Lattice Boltzmann approach to rarefied gas flows using half-range Gauss-Hermite quadratures: Comparison to DSMC results based on ab initio potentials

TL;DR

This study employs a lattice Boltzmann method with half-range Gauss-Hermite quadratures to simulate rarefied gas flows and compares results with DSMC simulations for helium atoms across various temperatures, showing good agreement at higher rarefaction levels.

Contribution

The paper introduces a lattice Boltzmann approach with half-range Gauss-Hermite quadratures for rarefied gas flows, validated against DSMC results with ab initio potentials.

Findings

Good agreement with DSMC at large rarefaction parameters

Relative errors in shear stress do not exceed 2.5%

Method effectively captures wall-induced discontinuities

Abstract

In this paper, we employ the lattice Boltzmann method to solve the Boltzmann equation with the Shakhov model for the collision integral in the context of the 3D planar Couette flow. The half-range Gauss-Hermite quadrature is used to account for the wall-induced discontinuity in the distribution function. The lattice Boltzmann simulation results are compared with direct simulation Monte Carlo (DSMC) results for ${}^3{\rm He}$ and ${}^4{\rm He}$ atoms interacting via ab initio potentials, at various values of the rarefaction parameter $\delta$, where the temperature of the plates varies from $1\ {\rm K}$ up to $3000\ {\rm K}$. Good agreement is observed between the results obtained using the Shakhov model and the DSMC data at large values of the rarefaction parameter. The agreement deteriorates as the rarefaction parameter is decreased, however we highlight that the relative errors in the non-diagonal component of the shear stress do not exceed $2.5\%$.