Lattice Nomenclature Survey from LGA to Modern LBM

Abstract

Lattice configuration is a core parameter in Lattice-Boltzmann (LB) methods, both from theoretical and implementation standpoints. As LB methods have progressed over the past decades, a variety of lattice configurations have been proposed and referred to according to a plurality of lattice nomenclature systems that usually include the Euclidean space dimensionality, the lattice velocity count and, in fewer instances, the discretization order in their format. This work surveys lattice nomenclature systems, or lattice naming schemes, along the history of LB methods, starting from their Lattice Gas Automata (LGA) predecessor method, up to the present time. Findings include multiple lattice categories, competing naming standards, ambiguous names particularly in higher-order models, naming systems of varying model parameter scopes, and lack of unambiguous naming schemes even for space-filling, Bravais lattice types.