Direct collocation meshless method for vector radiative transfer in scattering media

- A direct collocation meshless method (DCM) is developed to solve VRTE.
- The DCM is of high accuracy and excellent stability for solving VRTE.
- Polarized radiative transfer with highly angular dependence is simulated exactly.

A direct collocation meshless method based on a moving least-squares approximation is presented to solve polarized radiative transfer in scattering media. Contrasted with methods such as the finite volume and finite element methods that rely on mesh structures (e.g. elements, faces and sides), meshless methods utilize an approximation space based only on the scattered nodes, and no predefined nodal connectivity is required. Several classical cases are examined to verify the numerical performance of the method, including polarized radiative transfer in atmospheric aerosols and clouds with phase functions that are highly elongated in the forward direction. Numerical results show that the collocation meshless method is accurate, flexible and effective in solving one-dimensional polarized radiative transfer in scattering media. Finally, a two-dimensional case of polarized radiative transfer is investigated and analyzed.