A new scheme based on the Hermite expansion to construct lattice Boltzmann models associated with arbitrary specific heat ratio

TL;DR

This paper introduces a novel lattice Boltzmann scheme utilizing Hermite expansion to model fluids with arbitrary specific heat ratios, improving flexibility and accuracy in simulating complex thermodynamic behaviors.

Contribution

The paper develops a new lattice Boltzmann model that incorporates internal energy for arbitrary specific heat ratios using Hermite expansion, reducing the evolution equations to two for simplicity.

Findings

Accurately simulates shock tube problems in 1D.

Shows good agreement with analytical solutions.

Provides a flexible framework for different specific heat ratios.

Abstract

A new lattice Boltzmann scheme associated with flexible specific heat ratio is proposed. The new free degree is introduced via the internal energy associated with the internal structure. The evolution equation of the distribution function is reduced to two evolution equations. One is connected to the density and velocity, the other is of the energy. A two-dimensional lattice Boltzmann model and a three-dimensional lattice Boltzmann model are derived via the Hermite expansion. The two lattice Boltzmann models are applied to simulating the shock tube of one dimension. Good agreement between the numerical results and the analytical solutions are obtained.