A Saint-Venant Model for Overland Flows with Precipitation and Recharge - Archive ouverte HAL Access content directly
Journal Articles Mathematical and computational applications Year : 2020

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

Omar Lakkis
  • Function : Author
  • PersonId : 986359
Philip Townsend
  • Function : Author
  • PersonId : 986360

Abstract

We propose a one-dimensional Saint-Venant (also known as open channel or shallow water) equation model for overland flows including a water input--output source term. We derive the model from the two-dimensional Navier--Stokes equations under the shallow water assumption, with boundary conditions including recharge via ground infiltration and runoff. We show that the energy-consistency of the resulting Saint-Venant model is strictly dependent upon the assumed level of rain- or recharge-induced friction. The proposed model extends most extant models by adding more scope depending on friction terms that depend on the rate of water entering or exiting the flow via recharge and infiltration. The obtained entropy relation for our model validate it both mathematically and physically. We compare both models computationally based on a kinetic finite volume scheme; in particular, we provide numerical evidence that the two models may show drastically different results, where the model conditioned on the flow velocity provides what may not be the physically relevant solution because of the lack of the appropriate friction terms depending on a master parameter ($\alpha$). We also look at a comparison with real-life data.
Fichier principal
Vignette du fichier
ErsoyLakkisTownsend-arxiv-170515-v1.pdf (693.26 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01347163 , version 1 (07-06-2017)

Identifiers

Cite

Mehmet Ersoy, Omar Lakkis, Philip Townsend. A Saint-Venant Model for Overland Flows with Precipitation and Recharge. Mathematical and computational applications, 2020, ⟨10.3390/mca26010001⟩. ⟨hal-01347163⟩
350 View
426 Download

Altmetric

Share

Gmail Facebook X LinkedIn More