Local radial basis function meshless scheme for vector radiative transfer in participating media with randomly...

Area of Science:

• Computational physics
• Radiative transfer theory
• Numerical methods

Background:

• Radiative transfer in participating media is crucial for many applications.
• Solving polarized radiative transfer equations is computationally challenging.
• Existing methods often require complex mesh generation and numerical integration.

Purpose of the Study:

• To develop a novel meshless method for solving polarized radiative transfer.
• To address challenges in simulating radiative transfer in media with complex particle orientations.
• To provide an accurate and efficient numerical tool for these problems.

Main Methods:

• A local radial basis function meshless scheme (LRBFM) was developed.
• Trial functions were constructed using radial basis functions augmented with polynomial basis.
• The vector radiative transfer equation was discretized using the discrete-ordinates approach and a collocation method.
• The method is truly meshless, avoiding the need for mesh generation or numerical integration.

Main Results:

• The LRBFM was validated against analytical solutions and existing numerical results.
• Five diverse test cases demonstrated the method's performance.
• Predicted angular distributions of brightness temperature and Stokes vectors showed excellent agreement with benchmarks.
• The LRBFM proved accurate for vector radiative transfer in participating media with randomly oriented axisymmetric particles.

Conclusions:

• The LRBFM is a highly accurate and effective numerical technique.
• It offers a meshless alternative for solving polarized radiative transfer.
• The method shows significant promise for applications involving participating media with complex particle distributions.