A finite-difference lattice Boltzmann approach for gas microflows

TL;DR

This paper introduces a finite-difference lattice Boltzmann method using half-range Gauss-Hermite quadrature for more accurate simulation of gas microflows, especially near boundaries, in microscale devices.

Contribution

It proposes a novel LB model employing half-range Gauss-Hermite quadrature nodes, enabling better boundary condition treatment and improved accuracy over standard models.

Findings

Enhanced accuracy in finite Knudsen flow simulations.

Effective treatment of kinetic boundary conditions.

Successful application to microflow problems.

Abstract

Finite-difference Lattice Boltzmann (LB) models are proposed for simulating gas flows in devices with microscale geometries. The models employ the roots of half-range Gauss-Hermite polynomials as discrete velocities. Unlike the standard LB velocity-space discretizations based on the roots of full-range Hermite polynomials, using the nodes of a quadrature defined in the half-space permits a consistent treatment of kinetic boundary conditions. The possibilities of the proposed LB models are illustrated by studying the one-dimensional Couette flow and the two-dimensional driven cavity flow. Numerical and analytical results show an improved accuracy in finite Knudsen flows as compared with standard LB models.