Study of the 1D lattice Boltzmann shallow water equation and its coupling to build a canal network

Thang, Pham van; Chopard, Bastien; Lefèvre, Laurent; Ondo, Diemer Anda; Mendes, Eduardo

doi:10.1016/j.jcp.2010.06.022

Cited by 47 publications

(39 citation statements)

References 13 publications

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“…It can be shown [6,7] that this model reproduces the shallow water equations (1) for F = 0. It is also shown that the stability region of the 1D-LB model is restricted to Fr ≤ 1 and the Courant's conditions…”

Section: The One-dimensional Lb Modelmentioning

confidence: 68%

“…However, our previous study [6] shows that the LB SW model is numerically unstable for Froude numbers equal to or larger than 1. More precisely, we found that for a given height h 0 , the numerical scheme requires a speed u 0 smaller than √ gh 0 .…”

Section: Introductionmentioning

confidence: 91%

“…Note that it is found [6] that the value of the relaxation time τ is not affecting the stability provided that τ > 1/2.…”

Section: The One-dimensional Lb Modelmentioning

confidence: 99%

“…Following the standard procedure (see for instance [6] where it is done in detail for the 1D LB shallow 6 water model), we obtain…”

Section: Chapman-enskog Expansionmentioning

confidence: 99%

“…One-dimensional applications are studied by Frandsen [5] and we recently proposed a very detailed analysis of the 1D model [6,7] in the context of irrigation canals. In this study, we showed that the LB scheme is numerically faster than other standard methods, for the same accuracy.…”

Section: Introductionmentioning

confidence: 99%

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Asymmetric lattice Boltzmann model for shallow water flows

2013

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To cite this version:B. Chopard, P Van Thang, Laurent Lefevre. Asymmetric lattice Boltzmann model for shallow water flows. Computers and Fluids, Elsevier, 2013, 88, pp.225-231. 10.1016/j.compfluid.2013 AbstractWe consider a Galilean transformation of the lattice Boltzmann model for shallow water flows. In this new reference frame, the velocity lattice is asymmetrical but it is possible to simulate flows with Froude number larger than 1 and to model the transition from a torrential to a fluvial regime.

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Section: The One-dimensional Lb Modelmentioning

confidence: 68%

Section: Introductionmentioning

confidence: 91%

“…Note that it is found [6] that the value of the relaxation time τ is not affecting the stability provided that τ > 1/2.…”

Section: The One-dimensional Lb Modelmentioning

confidence: 99%

“…Following the standard procedure (see for instance [6] where it is done in detail for the 1D LB shallow 6 water model), we obtain…”

Section: Chapman-enskog Expansionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Asymmetric lattice Boltzmann model for shallow water flows

2013

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A finite element/volume method model of the depth‐averaged horizontally 2D shallow water equations

Yoshioka

Unami

Fujihara

2014

Numerical Methods in Fluids

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SUMMARYAnalysis of surface water flows is of central importance in understanding and predicting a wide range of water engineering issues. Dynamics of surface water is reasonably well described using the shallow water equations (SWEs) with the hydrostatic pressure assumption. The SWEs are nonlinear hyperbolic partial differential equations that are in general required to be solved numerically. Application of a simple and efficient numerical model is desirable for solving the SWEs in practical problems. This study develops a new numerical model of the depth‐averaged horizontally 2D SWEs referred to as 2D finite element/volume method (2D FEVM) model. The continuity equation is solved with the conforming, standard Galerkin FEM scheme and momentum equations with an upwind, cell‐centered finite volume method scheme, utilizing the water surface elevation and the line discharges as unknowns aligned in a staggered manner. The 2D FEVM model relies on neither Riemann solvers nor high‐resolution algorithms in order to serve as a simple numerical model. Water at a rest state is exactly preserved in the model. A fully explicit temporal integration is achieved in the model using an efficient approximate matrix inversion method. A series of test problems, containing three benchmark problems and three experiments of transcritical flows, are carried out to assess accuracy and versatility of the model. Copyright © 2014 John Wiley & Sons, Ltd.

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