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A confrontation of 1D and 2D RKDG numerical simulation of transitional flow at open‐channel junction
Author(s) -
Ghostine R.,
Kesserwani G.,
Mosé R.,
Vazquez J.,
Ghenaim A.,
Grégoire C.
Publication year - 2009
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.1977
Subject(s) - flow (mathematics) , conservation law , open channel flow , channel (broadcasting) , shallow water equations , momentum (technical analysis) , discontinuous galerkin method , mathematics , mechanics , computer science , mathematical analysis , geometry , physics , finite element method , telecommunications , thermodynamics , finance , economics
In this study, a comparison between the 1D and 2D numerical simulation of transitional flow in open‐channel networks is presented and completely described allowing for a full comprehension of the modeling water flow. For flow in an open‐channel network, mutual effects exist among the channel branches joining at a junction. Therefore, for the 1D study, the whole system (branches and junction) cannot be treated individually. The 1D Saint Venant equations calculating the flow in the branches are then supplemented by various equations used at the junction: a discharge flow conservation equation between the branches arriving and leaving the junction, and a momentum or energy conservation equation. The disadvantages of the 1D study are that the equations used at the junction are of empirical nature due to certain parameters given by experimental results and moreover they often present a reduced field of validity. On the contrary, for the 2D study, the entire network is considered as a single unit and the flow in all the branches and junctions is solved simultaneously. Therefore, we simply apply the 2D Saint Venant equations, which are solved by a second‐order Runge–Kutta discontinuous Galerkin method. Finally, the experimental results obtained by Hager are used to validate and to compare the two approaches 1D and 2D. Copyright © 2009 John Wiley & Sons, Ltd.