Acoustic multipole sources for the lattice Boltzmann method.

Area of Science:

• Computational physics
• Acoustics
• Fluid dynamics

Background:

• The lattice Boltzmann method (LBM) is a powerful numerical technique for simulating fluid flow and related phenomena.
• Implementing acoustic sources within LBM requires careful consideration of source terms and their impact on macroscopic equations.
• Previous methods may have limitations in accurately simulating acoustic generation and propagation, especially at low viscosities.

Purpose of the Study:

• To introduce and analyze oscillating particle source terms for implementing acoustic multipole sources in the lattice Boltzmann method.
• To investigate the effect of these source terms on macroscopic conservation equations using Chapman-Enskog expansion.
• To evaluate the accuracy of the regularized collision operator for simulating 2D acoustic phenomena.

Main Methods:

• Inclusion of an oscillating particle source term in the LBM.
• Application of Chapman-Enskog expansion to analyze the source term's effect on macroscopic equations.
• Decomposition of the source term into orthogonal multipoles for a lattice with q particle velocities.
• Comparison of analytical solutions with inviscid multipole simulations.
• Utilizing the regularized collision operator for simulations.

Main Results:

• The source term can be decomposed into orthogonal multipoles, allowing for the superposition of complex sources.
• Analytical solutions derived from macroscopic equations and lattice Boltzmann wavenumber show good agreement with inviscid multipole simulations.
• The regularized collision operator demonstrates capability in accurately simulating 2D acoustic generation and propagation at zero viscosity.
• The BGK operator was found to be less capable for these specific simulations.

Conclusions:

• Oscillating particle source terms provide an effective way to implement acoustic multipole sources in LBM.
• The regularized collision operator is a suitable choice for accurate simulations of 2D acoustics in LBM, particularly at low viscosity.
• The study validates the theoretical framework and numerical implementation for acoustic source modeling in LBM.