Generalized lattice Boltzmann method for radiative transfer problem in slab and irregular graded-index media

Area of Science:

• Computational fluid dynamics
• Radiative heat transfer
• Computational physics

Background:

• The lattice Boltzmann method (LBM) is a powerful tool for fluid dynamics and heat transfer.
• Existing LBM for radiative transfer equation (RTE) has limitations, especially in complex scenarios.
• Solving RTE in irregular geometries with graded refractive indices is challenging.

Purpose of the Study:

• To propose a generalized lattice Boltzmann model for the multidimensional radiative transfer equation (RTE).
• To handle irregular geometries and graded-index media using body-fitted coordinates.
• To analyze radiation transport in complex, inhomogeneous media.

Main Methods:

• Developed a generalized lattice Boltzmann model for the RTE.
• Employed Chapman-Enskog analysis to recover the macroscopic RTE.
• Validated the model using 1D and 2D RTE problems against benchmark solutions.
• Investigated radiation transport in graded-index media with varying parameters.

Main Results:

• The generalized LBM accurately solves the RTE in irregular geometries with graded indices.
• Chapman-Enskog analysis yielded two formulations for the Boltzmann equation in complex media.
• Graded-index function and geometry significantly impact radiative transport.
• The model demonstrated efficiency, robustness, and accuracy.

Conclusions:

• The developed LBM is an efficient and accurate solver for radiative transport.
• It is suitable for inhomogeneous media with graded-index functions and irregular geometries.
• This method advances the application of LBM in radiative heat transfer.