LBM for acoustics and aeroacoustics

Noise has become a significant contributor to environmental pollution, particularly in urban, industrial, and transportation-related environments, where acoustic disturbances can influence comfort, health, and quality of life. Because acoustic noise is associated with the generation and propagation of pressure, density, and velocity fluctuations, its prediction requires numerical tools that can resolve weak acoustic signals over long propagation distances and in the presence of flow, walls, obstacles, and boundary reflections. This task is especially challenging in aeroacoustics, where the acoustic field is typically much weaker than the underlying hydrodynamic field, and where small numerical errors in dissipation, dispersion, source modelling, or boundary treatment can accumulate and distort the physical signal. This thesis examines the capability of the Lattice Boltzmann Method (LBM) for acoustic and aeroacoustic simulations. In this thesis, the method is treated not only as an alternative flow solver, but also as a mesoscopic numerical framework in which macroscopic quantities such as density, velocity, pressure, and temperature can be recovered from the evolution of particle distribution functions. This structure is particularly appealing for aeroacoustics since weak compressibility, wave propagation, acoustic sources, boundary interaction, and flow-acoustic coupling can be addressed within a unified formulation. At the same time, the application of LBM to acoustic problems requires careful investigation, because the lattice structure, relaxation time, collision model, source implementation, and boundary conditions can all affect the resulting acoustic field. For this reason, the objective of the thesis is not limited to showing that LBM can reproduce qualitatively plausible acoustic waves. Instead, the study concentrates on evaluating how acoustic information is produced, propagated, attenuated, reflected, and modified inside LBM simulations, and on identifying the numerical conditions under which the reliable application of the method is possible. The study relies on in-house Fortran solvers developed during the research. The D2Q9 lattice is adopted as the main framework for low-Mach-number acoustic and hydrodynamic simulations, with both BGK and MRT collision models considered. Additional formulations are used where needed, including thermal LBM with turbulence modelling for natural-convection cases and a D2Q13 double-distribution-function finite-difference LBM with WENO reconstruction for compressible external-flow simulations. A key contribution of the thesis is the development of a progressive validation strategy for acoustic LBM. Simple and controlled configurations are first used to isolate the basic behavior of source implementation and wave propagation. These studies demonstrate that the way in which an acoustic source is coupled to the lattice populations can strongly influence the effective radiated field, even when the imposed nominal fluctuation is the same. Therefore, source behavior and wave propagation should be interpreted separately. After a coherent wave has been emitted, the main propagation characteristics are governed mainly by the common acoustic response of the lattice model, while near-source differences are generally related to the numerical coupling of the source itself. The plane-wave studies demonstrate that the implemented LBM framework is able to propagate weak acoustic waves with high fidelity in lattice units. The phase speed, wavelength preservation, attenuation characteristics, impedance consistency, harmonic purity, and transverse uniformity remain accurate over the investigated parameter range. These results establish a reliable basis for the more complex studies that follow and show that, under controlled conditions, the method can reproduce the main features that are expected from linear acoustic propagation. However, the study also reveals that evaluating acoustic accuracy cannot be based only on field contours or visual wavefronts. Quantitative diagnostics are required to distinguish physical propagation from numerical error. Another important part of the thesis concerns viscous attenuation and wall-bounded propagation. In periodic traveling-wave configurations, the measured bulk attenuation aligns with the theoretical viscous trend. Yet, when no-slip walls are present, the total attenuation rises dramatically. The wall-induced component is distinct from the bulk viscous contribution and is linked to the oscillatory boundary-layer behavior near solid surfaces. This separation is important for interpreting acoustic ducts and reflected waves, since wall friction modifies the amplitude balance between incident and reflected waves and alters the observed standing-wave pattern. Analyzing the superimposition of direct and reflected waves also demonstrates that, in a viscous LBM duct, the ideal nodes of an inviscid standing wave are replaced by locations of minimum amplitude for the envelope of spatial profiles. Their estimated spacing is primarily controlled by wavelength, whereas their sharpness and contrast are influenced by dissipation, reflection phase, and numerical dispersion. This interpretation provides a more realistic description of wave interference in wall-bounded LBM simulations and avoids viewing the reflected field as an ideal standing wave. It also explains why nodal structures may continue to be physically meaningful even when the envelope minima do not vanish completely. Moving-source simulations are used to study how LBM represents Doppler-related acoustic behavior and how non-stationary source motion modifies the emitted acoustic field. Comparing a stationary source in a moving medium with a source moving through a quiescent medium demonstrates that the resolved wave field follows the expected wavelength-level Doppler response away from the immediate source region. However, when a moving source in a quiescent medium is modeled, a localized numerical signature emerges due to the repeated relocation of the source on the fixed lattice. Using a distributed moving-source support reduces this near-source artefact without suppressing the physical Doppler effect. In confined-channel configurations, the response becomes more complex because source motion, boundary reflections, absorbing regions, confinement, and background flow together lead to a redistribution of the acoustic energy into modulation components around the carrier frequency. This thesis also studies finite-amplitude nonlinear acoustic propagation. By comparing LBM results with Burgers-type reference solutions, the study shows that the D2Q9-BGK model can reproduce nonlinear steepening over identifiable ranges of amplitude, wavelength, and relaxation time. However, the method’s validity cannot be reduced to a single universal amplitude threshold. The earliest significant deviations are typically associated with waveform-shape distortion and localized overshoot near steepened fronts, whereas the spectral content and global phase can still appear acceptable. This finding emphasizes the need to assess nonlinear acoustic accuracy through waveform-sensitive indicators, not through frequency or phase information alone. The comparison with MRT formulations further demonstrates that additional relaxation freedom does not automatically increase nonlinear acoustic accuracy; in the present setting, BGK remains the more robust baseline, whereas calibrated MRT is mainly useful as a stability-oriented alternative near the low-relaxation-time limit. Finally, the validated numerical components are extended toward representative aeroacoustic applications. Acoustic propagation is studied in a high-Rayleigh-number natural-convection cavity, in which the sound field interacts with a non-uniform turbulent thermal background. Compressible flow around a NACA-0012 airfoil is examined by means of a higher-order finite-difference LBM formulation, allowing the acoustic interpretation of pressure signals in transonic and supersonic regimes. A dipole source is also imposed in the wake of a circular cylinder, in which curved-boundary treatment, wake dynamics, and source directivity become relevant. These applications are not intended as exhaustive parametric studies; instead, they reveal how the validated acoustic framework can be extended to more realistic flow-acoustic configurations when it is supported by suitable physical and numerical interpretation. Overall, this thesis shows that the Lattice Boltzmann Method can provide a flexible framework for acoustic and aeroacoustic simulations, provided that its results are interpreted through suitable diagnostics. The study clarifies how source implementation, relaxation time, wall treatment, moving-source representation, and nonlinear effects influence the acoustic response obtained from LBM calculations. Therefore, the main contribution of this thesis is both numerical and interpretive. It offers a validated set of LBM tools for acoustic propagation, source modelling, attenuation, reflection, moving-source effects, nonlinear wave evolution, and selected aeroacoustic applications. It also clarifies how the acoustic results that are produced by these tools should be understood.