, shallow water, Saint-Venant, rainfall, recharge, precipitation, friction, water
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
SWORD Depositor: Mx Elements Account
Depositing User: Mx Elements Account
Date Deposited: 04 Jan 2021 12:18
Last Modified: 04 Jan 2021 12:30
URI: http://sro.sussex.ac.uk/id/eprint/96250

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