Premium
A kinetic interpretation of the section‐averaged Saint‐Venant system for natural river hydraulics
Author(s) -
Goutal N.,
SainteMarie J.
Publication year - 2010
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2401
Subject(s) - discretization , shallow water equations , hydraulics , robustness (evolution) , numerical analysis , mathematics , computer science , mathematical analysis , engineering , biochemistry , chemistry , gene , aerospace engineering
The classical Saint‐Venant system is well suited for the modeling of dam breaks, hydraulic jumps, reservoir emptying, flooding etc. For many applications, the extension of the Saint‐Venant system to the case of non‐rectangular channels is necessary and this section‐averaged Saint‐Venant system exhibits additional source terms. The main difficulty of these equations consists of the discretization of these source terms. In this paper we propose a kinetic interpretation for the section averaged Saint‐Venant system and derive an associated numerical scheme. The numerical scheme—2nd order in space and time—preserves the positivity of the water height, and is well‐balanced. Numerical results including comparisons with analytic and experimental test problems illustrate the accuracy and the robustness of the numerical algorithm. Copyright © 2010 John Wiley & Sons, Ltd.