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Title: Lattice Boltzmann models for the convection-diffusion equation: D2Q5 vs D2Q9

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Publication Date:
Sponsoring Org.:
USDOE Advanced Research Projects Agency - Energy (ARPA-E)
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Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
International Journal of Heat and Mass Transfer
Additional Journal Information:
Journal Volume: 108; Journal Issue: PA; Related Information: CHORUS Timestamp: 2017-12-07 12:28:53; Journal ID: ISSN 0017-9310
Country of Publication:
United Kingdom

Citation Formats

Li, Like, Mei, Renwei, and Klausner, James F. Lattice Boltzmann models for the convection-diffusion equation: D2Q5 vs D2Q9. United Kingdom: N. p., 2017. Web. doi:10.1016/j.ijheatmasstransfer.2016.11.092.
Li, Like, Mei, Renwei, & Klausner, James F. Lattice Boltzmann models for the convection-diffusion equation: D2Q5 vs D2Q9. United Kingdom. doi:10.1016/j.ijheatmasstransfer.2016.11.092.
Li, Like, Mei, Renwei, and Klausner, James F. 2017. "Lattice Boltzmann models for the convection-diffusion equation: D2Q5 vs D2Q9". United Kingdom. doi:10.1016/j.ijheatmasstransfer.2016.11.092.
title = {Lattice Boltzmann models for the convection-diffusion equation: D2Q5 vs D2Q9},
author = {Li, Like and Mei, Renwei and Klausner, James F.},
abstractNote = {},
doi = {10.1016/j.ijheatmasstransfer.2016.11.092},
journal = {International Journal of Heat and Mass Transfer},
number = PA,
volume = 108,
place = {United Kingdom},
year = 2017,
month = 5

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1016/j.ijheatmasstransfer.2016.11.092

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  • In this paper, a lattice Boltzmann (LB) scheme for convection diffusion on irregular lattices is presented, which is free of any interpolation or coarse graining step. The scheme is derived using the axioma that the velocity moments of the equilibrium distribution equal those of the Maxwell-Boltzmann distribution. The axioma holds for both Bravais and irregular lattices, implying a single framework for LB schemes for all lattice types. By solving benchmark problems the authors have shown that the scheme is indeed consistent with convection diffusion. Furthermore, they have compared the performance of the LB schemes with that of finite difference andmore » finite element schemes. The comparison shows that the LB scheme has a similar performance as the one-step second-order Lax-Wendroff scheme: it has little numerical diffusion, but has a slight dispersion error. By changing the relaxation parameter {omega} the dispersion error can be balanced by a small increase of the numerical diffusion.« less
  • In this paper, the lattice Boltzmann equation is directly derived from the Boltzmann equation. It is shown that the lattice Boltzmann equation is a special discretized form of the Boltzmann equation. Various approximations for the discretization of the Boltzmann equation in both time and phase space are discussed in detail. A general procedure to derive the lattice Boltzmann model from the continuous Boltzmann equation is demonstrated explicitly. The lattice Boltzmann models derived include the two-dimensional 6-bit, 7-bit, and 9-bit, and three-dimensional 27-bit models. {copyright} {ital 1997} {ital The American Physical Society}
  • Diffusion phenomena in a multiple component lattice Boltzmann equation (LBE) model are discussed in detail. The mass fluxes associated with different mechanical driving forces are obtained using a Chapman-Enskog analysis. This model is found to have correct diffusion behavior and the multiple diffusion coefficients are obtained analytically. The analytical results are further confirmed by numerical simulations in a few solvable limiting cases. The LBE model is established as a useful computational tool for the simulation of mass transfer in fluid systems with external forces. {copyright} {ital 1996 The American Physical Society.}
  • In this note, we show that the lattice Boltzmann BGK method in common use can be derived from the Boltzmann equation itself. According to the present derivation, it is apparent that the equation thus derived can be reduced to the Navier-Stokes equation at a limit of small Knudsen number since the equation thus derived is the Boltzmann equation itself. Hence the present derivation method gives us a simple and flexible recipe to construct the lattice Boltzmann method, and makes it easy to construct an extended lattice Boltzmann method in various ways. 15 refs., 1 fig.
  • Exact results are presented for the surface diffusion of small two-dimensional clusters, the constituent atoms of which are commensurate with a square lattice of adsorption sites. Cluster motion is due to the hopping of atoms along the cluster perimeter with various rates. We apply the formalism of Titulaer and Deutch [J. Chem. Phys. {bold 77}, 472 (1982)], which describes evolution in reciprocal space via a linear master equation with dimension equal to the number of cluster configurations. We focus on the regime of rapid hopping of atoms along straight close-packed edges, where certain subsets of configurations cycle rapidly between eachmore » other. Each such subset is treated as a single quasiconfiguration, thereby reducing the dimension of the evolution equation, simplifying the analysis, and elucidating limiting behavior. We also discuss the influence of concerted atom motions on the diffusion of tetramers and larger clusters. {copyright} {ital 1999} {ital The American Physical Society}« less