Modelling solute transport in shallow water with the lattice Boltzmann method

Peng, Yong; Zhou, Jian Guo; Burrows, Roger

doi:10.1016/j.compfluid.2011.07.008

Cited by 40 publications

(21 citation statements)

References 28 publications

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“…In addition, the LBM has been applied successfully to solve the shallow water equations (Dellar, 2002;Li and Huang, 2008;Liu et al, 2009aLiu et al, , 2009bLiu et al, 2010;Peng et al, 2011aPeng et al, , 2011bSalmon, 1999;Zhou, 2004). However, based on the current knowledge, there is no LBM developed for solution of the morphological evolution related to the sediment transport due to the direct inclusion of the empirical estimation of the bed-load transport in the equation.…”

Section: Introductionmentioning

confidence: 97%

Mixed numerical method for bed evolution

Peng

Zhou

Zhang

2015

Proceedings of the Institution of Civil Engineers - Water Manag

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The morphological evolution in shallow water flows was investigated in this study. The shallow water equations were solved for the flows using the lattice Boltzmann method with multiple-relaxation time and an improved scheme for the momentum source terms in which the bed elevation gradients were included. The fifth-order Euler-WENO scheme was coupled with the lattice Boltzmann method to solve the Exner equation for the bed evolution caused by bed-load sediment transport. Five typical test cases were simulated by the coupled model and the numerical results agreed well with either the corresponding experimental data or the analytical solutions. This suggests that the present model has great potential to predict morphological change in shallow water flows. Furthermore, the effect of different values of time step for morphodynamic evolution and flow field were studied and no obvious difference was produced for these two kinds of method in the range tested in the present study.

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Section: Introductionmentioning

confidence: 97%

Mixed numerical method for bed evolution

Peng

Zhou

Zhang

2015

Proceedings of the Institution of Civil Engineers - Water Manag

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“…Several papers have been published concerning the application of the LBM to particular domains of interest. The shallow water°ow equations have been successfully modeled by Liu et al, 3 Th€ ommes et al, 4 Liu et al, 5 Linhao et al 6 and Rocca et al, 7 while coupling of shallow°ow with transport phenomena was investigated by Li and Huang, 8 Li and Huang, 9 Banda et al 10 and Peng et al 11 Free surface problems representing significant segments of river and coastal hydraulics (breaking dams, wave impact on o®shore structures, hydraulic jumps,°ood waves), including very demanding three-dimensional simulations of turbulent°ow, were investigated by Janßen and Krafczyk, 12 Attar and K€ orner 13 and Janssen and Krafczyk. 14 Furthermore, cases of discontinuous°ow have been explored by Zhou,15 while simulation of°ow in channel junctions À À À a very frequent phenomenon À À À is modeled by Liu et al 16 According to the trend by which the LBM is becoming an inevitable tool in solving demanding practical problems, application of the method on groundwater°o w-related problems is getting more attention.…”

Section: Introductionmentioning

confidence: 99%

Modeling groundwater flow by lattice Boltzmann method in curvilinear coordinates

Budinski

Fabian

Stipić

2015

Int. J. Mod. Phys. C

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In order to promote the use of the lattice Boltzmann method (LBM) for the simulation of isotropic groundwater°ow in a con¯ned aquifer with arbitrary geometry, Poisson's equation was transformed into a curvilinear coordinate system. With the metric function between the physical and the computational domain established, Poisson's equation written in Cartesian coordinates was transformed in curvilinear coordinates. Following, the appropriate equilibrium function for the D2Q9 square lattice has been de¯ned. The resulting curvilinear formulation of the LBM for groundwater°ow is capable of modeling°ow in domains of complex geometry with the opportunity of local re¯ning/coarsening of the computational mesh corresponding to the complexity of the°ow pattern and the required accuracy. Since the proposed form of the LBM uses the transformed equation of°ow implemented in the equilibrium function,¯nding a solution does not require supplementary procedures along the curvilinear boundaries, nor in the zones requiring mesh density adjustments. Thus, the basic concept of the LBM is completely maintained. The improvement of the proposed LBM over the previously published classical methods is completely veri¯ed by three examples with analytical solutions. The results demonstrate the advantages of the proposed curvilinear LBM in modeling groundwater°ow in complex°ow domains.

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“…In this study, MRT-LBM is used to solve shallow water equations, and it has already been applied successfully by numerous researchers [6,29,31,32]. Our simulation is based on the D 2 Q 9 model and space is discretized into a nine-speed square lattice (see Figure 1).…”

Section: A Sub-grid Lattice Boltzmann Modelmentioning

confidence: 99%

“…Ginzburg [13] first proposed the general form of the transformation matrix M which can be defined as [6,15,31]:…”

Section: Collision and Forcingmentioning

confidence: 99%

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Application of a Steady Meandering River with Piers Using a Lattice Boltzmann Sub-Grid Model in Curvilinear Coordinate Grid

Chen

Zhao

Huang

2018

Water

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Abstract:A sub-grid multiple relaxation time (MRT) lattice Boltzmann model with curvilinear coordinates is applied to simulate an artificial meandering river. The method is based on the D2Q9 model and standard Smagorinsky sub-grid scale (SGS) model is introduced to simulate meandering flows. The interpolation supplemented lattice Boltzmann method (ISLBM) and the non-equilibrium extrapolation method are used for second-order accuracy and boundary conditions. The proposed model was validated by a meandering channel with a 180 • bend and applied to a steady curved river with piers. Excellent agreement between the simulated results and previous computational and experimental data was found, showing that MRT-LBM (MRT lattice Boltzmann method) coupled with a Smagorinsky sub-grid scale (SGS) model in a curvilinear coordinates grid is capable of simulating practical meandering flows.

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Modelling solute transport in shallow water with the lattice Boltzmann method

Cited by 40 publications

References 28 publications

Mixed numerical method for bed evolution

Mixed numerical method for bed evolution

Modeling groundwater flow by lattice Boltzmann method in curvilinear coordinates

Application of a Steady Meandering River with Piers Using a Lattice Boltzmann Sub-Grid Model in Curvilinear Coordinate Grid

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