Analysis of the absorbing layers for the weakly-compressible lattice Boltzmann methods

It has been demonstrated that Lattice Boltzmann methods (LBMs) are very efficient for Computational Aeroacoustics (CAA). In order to address the issue of absorbing acoustic boundary conditions for LBM, three kinds of damping terms are proposed and added to the right hand side of the LBM governing equations. According to the classical theory, these terms play an important role to damp and minimize the acoustic wave reflections from computational boundaries. The corresponding macroscopic equations with the damping terms are recovered for analyzing the macroscopic behaviors of the these damping terms and determining the critical absorbing strength. The dissipative and dispersive properties of the proposed absorbing layer terms are then further analyzed considering the linearized LBM equations. They are explored in the wave-number spaces via the Von Neumann analysis. The related damping strength critical values and the optimal absorbing term are discussed. Finally, some benchmark problems are implemented to assess the theoretical results.