A lattice Boltzmann method with source term for acoustic problems.

Area of Science:

• Computational physics
• Acoustics
• Fluid dynamics

Background:

• Acoustic problems require accurate simulation of wave propagation.
• Existing methods for simulating acoustic sources have limitations in generality and implementation.

Purpose of the Study:

• To propose a novel lattice Boltzmann method (LBM) incorporating source terms for acoustic wave propagation.
• To validate the accuracy and generality of the proposed LBM scheme through numerical experiments.

Main Methods:

• Inclusion of mass source, force source, and force source derivative terms in the LBM evolution equation.
• Simulation of acoustic monopole, dipole, quadrupole, and supercardioid point sources.
• Validation using both simple and complex acoustic problem scenarios.

Main Results:

• The proposed LBM accurately recovers macroscopic wave equations with source terms.
• Numerical experiments confirm the scheme's ability to simulate various acoustic source types.
• The method demonstrates greater theoretical generality and avoids unphysical flow disturbances near sources.

Conclusions:

• The developed lattice Boltzmann method with source terms provides a robust and accurate solution for acoustic problems.
• This approach offers a simpler and more convenient implementation compared to boundary-based methods and previous works.
• The method is well-suited for simulating complex acoustic phenomena involving various source types.