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

TL;DR

This paper investigates absorbing layers in weakly-compressible lattice Boltzmann schemes, proposing damping terms to reduce boundary reflections, analyzing their effects, and validating results through benchmark problems.

Contribution

It introduces three damping terms into Lattice Boltzmann schemes for better acoustic boundary absorption and analyzes their macroscopic and wave properties.

Findings

Identified critical damping strengths for effective absorption

Derived macroscopic equations with damping terms

Validated damping effectiveness through benchmark tests

Abstract

It has been demonstrated that Lattice Boltzmann schemes (LBSs) are very efficient for Computational AeroAcoustics (CAA). In order to handle the issue of absorbing acoustic boundary conditions for LBS, three kinds of damping terms are proposed and added into the right hand sides of the governing equations of LBS. From the classical theory, these terms play an important role to absorb and minimize the acoustic wave reflections from computational boundaries. Meanwhile, 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. Further, in order to detect the dissipation and dispersion behaviors, the linearized LBS with the damping terms is derived and analyzed. The dispersive and dissipative properties are explored in the wave-number spaces via the Von Neumann analysis. The related damping strength critical values and the optimal absorbing term are addressed. Finally, some benchmark problems are implemented to assess the theoretical results.