Analysis of Aeroacoustic Properties of the Local Radial Point Interpolation Cumulant Lattice Boltzmann Method

Mohsen Gorakifard, Clara Salueña, Ildefonso Cuesta and Ehsan Kian Far
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Mohsen Gorakifard: Department of Mechanical Engineering, ETSEQ, Rovira i Virgili University, Països Catalans, 26, 43007 Tarragona, Spain
Clara Salueña: Department of Mechanical Engineering, ETSEQ, Rovira i Virgili University, Països Catalans, 26, 43007 Tarragona, Spain
Ildefonso Cuesta: Department of Mechanical Engineering, ETSEQ, Rovira i Virgili University, Països Catalans, 26, 43007 Tarragona, Spain
Ehsan Kian Far: Department of Mechanical Engineering, The University of Manchester, Oxford Rd, Manchester M13 9PL, UK

Energies, 2021, vol. 14, issue 5, 1-18

Abstract: The lattice Boltzmann method (LBM) has recently been used to simulate wave propagation, one of the challenging aspects of wind turbine modeling and simulation. However, standard LB methods suffer from the instability that occurs at low viscosities and from its characteristic lattice uniformity, which results in issues of accuracy and computational efficiency following mesh refinement. The local radial point interpolation cumulant lattice Boltzmann method (LRPIC-LBM) is proposed in this paper to overcome these shortcomings. The LB equation is divided into collision and streaming steps. The collision step is modeled by the cumulant method, one of the stable LB methods at low viscosities. In addition, the streaming step, which is naturally a pure advection equation, is discretized in time and space using the Lax–Wendroff scheme and the local radial point interpolation method (RPIM), a mesh free method. We describe the propagation of planar acoustic waves, including the temporal decay of a standing plane wave and the spatial decay of a planar acoustic pulse. The analysis of these specific benchmark problems has yielded qualitative and quantitative data on acoustic dispersion and dissipation, and their deviation from analytical results demonstrates the accuracy of the method. We found that the LRPIC-LBM replicates the analytical results for different viscosities, and the errors of the fundamental acoustic properties are negligible, even for quite low resolutions. Thus, this method may constitute a useful platform for effectively predicting complex engineering problems such as wind turbine simulations, without parameter dependencies such as the number of points per wavelength N p p w and resolution σ or the detrimental effect caused by the use of coarse grids found in other accurate and stable LB models.

Keywords: local radial point interpolation cumulant LBM; aeroacoustics; dispersion; dissipation; wind turbine (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2021
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