Lattice Boltzmann model for a steady radiative transfer equation.

Area of Science:

• Computational Physics
• Radiative Transfer Theory
• Numerical Methods

Background:

• The steady radiative transfer equation (RTE) governs energy transport in participating media, crucial for fields like atmospheric science and astrophysics.
• Traditional numerical methods for RTE can be computationally intensive and face challenges with complex geometries and optically thick or thin regimes.
• The lattice Boltzmann method (LBM) offers a promising mesoscopic approach for solving complex fluid dynamics and transport phenomena.

Purpose of the Study:

• To develop and validate a complete lattice Boltzmann model (LBM) for the steady radiative transfer equation (RTE).
• To demonstrate the accuracy, stability, and convergence properties of the proposed LBM for multidimensional radiative transfer simulations.
• To establish a theoretical link between the mesoscopic LBE and the macroscopic RTE via multiscale analysis.

Main Methods:

• The steady RTE was reformulated as a convection-diffusion equation by introducing an artificial isotropic diffusion term.
• A lattice Boltzmann equation (LBE) was derived, showing exact applicability to the steady RTE when the dimensionless relaxation time is 0.5.
• Chapman-Enskog expansion was employed for multiscale analysis to recover the macroscopic RTE from the mesoscopic LBE.
• The D2Q9 lattice model was utilized to solve the LBE, and numerical results were compared against existing methods and analytical solutions.

Main Results:

• The proposed LBM demonstrated high accuracy and stability in simulating multidimensional radiative transfer.
• Numerical results from the LBM were in excellent agreement with other established numerical methods and analytical solutions.
• The convergence rate of the LBM was found to be dependent on the transport properties of the RTE: second-order for diffusion-dominated cases (large optical thickness) and lower for convection-dominated cases (small optical thickness).

Conclusions:

• The developed lattice Boltzmann model provides a robust and efficient tool for solving the steady radiative transfer equation.
• The LBM is a viable alternative to traditional methods for simulating radiative transfer phenomena across various optical thickness regimes.
• Understanding the dependency of convergence rates on RTE properties allows for informed application and optimization of the LBM.