An Absorbing Boundary Condition for the Lattice Boltzmann Method Based on the Perfectly Matched Layer

Area of Science:

• Computational fluid dynamics
• Acoustics
• Numerical methods

Background:

• The Lattice Boltzmann Method (LBM) is a powerful computational tool for fluid flow simulations.
• Recent applications of LBM extend to low Mach number computational aeroacoustics.
• Robust, nonreflective boundary conditions are essential for accurate LBM-based aeroacoustics simulations, analogous to those used in Navier-Stokes solvers.

Purpose of the Study:

• To develop and present a novel absorbing boundary condition for LBM simulations.
• The core of the development is based on the perfectly matched layer (PML) concept.
• Formulations for both two- and three-dimensional problems are derived and discussed.

Main Methods:

• Derivation of PML formulations for 2D and 3D LBM problems.
• Analysis of the macroscopic behavior of the proposed PML boundary condition.
• Testing the new formulation using established benchmark acoustic problems.

Main Results:

• The perfectly matched layer (PML) concept is highly compatible with the Lattice Boltzmann Method (LBM).
• The developed PML absorbing boundary condition demonstrated very low acoustic reflection factors.
• The new formulation proved effective in benchmark acoustic simulations.

Conclusions:

• The proposed PML-based absorbing boundary condition is well-suited for LBM aeroacoustics.
• This advancement offers a robust solution for reducing unwanted reflections in LBM simulations.
• The method enhances the accuracy and reliability of computational aeroacoustics using LBM.