Stable lattice Boltzmann model for Maxwell equations in media.

Area of Science:

• Computational physics
• Electromagnetism
• Numerical methods

Background:

• Existing lattice Boltzmann (LB) models for electromagnetic (EM) wave propagation in homogeneous media exhibit numerical instability at sharp transitions.
• Previous models struggle to accurately simulate EM wave behavior in media with complex or rapidly changing properties.

Purpose of the Study:

• To develop a stable and accurate numerical method for simulating electromagnetic waves in homogeneous and complex media using the lattice Boltzmann model.
• To address the limitations of existing LB models concerning numerical instability in the presence of sharp media transitions.

Main Methods:

• Utilized an extension of a known lattice Boltzmann model for EM waves in vacuum, separating polarization and magnetization effects.
• Applied Strang splitting for simulations in conductive media, analyzing the skin effect.
• Quantified error scaling, stability, accuracy, and time scaling through simulations of EM waves entering different media.

Main Results:

• The extended LB method demonstrates stable simulations even with sharp media transitions.
• Error analysis for EM wave propagation and static limits in conductive media showed accuracy less than 1%.
• The method provides accurate simulations for the skin effect in conductive media.

Conclusions:

• The presented lattice Boltzmann method offers a stable and easily implementable solution for simulating electromagnetic wave propagation in complex structured media.
• This approach enhances the accuracy and stability of simulations, particularly for arbitrary transitions in material properties.
• The method serves as a valuable alternative for researchers and engineers working with electromagnetic wave phenomena in diverse media.