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Acoustic multipole sources for the lattice Boltzmann method.

Erlend Magnus Viggen1

  • 1Department of Electronics and Telecommunications, NTNU, 7034 Trondheim, Norway. erlend.viggen@ntnu.no

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 19, 2013
PubMed
Summary

This study implements acoustic multipole sources in the lattice Boltzmann method using oscillating particle sources. The regularized collision operator accurately simulates 2D acoustic generation and propagation, unlike the BGK operator.

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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.