Lattice Boltzmann Methods with Anisotropic Equilibrium Distributions

@misc{kellers2026lattice,
  title = {{Lattice Boltzmann Methods with Anisotropic Equilibrium Distributions}},
  author = {Benjamin Kellers and Julius Weinmiller and Arnulf Latz and Timo Danner},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.27004},
  eprint = {2605.27004},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.27004},
}

TY  - UNPB
TI  - Lattice Boltzmann Methods with Anisotropic Equilibrium Distributions
AU  - Benjamin Kellers
AU  - Julius Weinmiller
AU  - Arnulf Latz
AU  - Timo Danner
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2605.27004
UR  - https://arxiv.org/abs/2605.27004
AB  - Lattice Boltzmann methods are usually derived under the assumption of isotropy. In this work, we present a derivation of a Lattice Boltzmann method for anisotropic fluid flow. Starting from an anisotropic equilibrium distribution, we show a full derivation of the resulting lattice Boltzmann method. We ensure that our method correctly reproduces macroscopic behavior via Chapman-Enskog analysis for a single-relaxation time collision operator. As a result, we are able to show that a properly discretized anisotropic Maxwell-Boltzmann equilibrium does macroscopically in fact lead to an anisotropic variation of the Navier-Stokes equations. All desired properties of lattice Boltzmann methods, such as locality of the collision operator, isotropic discrete position and velocity space, or mass and momentum conservation are retained. While it is explicitly shown in the context of fluid flow, the presented scheme is straight-forward to adopt to advection-diffusion problems.
ER  -