NUMERICAL METHODS AND THE BASIS FOR THEIR APPLICATION

Investigation of the accuracy of the lattice Boltzmann method in calculating acoustic wave propagation

K. K. Zabello, A. V. Garbaruk

Saint-Petersburg Polytechnic University, 29 Polytechnic st., Saint-Petersburg, 195251, Russia

Abstract: The article presents a systematic investigation of the capabilities of the lattice Boltzmann method (LBM) for modeling the propagation of acoustic waves. The study considers the problem of wave propagation from a point harmonic source in an unbounded domain, both in a quiescent medium (Mach number $M=0$) and in the presence of a uniform mean flow ($M=0.2$). Both scenarios admit analytical solutions within the framework of linear acoustics, allowing for a quantitative assessment of the accuracy of the numerical method.
The numerical implementation employs the two-dimensional D2Q9 velocity model and the Bhatnagar – Gross – Krook (BGK) collision operator. The oscillatory source is modeled using Gou’s scheme, while spurious high-order moment noise generated by the source is suppressed via a regularization procedure applied to the distribution functions. To minimize wave reflections from the boundaries of the computational domain, a hybrid approach is used, combining characteristic boundary conditions based on Riemann invariants with perfectly matched layers (PML) featuring a parabolic damping profile.
A detailed analysis is conducted to assess the influence of computational parameters on the accuracy of the method. The dependence of the error on the PML thickness ($L_{\mathrm{PML}}$) and the maximum damping coefficient ($\sigma_{\max}$), the dimensionless source amplitude ($Q'_0$), and the grid resolution is thoroughly examined. The results demonstrate that the LBM is suitable for simulating acoustic wave propagation and exhibits second-order accuracy. It is shown that achieving high accuracy (relative pressure error below 1%) requires a spatial resolution of at least 20 grid points per wavelength ($\lambda$). The minimal effective PML parameters ensuring negligible boundary reflections are identified as $\sigma_{\max}\geq 0.02$ and $L_{\mathrm{PML}}\geq 2\lambda$. Additionally, it is shown that for source amplitudes $Q'_0\geq 0.1$, nonlinear effects become significant compared to other sources of error.

Keywords: lattice Boltzmann method (LBM), aeroacoustics, numerical simulation, regularization, PML layer, characteristic boundary conditions

UDC: 519.8

Received: 24.10.2025
Revised: 23.11.2025
Accepted: 25.11.2025

DOI: 10.20537/2076-7633-2025-17-6-1069-1081