An absorbing boundary condition for the lattice Boltzmann method based on the perfectly matched layer

The lattice Boltzmann method (LBM) is a well established computational tool for fluid flow simulations. This method has been recently utilized for low Mach number computational aeroacoustics. Robust and nonreflective boundary conditions, similar to those used in Navier–Stokes solvers, are needed for LBM-based aeroacoustics simulations. The goal of the present study was to develop an absorbing boundary condition based on the perfectly matched layer (PML) concept for LBM. The derivation of formulations for both two and three dimensional problems is presented. The macroscopic behavior of the new formulation is discussed. The new formulation was tested using benchmark acoustic problems. The perfectly matched layer concept appears to be very well suited for LBM, and yielded very low acoustic reflection factor.

► An absorbing boundary condition based on the perfectly matched layer (PML) concept for LBM is developed.
► The derivation of formulations for both two and three dimensional problems is presented.
► A stability analysis of the PML formulation for LBM is presented.
► The macroscopic behaviour of the new formulation is also discussed.
► The new formulation is tested using benchmark acoustic problems.