Uniform Polynomial Equations Providing Higher-order Multi-dimensional Models in Lattice Boltzmann Theory

TL;DR

This paper introduces polynomial equations that enable the construction of high-accuracy, multi-dimensional lattice Boltzmann models suitable for simulating complex thermal compressible flows, extending the theory's applicability.

Contribution

It provides a general framework of polynomial equations for creating lattice Boltzmann models in any dimension with arbitrary accuracy, including explicit 2D and 3D thermal flow models.

Findings

Derived polynomial equations for multi-dimensional lattice Boltzmann models

Explicit models for 2D and 3D thermal compressible flows

Models match Navier-Stokes level of accuracy

Abstract

We present a set of polynomial equations that provides models of the lattice Boltzmann theory for any required level of accuracy and for any dimensional space in a general form. We explicitly derive two- and three-dimensional models applicable to describe thermal compressible flows of the level of the Navier-Stokes equations.