The meshless local Petrov-Galerkin cumulant lattice Boltzmann method: strengths and weaknesses in aeroacoustic analysis

The lattice Boltzmann method (LBM) suffers from an instability at low viscosities and from having to compromise between accuracy and computational efficiency due to its lattice uniformity. Thus, in this paper, the meshless local Petrov-Galerkin cumulant lattice Boltzmann method (MLPGC-LBM) is proposed to remedy these shortcomings. The collision step is modeled by the cumulant method, stable at low viscosities, and the streaming step is discretized first in time based on the Lax-Wendroff scheme, then in space according to the meshless local Petrov-Galerkin method, a mesh-free method (MLPG). To substantiate the accuracy of this method in aeroacoustics, the temporal decay of a standing plane wave, the spatial decay of a planar acoustic pulse, and the propagation of circular waves are considered, and the results are compared with numerical and analytical solutions. The comparisons show that MLPGC-LBM presents better results than standard LB methods, replicating the local radial point interpolation cumulant lattice Boltzmann method (LRPIC-LBM) results with relatively shorter runtimes, and being in a good agreement with the analytical solutions. The errors of the acoustic dispersion and dissipation are irrelevant, even for quite low resolutions. Therefore, MLPGC-LBM can offer an alternative to conventional aeroacoustics simulations alongside LRPIC-LBM with shorter runtimes, without parametric dependency on the number of points per wavelength and the resolution