Lattice ellipsoidal statistical BGK model for thermal non-equilibrium flows

TL;DR

This paper develops a thermal lattice Boltzmann model based on the ES-BGK collision operator, capable of accurately simulating microscale non-equilibrium flows with adjustable Prandtl number, demonstrating good accuracy in slip-flow and transition regimes.

Contribution

The paper introduces a lattice ES-BGK model using a single distribution function with an adjustable Prandtl number, suitable for microscale thermal non-equilibrium flow simulations.

Findings

Accurately recovers steady and transient solutions in slip-flow and early transition regimes.

Good agreement with other numerical methods up to Knudsen number ~0.5.

Model's accuracy improves with increased discrete velocities.

Abstract

A thermal lattice Boltzmann model is constructed on the basis of the ellipsoidal statistical Bhatnagar-Gross-Krook (ES-BGK) collision operator via the Hermite moment representation. The resulting lattice ES-BGK model uses a single distribution function and features an adjustable Prandtl number. Numerical simulations show that using a moderate discrete velocity set, this model can accurately recover steady and transient solutions of the ES-BGK equation in the slip-flow and early transition regimes in the small Mach number limit that is typical of microscale problems of practical interest. In the transition regime in particular, comparisons with numerical solutions of the ES-BGK model, direct Monte Carlo and low-variance deviational Monte Carlo simulations show good accuracy for values of the Knudsen number up to approximately 0.5. On the other hand, highly non-equilibrium phenomena characterized by high Mach numbers, such as viscous heating and force-driven Poiseuille flow for large values of the driving force, are more difficult to capture quantitatively in the transition regime using discretizations chosen with computational efficiency in mind such as the one used here, although improved accuracy is observed as the number of discrete velocities is increased.