A well-balanced scheme for the shallow-water equations with topography or Manning friction - GdR EGRIN Accéder directement au contenu
Article Dans Une Revue Journal of Computational Physics Année : 2017

A well-balanced scheme for the shallow-water equations with topography or Manning friction

Résumé

We consider the shallow-water equations with Manning friction and topography source terms. The main purpose of this work concerns the derivation of a non-negativity preserving and well-balanced scheme that approximates solutions of the system and preserves the associated steady states, including the moving ones. In addition, the scheme has to deal with vanishing water heights and transitions between wet and dry areas. To address such issues, a particular attention is paid to the study of the steady states related to the friction source term. Then, a Godunov-type scheme is obtained by using a relevant average of the source terms in order to enforce the required well-balance property. An implicit treatment of both topography and friction source terms is also exhibited to improve the scheme while dealing with vanishing water heights. A second-order well-balanced MUSCL extension is designed, as well as an extension for the two-dimensional case. Numerical experiments are performed in order to highlight the properties of the scheme.
Fichier principal
Vignette du fichier
MichelDansac_Berthon_Clain_Foucher.pdf (4.88 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01247813 , version 1 (22-12-2015)
hal-01247813 , version 2 (28-03-2017)

Identifiants

Citer

Victor Michel-Dansac, Christophe Berthon, Stéphane Clain, Françoise Foucher. A well-balanced scheme for the shallow-water equations with topography or Manning friction. Journal of Computational Physics, 2017, 335, pp.115-154. ⟨10.1016/j.jcp.2017.01.009⟩. ⟨hal-01247813v2⟩
687 Consultations
842 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More