Discretization of the divergence formulation of the bed slope term in the shallow-water equations and consequences in terms of energy balance

Bruwier, Martin; Archambeau, Pierre; Erpicum, Sébastien; Pirotton, Michel; Dewals, Benjamin

doi:10.1016/j.apm.2016.01.041

Article (Scientific journals)

Discretization of the divergence formulation of the bed slope term in the shallow-water equations and consequences in terms of energy balance

Bruwier, Martin; Archambeau, Pierre; Erpicum, Sébastien et al.

2016 • In Applied Mathematical Modelling, 40 (17-18), p. 7532–7544

Peer Reviewed verified by ORBi

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https://hdl.handle.net/2268/192948

DOI
10.1016/j.apm.2016.01.041

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Keywords :

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

Volume :

Issue :

17-18

Pages :

7532–7544

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

http://www.sciencedirect.com/science/article/pii/S0307904X16300373

Name of the research project :

ARC - Floodland

Available on ORBi :

since 05 February 2016

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