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

Zabello K.K., Garbaruk A.V.
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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 ($L_{\text{PML}}^{}$) 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 $\sigma_{\max}^{}\geqslant 0.02$ and $L_{\text{PML}}^{} \geqslant 2\lambda$. Additionally, it is shown that for source amplitudes $Q_0' \geqslant 0.1$, nonlinear effects become significant compared to other sources of error.

Keywords: lattice Boltzmann method (LBM), aeroacoustics, numerical simulation, regularization, PML layer, characteristic boundary conditions
Citation in English: Zabello K.K., Garbaruk A.V. Investigation of the accuracy of the lattice Boltzmann method in calculating acoustic wave propagation // Computer Research and Modeling, 2025, vol. 17, no. 6, pp. 1069-1081
Citation in English: Zabello K.K., Garbaruk A.V. Investigation of the accuracy of the lattice Boltzmann method in calculating acoustic wave propagation // Computer Research and Modeling, 2025, vol. 17, no. 6, pp. 1069-1081
DOI: 10.20537/2076-7633-2025-17-6-1069-1081
URL: http://crm-en.ics.org.ru/journal/article/3667/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

Copyright © 2025 Zabello K.K., Garbaruk A.V.

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