Finite Boltzmann schemes

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    17 Citations (Scopus)

    Abstract

    In the special case of relaxation parameter = 1 lattice Boltzmann schemes for (convection) diffusion and fluid flow are equivalent to finite difference/volume (FD) schemes, and are thus coined finite Boltzmann (FB) schemes. We show that the equivalence is inherent to the homology of the Maxwell-Boltzmann constraints for the equilibrium distribution, and the constraints for finite difference stencils as derived from Taylor series expansion. For convection¿diffusion we analyse the equivalence between FB and the Lax¿Wendroff FD scheme in detail. It follows that the Lax-Wendroff procedure is performed automatically in the finite Boltzmann schemes via the imposed Maxwell¿Boltzmann constraints. Furthermore, we make some remarks on FB schemes for fluid flows, and show that an earlier related study can be extended to rectangular grids. Finally, our findings are briefly checked with simulations of natural convection in a differentially heated square cavity.
    Original languageEnglish
    Pages (from-to)849-854
    JournalComputers & Fluids
    Volume35
    Issue number8-9
    DOIs
    Publication statusPublished - 2006

    Keywords

    • lattice boltzmann
    • diffusion lattice
    • equation

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