A Fluctuating Lattice Boltzmann Method for the Diffusion Equation
Alexander J. Wagner, Kyle Strand
TL;DR
This paper presents a new fluctuating lattice Boltzmann method specifically designed for the diffusion equation, improving upon previous models by providing a more accurate and simplified derivation.
Contribution
It introduces the first exact derivation of a fluctuating lattice Boltzmann method tailored for diffusion, addressing previous shortcomings.
Findings
Provides a simplified, exact derivation for diffusion systems
Enhances accuracy of fluctuating lattice Boltzmann methods
Highlights fundamental features of the new method
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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