Univariate Polynomial Equation Providing Models of Thermal Lattice Boltzmann Theory

TL;DR

This paper introduces a univariate polynomial equation that models the thermal lattice Boltzmann equation with high accuracy and stability, applicable to regular lattices for efficient simulations.

Contribution

It presents a novel polynomial-based model for the thermal lattice Boltzmann equation that achieves arbitrary accuracy and enhanced stability, satisfying Galilean invariance.

Findings

Models can be accurate up to any required level.

Simulations of thermal shock tube problems demonstrate high accuracy.

Models show remarkably enhanced stability.

Abstract

A univariate polynomial equation is presented. It provides models of the thermal lattice Boltzmann equation. The models can be accurate up to any required level and can be applied to regular lattices, which allow efficient and accurate approximate solutions of the Boltzmann equation. We derive models satisfying the complete Galilean invariant and providing accuracy of the 4th-order moment and beyond. We simulate thermal shock tube problems to illustrate the accuracy of our models and to show the remarkably enhanced stability obtained by our models and our discretized equilibrium distributions.