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Formulations of the bed slope term in the shallow water equations: implication for energy balance
Bruwier, Martin; Archambeau, Pierre; Erpicum, Sébastien et al.
2015In Workshop on Advances in Numerical Modelling of Hydrodynamics
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Keywords :
shallow water equation; bed slope term; energy
Abstract :
[en] For an incompressible, isothermal, continuous and frictionless flow, the exact resolution of the equation of conservation of mechanical energy is equivalent to the exact resolution of the equation of momentum conservation. However, the discrete solution of the equation of momentum conservation does not verify the equation of energy conservation. This is particularly the case as a result of the presence of a non-conservative bed slope term in the equation of momentum conservation. In this research, the influence of (i) the formulation and (ii) the discretization scheme of the non-conservative bed slope term on the energy conservation is analysed in the case of a 1D horizontal and frictionless channel with a topographic step. The results for two different formulations of the bed slope term are firstly compared: the standard formulation of the bed slope source term and a divergence formulation of the bed slope term. Then, different discretization schemes of the divergence formulation of the bed slope term are analyzed to determine the one minimizing the numerical variation of energy.
Disciplines :
Materials science & engineering
Author, co-author :
Bruwier, Martin ;  Université de Liège - ULiège > Département ArGEnCo > Hydraulics in Environmental and Civil Engineering
Archambeau, Pierre  ;  Université de Liège - ULiège > Département ArGEnCo > HECE (Hydraulics in Environnemental and Civil Engineering)
Erpicum, Sébastien  ;  Université de Liège - ULiège > Scientifiques attachés au Doyen (Sc.appliquées)
Pirotton, Michel ;  Université de Liège - ULiège > Département ArGEnCo > HECE (Hydraulics in Environnemental and Civil Engineering)
Dewals, Benjamin  ;  Université de Liège - ULiège > Département ArGEnCo > Hydraulics in Environmental and Civil Engineering
Language :
English
Title :
Formulations of the bed slope term in the shallow water equations: implication for energy balance
Publication date :
24 March 2015
Event name :
Workshop on Advances in Numerical Modelling of Hydrodynamics
Event date :
du 24 mars 2015 au 25 mars 2015
Audience :
International
Main work title :
Workshop on Advances in Numerical Modelling of Hydrodynamics
Peer reviewed :
Peer reviewed
Name of the research project :
ARC - Floodland
Available on ORBi :
since 13 February 2015

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