The Lattice Boltzmann Equation

Kusumaatmaja, Halim; Kuzmin, Alexandr; Shardt, Orest; Silva, Gonçalo; Viggen, Erlend Magnus

doi:10.1007/978-3-319-44649-3_3

Cited by 110 publications

(204 citation statements)

References 28 publications

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“…It is assumed that the reader is familiar with the LBM, if not, the reader may consult Refs. [41][42][43]. The CGM and PPM used for the benchmarks are, respectively, from Leclaire et al 35 and Porter et al 13 These models are not described in this article and the reader may consult the previously mention references for a better understanding.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional lattice Boltzmann method benchmarks between color-gradient and pseudo-potential immiscible multi-component models

Leclaire

Parmigiani

Chopard

et al. 2017

Int. J. Mod. Phys. C

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In this paper, a lattice Boltzmann color-gradient method is compared with a multi-component pseudo-potential lattice Boltzmann model for two test problems: a droplet deformation in a shear°ow and a rising bubble subject to buoyancy forces. With the help of these two problems, the behavior of the two models is compared in situations of competing viscous, capillary and gravity forces. It is found that both models are able to generate relevant scienti¯c results. However, while the color-gradient model is more complex than the pseudo-potential approach, numerical experiments show that it is also more powerful and su®ers fewer limitations.

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Section: Introductionmentioning

confidence: 99%

Three-dimensional lattice Boltzmann method benchmarks between color-gradient and pseudo-potential immiscible multi-component models

Leclaire

Parmigiani

Chopard

et al. 2017

Int. J. Mod. Phys. C

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“…Fluid flow was simulated under the assumptions of steady, saturated flow at small Mach number using the lattice Boltzmann (LB) method. The LB method solves the discrete-velocity Boltzmann equation for the fluid mass and momentum density distributions (Sterling and Chen, 1996; Maier et al, 1998; Maier and Bernard, 2010; Krüger et al, 2016). The method is a pseudo-transient, explicit scheme for recovering Navier-Stokes behavior in the low Mach-number limit.…”

Section: Models and Methodsmentioning

confidence: 99%

“…The method is a pseudo-transient, explicit scheme for recovering Navier-Stokes behavior in the low Mach-number limit. The LB equations are solved on a regular 3-D grid with the D3Q19 method (Maier et al, 1998; Wagner, 2008; Krüger et al, 2016), in which physical space is discretized on a computational grid and velocity space is represented at each point by a set of 19 direction vectors. The computational grid is superimposed on the packed bed geometry and calculations are carried out in the fluid region of the grid.…”

Section: Models and Methodsmentioning

confidence: 99%

Transport properties and size exclusion effects in wide-pore superficially porous particles

Maier

Schure²

2018

Chemical Engineering Science

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The effects of hydrodynamic radius on the transport of solute molecules in packed beds of wide-pore superficially porous particles (SPP) are studied using pore-scale simulation. The free molecular diffusion rate varies with radius through the Stokes-Einstein relation. Lattice Boltzmann and Langevin methods are used to model fluid motion and the transport of an ensemble of solute molecules in the fluid, providing statistics on solute concentration, flux, molecule age and residence time, as a function of depth in the SPP. Intraparticle effective diffusion and bed dispersion coefficients are calculated and correlated with the hydrodynamic radius and accessible porosity. The relative importance of convection and diffusion are found to depend on the molecule (tracer) size through the diffusion rate, and convection effects are more significant for larger, slower-diffusing molecules. When larger molecules are utilized, the intraparticle concentration is reduced in proportion to the local particle porosity, leading to a natural definition of the accessible porosity used in size exclusion chromatography (SEC). Although the pore shape is complex, the SEC constant K can be calculated directly from simulation. Simulation demonstrates that the effective diffusion coefficient is elevated near the particle hull, which is largely open to interstitial flow, and decreases with depth into the particle. All molecules studied here have transport access to the entire particle depth, although the accessible volume at a given depth depends on their size. The first passage time into the particle is well predicted by the diffusion rate, but residence time is influenced by convection, shortening the average visit duration. These results are of interest in “perfusion” chromatography where convection is thought to increase separation efficiency for large biomolecules.

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“…However, the simplicity of the BGK collision operator comes at a cost: reduced accuracy, particularly at large viscosities, and stability, particularly at small viscosities. 31 To overcome these shortcomings, the multi-relaxation-time (MRT) collision operator 32 is useful since each of the moments can be relaxed at different time scales to achieve better stability and accuracy. In order to do this, all populations f i must first be transformed to moment space, in which the collision step is performed, and then transformed back into population space, where the streaming step is performed.…”

Section: ( √ 3δtmentioning

confidence: 99%

“…Others implement bounce-back-based coupling algorithms that are not exactly mass conserving or that require interpolations, which may be troublesome in dense particle assemblies with small pore sizes. 31 To this end, a coupling algorithm was developed based on the volume-fraction approach 9 to consider three-dimensional convex polyhedral particles moving through the fluid mesh where the solid particles are modeled using DEM and the fluid phase is modeled using LBM. The coupling process is implemented using the multi-relaxation-time (MRT) LBM which offers improved numerical stability and accuracy.…”

Section: Introductionmentioning

confidence: 99%

Coupled three‐dimensional discrete element‐lattice Boltzmann methods for fluid‐solid interaction with polyhedral particles

Gardner

Sitar

2019

Num Anal Meth Geomechanics

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Summary Interaction between solid particles and fluid is of fundamental interest to scientists and engineers in many different applications—cardiopulmonary flows, aircraft and automobile aerodynamics, and wind loading on buildings to name a few. In geomechanics, particle shape significantly affects both particle‐particle and particle‐fluid interaction. Herein, we present a generalized method for modeling the interaction of arbitrarily shaped polyhedral particles and particle assemblages with fluid using a coupled discrete element method (DEM) and lattice Boltzmann method (LBM) formulation. The coupling between DEM and LBM is achieved through a new algorithm based on a volume‐fraction approach to consider three‐dimensional convex polyhedral particles moving through fluid. The algorithm establishes the interaction using linear programming and simplex integration and is validated against experimental data. This approach to modeling the interaction between complex polyhedral particles and fluid is shown to be accurate for directly simulating hydrodynamic forces on the particles.

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The Lattice Boltzmann Equation

Cited by 110 publications

References 28 publications

Three-dimensional lattice Boltzmann method benchmarks between color-gradient and pseudo-potential immiscible multi-component models

Three-dimensional lattice Boltzmann method benchmarks between color-gradient and pseudo-potential immiscible multi-component models

Transport properties and size exclusion effects in wide-pore superficially porous particles

Coupled three‐dimensional discrete element‐lattice Boltzmann methods for fluid‐solid interaction with polyhedral particles

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