Lattice Boltzmann method for radiative transfer in curvilinear coordinate systems

Area of Science:

• Computational physics
• Heat transfer
• Numerical methods

Background:

• Radiative transfer in curvilinear geometries is crucial for many engineering applications.
• Existing numerical methods for the radiative transfer equation (RTE) in curvilinear systems are complex and lack universality.

Purpose of the Study:

• To develop a universal and simple numerical method for solving the RTE in curvilinear coordinates.
• To present a lattice Boltzmann method (LBM) applicable to complex geometries.

Main Methods:

• The study derives a lattice Boltzmann method (LBM) from the curvilinear radiative transfer equation (RTE) using Chapman-Enskog analysis.
• The method incorporates the metric tensor and a curvilinear radiative transfer operator for simplicity and applicability.

Main Results:

• Numerical tests validated the accuracy and stability of the proposed LBM.
• Asymptotic analysis confirmed the method's second-order convergence.
• The LBM was applied to study thermal radiative transfer in fiber lasers.

Conclusions:

• The developed LBM provides an efficient and accurate tool for solving radiative transfer problems in curvilinear coordinates.
• This method offers a universal and simple approach, addressing limitations of existing techniques.
• The application to fiber lasers demonstrates its practical utility for optimizing designs.