Asymmetric lattice Boltzmann model for shallow water flows

Chopard, Bastien; Pham, Van Thang; Lefèvre, Laurent

doi:10.1016/j.compfluid.2013.09.014

Cited by 19 publications

(64 citation statements)

References 14 publications

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“…They proposed a set of stability criteria defined based on lattice speed and showed that the scheme remains stable for F = 1 provided that the stability criteria were met. Immediately following their work, Chopard et al (2013) proposed a new 1D shallow water lattice Boltzmann scheme that could be applied to a limited range of supercritical flow regimes. Chopard et al (2013) proposed applying a Galilean transformation to the standard scheme in order to resolve the stability problem in supercritical flow.…”

Section: Limitations For Supercritical Flow Modellingmentioning

confidence: 99%

“…Immediately following their work, Chopard et al (2013) proposed a new 1D shallow water lattice Boltzmann scheme that could be applied to a limited range of supercritical flow regimes. Chopard et al (2013) proposed applying a Galilean transformation to the standard scheme in order to resolve the stability problem in supercritical flow. In the new reference frame, moving at a constant speed, the lattice velocity vectors were asymmetric and therefore a new set of equilibrium functions were proposed to account for the moving reference frame.…”

Section: Limitations For Supercritical Flow Modellingmentioning

confidence: 99%

“…In the new reference frame, moving at a constant speed, the lattice velocity vectors were asymmetric and therefore a new set of equilibrium functions were proposed to account for the moving reference frame. Chopard et al (2013) adopted a fixed speed of half the lattice speed for the moving reference frame, i.e. e/2.…”

Section: Limitations For Supercritical Flow Modellingmentioning

confidence: 99%

“…This severely limits their application to many shallow water free surface flow problems. Chopard, Pham, and Lefèvre (2013) made a major advance to address this problem, proposing a Galilean transformation that yields an asymmetric scheme able to model supercritical flow. Nevertheless, the range of supercritical flow conditions remained limited.…”

Section: Introductionmentioning

confidence: 99%

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Generalized transformation of the lattice Boltzmann method for shallow water flows

Hedjripour

Callaghan

Baldock

2016

Journal of Hydraulic Research

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A one-dimensional lattice Boltzmann model is developed to solve the shallow water equations for steady and unsteady flows within both the subcritical and supercritical regimes. Previous work is extended through a generalized Galilean transformation applied to the standard scheme. The transformation yields a general asymmetric lattice Boltzmann model scheme which can successfully model a wide range of both subcritical and supercritical flow regimes, and enables implementation of the asymmetric model for practical purposes. In current work, a new set of equilibrium functions, boundary conditions and the external force weights are derived for the generalized transformed scheme. A new stability region is also defined, allowing selection of a lattice speed that maintains numerical stability for a wider range of sub-and supercritical flows and combinations of those flow conditions, compared to the previous scheme with fixed asymmetry. The model is validated against a range of benchmark cases in open-channel hydraulics that demonstrate the applicability of the new model.

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Section: Limitations For Supercritical Flow Modellingmentioning

confidence: 99%

Section: Limitations For Supercritical Flow Modellingmentioning

confidence: 99%

Section: Limitations For Supercritical Flow Modellingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Generalized transformation of the lattice Boltzmann method for shallow water flows

Hedjripour

Callaghan

Baldock

2016

Journal of Hydraulic Research

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“…In NSW-LBMs, depth-averaging yields a modified collision operator for subcritical [32] and supercritical [33] flows. Depth-averaged LBM was successfully applied to a variety of illustrative benchmark problems, including wave run-up on a sloping beach [34], applications featuring bed slope and friction terms [35], wind-and density-driven circulation over irregular bathymetry [36] and tank sloshing examples [37].…”

Section: Wave Propagation In Shallow Watersmentioning

confidence: 99%

Validation of the GPU-Accelerated CFD Solver ELBE for Free Surface Flow Problems in Civil and Environmental Engineering

et al. 2015

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This contribution is dedicated to demonstrating the high potential and manifold applications of state-of-the-art computational fluid dynamics (CFD) tools for free-surface flows in civil and environmental engineering.All simulations were performed with the academic research code ELBE (efficient lattice boltzmann environment, http://www.tuhh.de/elbe). The ELBE code follows the supercomputing-on-the-desktop paradigm and is especially designed for local supercomputing, without tedious accesses to supercomputers. ELBE uses graphics processing units (GPU) to accelerate the computations and can be used in a single GPU-equipped workstation of, e.g., a design engineer. The code has been successfully validated in very different fields, mostly related to naval architecture and mechanical engineering. In this contribution, we give an overview of past and present applications with practical relevance for civil engineers. The presented applications are grouped into three major categories: (i) tsunami simulations, considering wave propagation, wave runup, inundation and debris flows; (ii) dam break simulations; and (iii) numerical wave tanks for the calculation of hydrodynamic loads on fixed and moving bodies. This broad range of applications in combination with accurate numerical results and very competitive times to solution demonstrates that modern CFD tools in general, and the ELBE code in particular, can be a helpful design tool for civil and environmental engineers.

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A modified lattice Boltzmann model for shallow water flows over complex topography

Huang

2014

Numerical Methods in Fluids

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Summary A modified lattice Boltzmann model is proposed to describe shallow water flows over complex topography. In the proposed model, the quadratic depth term is excluded from the equilibrium distribution functions (EDFs), and the hydrostatic pressure term is combined with the bed slope term to be treated as a part of the sourcing term in the lattice Boltzmann equation (LBE). Therefore, it is unnecessary to match the coefficients of the quadratic depth term in the EDFs with those of the bed slope term in the sourcing terms in the LBE. This would bring more flexibility to the treatment of the sourcing terms in the LBE. In order to recover the shallow water equations (SWEs), the basic constraints are redefined, and under these constraints, the coefficients of the EDFs are derived afterwards. Several benchmark problems are used to validate the proposed model, including stationary case, steady flows over a two‐dimensional bump and tidal wave flows over irregular bed elevation. The computed results are in excellent agreement with the results of the other numerical methods and the analytical solutions, indicating that the proposed model is capable of simulating shallow water flows over complex bathymetry. It also proves that the proposed model has potential to produce competitive solutions to shallow water flows over complex bed topography. Copyright © 2014 John Wiley & Sons, Ltd.

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Asymmetric lattice Boltzmann model for shallow water flows

Cited by 19 publications

References 14 publications

Generalized transformation of the lattice Boltzmann method for shallow water flows

Generalized transformation of the lattice Boltzmann method for shallow water flows

Validation of the GPU-Accelerated CFD Solver ELBE for Free Surface Flow Problems in Civil and Environmental Engineering

A modified lattice Boltzmann model for shallow water flows over complex topography

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