bed slope term; divergence formulation; discretization schemes; energy balance; flux-vector splitting; shallow-water
Abstract :
[en] In this research, the influence on energy balance of the discretization scheme of the divergence
formulation of the bed slope term in the shallow-water equations is analysed theoretically (for a single topographic step) and based on two numerical tests. Different values of the main parameter controlling the discretization scheme of the divergence formulation are analysed to identify the formulation which minimizes the energy variation resulting from the discretization. For a wide range of ambient Froude numbers and relative step heights, the theoretical value of the control parameter minimizing the energy variation falls within a very narrow range, which can reasonably be approximated by a single “optimal” value. This is a result of high practical relevance for the design of accurate numerical schemes, as confirmed by the results of the numerical tests.
Disciplines :
Civil engineering
Author, co-author :
Bruwier, Martin ; Université de Liège > Département ArGEnCo > Hydraulics in Environmental and Civil Engineering
Archambeau, Pierre ; Université de Liège > Département ArGEnCo > HECE (Hydraulics in Environnemental and Civil Engineering)
Erpicum, Sébastien ; Université de Liège > Scientifiques attachés au Doyen (Sc.appliquées)
Pirotton, Michel ; Université de Liège > Département ArGEnCo > HECE (Hydraulics in Environnemental and Civil Engineering)
Dewals, Benjamin ; Université de Liège > Département ArGEnCo > Hydraulics in Environmental and Civil Engineering
Language :
English
Title :
Discretization of the divergence formulation of the bed slope term in the shallow-water equations and consequences in terms of energy balance
Publication date :
2016
Journal title :
Applied Mathematical Modelling
ISSN :
0307-904X
eISSN :
1872-8480
Publisher :
Elsevier Science, New York, United States - New York
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