On the Generalized Hermite-Based Lattice Boltzmann Construction, Lattice Sets, Weights, Moments, Distribution Functions and High-Order Models

TL;DR

This paper explores the use of generalized Hermite polynomials in lattice Boltzmann models, proposing a new moment system that enables high-order models to accurately match hydrodynamic moments on Cartesian lattices with thermal weights.

Contribution

It introduces a novel Hermite-based LB construction with a new moment system for high-order accuracy on Cartesian lattices using thermal weights.

Findings

High-order LB models can exactly match hydrodynamic moments thermally.

The approach allows for shortest lattice sets with fixed temperatures.

Theoretical analysis confirms the feasibility of the proposed models.

Abstract

The influence of the use of the generalized Hermite polynomial on the Hermite-based lattice Boltzmann (LB) construction approach, lattice sets, the thermal weights, moments and the equilibrium distribution function (EDF) are addressed. A new moment system is proposed. The theoretical possibility to obtain a high-order Hermite-based LB model capable to exactly match some first hydrodynamic moments thermally 1) on-Cartesian lattice, 2) with thermal weights in the EDF, 3) whilst the highest possible hydrodynamic moments that are exactly matched are obtained with the shortest on-Cartesian lattice sets with some fixed real-valued temperatures, is also analyzed. Keywords: Lattice Boltzmann, fluid dynamics, kinetic theory, distribution function