Comprehensive comparison between the lattice Boltzmann and Navier-Stokes methods for aerodynamic and aeroacoustic applications

In an effort to determine which Computational Fluid Dynamics method offers the best trade-off between accuracy and computational cost for aerodynamic and aeroacoustic applications, the lattice Boltzmann and finite-volume Navier-Stokes methods are compared. Unlike previous studies, the present framework enables a fair and unbiased comparison of the core capabilities of each numerical approach and focuses on schemes of practical relevance. With the aim of providing a comprehensive comparison of the methods, an extended von Neumann analysis is performed and the High-Performance Computing capacities of both methods are thoroughly discussed. In addition, it is also shown through computations on canonical test cases that a "time to solution"metric has to be considered in order to objectively assess the suitability of one particular numerical method over the other. Three main conclusions are drawn: (1) both the lattice Boltzmann and Navier-Stokes schemes exhibit an anisotropic dissipative behaviour, (2) a cell update using the lattice Boltzmann method is 2 to 3 times faster than with the Navier-Stokes method dedicated to cartesian grids, and (3) the use of the "time to solution"metric demonstrates that the relevance of one method over the other is closely linked to the underlying physics and the intended error target. In light of these results, decision aids are provided to assist in selecting the most efficient method for a given application.