Lattice Boltzmann model for wave propagation

Area of Science:

• Computational physics
• Fluid dynamics
• Wave propagation modeling

Background:

• The wave equation is fundamental in physics, describing phenomena from acoustics to electromagnetism.
• Existing lattice Boltzmann models often face limitations in accuracy and temporal reversibility.
• Higher-order moment methods offer a path to improved numerical simulations.

Purpose of the Study:

• To develop a higher-order accurate lattice Boltzmann model for the two-dimensional wave equation.
• To achieve temporal reversibility in the lattice Boltzmann simulation of wave propagation.
• To validate the model's performance with classical wave phenomena.

Main Methods:

• Utilized the higher-order moment method, involving multiscale techniques and Chapman-Enskog expansion.
• Derived a lattice Boltzmann model by solving partial differential equations.
• Achieved higher-order accuracy by removing specific dissipation and dispersion terms using fourth-order moments.

Main Results:

• The proposed lattice Boltzmann model demonstrates higher-order accuracy.
• Temporal reversibility was achieved by eliminating second-order dissipation and third-order dispersion terms.
• Numerical simulations of interference, diffraction, and wave lensing were successfully performed.

Conclusions:

• The developed lattice Boltzmann model provides an accurate and reversible method for simulating two-dimensional wave propagation.
• This approach offers a robust tool for studying complex wave phenomena computationally.
• The model's success in simulating classical examples validates its applicability in wave physics.