Velocity Discretization for Lattice Boltzmann Method for Noncontinuum Bounded Gas Flows at the Micro and Nanoscale

TL;DR

This paper introduces a novel velocity discretization approach using Gauss Legendre quadrature in lattice Boltzmann models, significantly improving accuracy for simulating noncontinuum gas flows at micro and nanoscale with high Knudsen numbers.

Contribution

It proposes a new velocity discretization method with Gauss Legendre quadrature, enhancing the lattice Boltzmann method's accuracy for noncontinuum micro and nanoscale gas flows.

Findings

GL-based LB models achieve high accuracy at large Knudsen numbers

Conventional HGH quadrature models show poor accuracy in noncontinuum regimes

New discretization approach effectively simulates free molecular flows

Abstract

The lattice Boltzmann (LB) method intrinsically links to the Boltzmann equation with the Bhatnagar-Gross-Krook collision operator; however, it has been questioned to be able to simulate noncontinuum bounded gas flows at the micro and nanoscale, where gas moves at a low speed but has a large Knudsen number. In this article, this point has been verified by simulating Couette flows at moderate and large Knudsen numbers (e.g., Kn=10 and Kn=100) by the linearized LB models based on the popular half-space Gaussian Hermite (HGH) quadrature. The underlying cause for poor accuracy of these conventional models is analyzed in light of numerical evaluation of the involved Abramowitz functions. A different thought on velocity discretization is then proposed using Gauss Legendre (LG) quadrature. Strikingly, the resulting GL-based LB models have achieved high accuracy in simulating Couette flows in the strong transition and even free molecular flow regimes. The numerical study in this article reveals an essentially different while workable way in constructing LB models for simulating micro and nanoscale low-speed gas flows with strong noncontinuum effects.