Hermite regularization of the Lattice Boltzmann Method for open source computational aeroacoustics

TL;DR

This paper introduces a Hermite polynomial-based regularization technique for the lattice Boltzmann method, significantly enhancing its accuracy and stability for aeroacoustic simulations while maintaining computational efficiency and open-source accessibility.

Contribution

The authors develop an original Hermite regularization approach for LBM that improves stability and accuracy without increasing computational complexity, and implement it in an open-source framework.

Findings

Excellent agreement with experimental data on benchmark cases

Enhanced stability and accuracy in low Mach number aeroacoustic simulations

Open-source implementation facilitates wider adoption

Abstract

The lattice Boltzmann method (LBM) is emerging as a powerful engineering tool for aeroacoustic computations. However, the LBM has been shown to present accuracy and stability issues in the medium-low Mach number range, that is of interest for aeroacoustic applications. Several solutions have been proposed but often are too computationally expensive, do not retain the simplicity and the advantages typical of the LBM, or are not described well enough to be usable by the community due to proprietary software policies. We propose to use an original regularized collision operator, based on the expansion in Hermite polynomials, that greatly improves the accuracy and stability of the LBM without altering significantly its algorithm. The regularized LBM can be easily coupled with both non-reflective boundary conditions and a multi-level grid strategy, essential ingredients for aeroacoustic simulations. Excellent agreement was found between our approach and both experimental and numerical data on two different benchmarks: the laminar, unsteady flow past a 2D cylinder and the 3D turbulent jet. Finally, most of the aeroacoustic computations with LBM have been done with commercial softwares, while here the entire theoretical framework is implemented on top of an open source library (Palabos).