Recovery of Galilean Invariance in Thermal Lattice Boltzmann Models for Arbitrary Prandtl Number

Abstract

In this paper, we demonstrate a set of fundamental conditions required for the formulation of a thermohydrodynamic lattice Boltzmann model at an arbitrary Prandtl number. A specific collision operator form is then proposed that is in compliance with these conditions. It admits two independent relaxation times, one for viscosity and another for thermal conductivity. But more importantly, the resulting thermohydrodynamic equations based on such a collision operator form is theoretically shown to remove the well known non-Galilean invariant artifact at non-unity Prandtl numbers in previous thermal lattice Boltzmann models with multiple relaxation times.

References in corpus (3)

• Efficient kinetic method for fluid simulation beyond the Navier-Stokes equation
• Galilean invariance of lattice Boltzmann models
• Fundamental Conditions for N-th Order Accurate Lattice Boltzmann Models

Cited by in corpus (6)

• Modeling incompressible thermal flows using a central-moment-based lattice Boltzmann method
• Cross-platform programming model for many-core lattice Boltzmann simulations
• A comparative study of 3D Cumulant and Central Moments lattice Boltzmann schemes with interpolated boundary conditions for the simulation of thermal flows in high Prandtl number regime
• Rotation symmetry of the multiple-relaxation-time collision model
• Volumetric Lattice Boltzmann Models in General Curvilinear Coordinates: Theoretical Formulation
• A non-local quasi-equilibrium state in the Bhatnagar-Gross-Krook Boltzmann equation for thermo-hydrodynamics: Conservation laws, the Boltzmann H-theorem, and the fluctuation-dissipation theorem