2016•Physical review. EOpen access

Fluctuating lattice Boltzmann method for the diffusion equation

Alexander J. Wagner, Kyle Strand

Abstract

We derive a fluctuating lattice Boltzmann method for the diffusion equation. The derivation removes several shortcomings of previous derivations for fluctuating lattice Boltzmann methods for hydrodynamic systems. The comparative simplicity of this diffusive system highlights the basic features of this first exact derivation of a fluctuating lattice Boltzmann method.

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Key concepts: Lattice Boltzmann methods, HPP model, Boltzmann equation, Bhatnagar–Gross–Krook operator, Lattice gas automaton, Statistical physics, Lattice (music), Diffusion equation