Use of the Boltzmann Equation to Simulate Lattice-Gas Automata

McNamara, Guy R.; Zanetti, Gianluigi

doi:10.1103/physrevlett.61.2332

Cited by 1,828 publications

(1,033 citation statements)

References 6 publications

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“…In contrast to the LGCA coarse, graining of the molecular processes is not obtained by tracking individual discrete mesoscopic fluid packets anymore. Instead, in the LBM, the dynamics of the single-particle distribution function f (x, v, t) representing the probability to find a fluid particle with position x and velocity v at time t is tracked [48][49][50][51][52]. Then, the density and velocity of the macroscopically observable fluid are given by ρ(x, t) = f dv and u(x, t) = f vdv, respectively.…”

Section: The Lattice Boltzmann Methodsmentioning

confidence: 99%

“…The lattice must be chosen carefully to ensure isotropic behaviour of the simulated fluid [26]. The lattice Boltzmann formulation can be obtained using alternative routes, including discretizing the continuum Boltzmann equation [56] or regarding it as a Boltzmann-level approximation of the LGCA [57].…”

Section: The Lattice Boltzmann Methodsmentioning

confidence: 99%

“…56 in the Navier-Stokes equations,p can be simply incorporated in the modified equilibrium distribution function and the interfacial force term, F S = −μ∇φ, can be treated as an external force in the lattice Boltzmann implementation. Following the work of Liu and Zhang [131], the time evolution equation for f i can be replaced by, (57) when the chemical potential form is employed. In order to recover the correct Navier-Stokes equations, the moments of f eq i and H i should satisfy,…”

Section: Free-energy Modelmentioning

confidence: 99%

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Multiphase lattice Boltzmann simulations for porous media applications

et al. 2015

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Over the last two decades, lattice Boltzmann methods have become an increasingly popular tool to compute the flow in complex geometries such as porous media. In addition to single phase simulations allowing, for example, a precise quantification of the permeability of a porous sample, a number of extensions to the lattice Boltzmann method are available which allow to study multiphase and multicomponent flows on a pore scale level. In this article, we give an extensive overview on a number of these diffuse interface models and discuss their advantages and disadvantages. Furthermore, we shortly report on multiphase flows containing solid particles, as well as implementation details and optimization issues.

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Section: The Lattice Boltzmann Methodsmentioning

confidence: 99%

Section: The Lattice Boltzmann Methodsmentioning

confidence: 99%

Section: Free-energy Modelmentioning

confidence: 99%

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Multiphase lattice Boltzmann simulations for porous media applications

et al. 2015

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“…For instance, the large statistical fluctuation limits the practical usage of the LGA method. To suppress the statistical noise, McNamara and Zanetti (3) suggested modeling the LGA with a lattice Boltzmann equation. Mean population, instead of the discrete particles, are used to simulate fluid flows.…”

Section: Introductionmentioning

confidence: 99%

Multicomponent lattice-Boltzmann model with interparticle interaction

1995

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A previously proposed [X. H. Chen, Phys. Rev. E 47, 1815, (1993) ] latticeBoltzmann model for simulating fluids with multiple components and interparticle forces is described in detail. Macroscopic equations governing the motion of each component are derived by using Chapman-Enskog method. The mutual diffusivity in a binary mixture is calculated analytically and confirmed by numerical simulation. The diffusivity is generally a function of the concentrations of the two components but independent of the fluid velocity so that the diffusion is Galilean invariant. The analytically calculated shear kinematic viscosity of this model is also confirmed numerically.

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“…We include hydrodynamic interactions by using a Lattice Boltzmann algorithm [16] that is interacting with the beads in the MD simulations via a frictionally coupling introduced by Ahlrichs et al [17]. The mesoscopic LB fluid is described by a velocity field generated by discrete momentum distributions on a spatial grid rather than explicit fluid particles.…”

Section: Modelmentioning

confidence: 99%

Mesoscale modelling of polyelectrolyteelectrophoresis

Grass

Holm

2010

Faraday Discuss.

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The electrophoretic behaviour of flexible polyelectrolyte chains ranging from single monomers up to long fragments of hundred repeat units is studied by a mesoscopic simulation approach. Abstracting from the atomistic details of the polyelectrolyte and the fluid, a coarse-grained molecular dynamics model connected to a mesoscopic fluid described by the Lattice Boltzmann approach is used to investigate free-solution electrophoresis. Our study demonstrates the importance of hydrodynamic interactions for the electrophoretic motion of polyelectrolytes and quantifies the influence of surrounding ions. The length-dependence of the electrophoretic mobility can be understood by evaluating the scaling behavior of the effective charge and the effective friction. The perfect agreement of our results with experimental measurements shows that all chemical details and fluid structure can be safely neglected, and a suitable coarse-grained approach can yield an accurate description of the physics of the problem, provided that electrostatic and hydrodynamic interactions between all entities in the system, i.e., the polyelectrolyte, dissociated counterions, additional salt and the solvent, are properly accounted for. Our model is able to bridge the single molecule regime of a few nm up to macromolecules with contour lengths of more than 100 nm, a length scale that is currently not accessible to atomistic simulations.

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Use of the Boltzmann Equation to Simulate Lattice-Gas Automata

Cited by 1,828 publications

References 6 publications

Multiphase lattice Boltzmann simulations for porous media applications

Multiphase lattice Boltzmann simulations for porous media applications

Multicomponent lattice-Boltzmann model with interparticle interaction

Mesoscale modelling of polyelectrolyteelectrophoresis

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