A decoupled scheme based on the Hermite expansion to construct lattice Boltzmann models for the compressible Navier-Stokes equations with arbitrary specific heat ratio

TL;DR

This paper introduces a novel decoupled lattice Boltzmann scheme based on Hermite expansion for simulating compressible Navier-Stokes equations with arbitrary specific heat ratios, enabling higher-order accuracy and effective modeling of rotational effects.

Contribution

The paper presents a decoupled Hermite expansion-based lattice Boltzmann model for compressible flows with arbitrary specific heat ratios, separating translational and rotational velocities for improved accuracy.

Findings

Numerical results from shock tube simulations match analytical solutions well.

The scheme effectively models rotational effects in compressible flows.

Higher-order accuracy schemes can be easily constructed using Hermite expansion.

Abstract

A decoupled scheme based on the Hermite expansion to construct lattice Boltzmann models for the compressible Navier-Stokes equations with arbitrary specific heat ratio is proposed. The local equilibrium distribution function including the rotational velocity of particle is decoupled into two parts, i.e. the local equilibrium distribution function of the translational velocity of particle and that of the rotational velocity of particle. From these two local equilibrium functions, two lattice Boltzmann models are derived via the Hermite expansion, namely one is in relation to the translational velocity and the other is connected with the rotational velocity. Accordingly, the distribution function is also decoupled. After this, the evolution equation is decoupled into the evolution equation of the translational velocity and that of the rotational velocity. The two evolution equations evolve separately. The lattice Boltzmann models used in the scheme proposed by this work are constructed via the Hermite expansion, so it is easy to construct new schemes of higher-order accuracy. To validate the proposed scheme, a shock tube simulation is performed. The numerical results agree with the analytical solutions very well.