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

A local radial basis function meshless scheme (LRBFM) is developed to solve polarized radiative transfer in participating media containing randomly oriented axisymmetric particles in which radial basis functions augmented with polynomial basis are employed to construct the trial functions, and the vector radiative-transfer equation based on the discrete-ordinates approach is discretized directly by collocation method. The LRBFM belongs to a class of truly meshless methods that do not need any mesh or any numerical integration scheme. Performances of the LRBFM are verified with analytical solutions and other numerical results reported earlier in the literature via five various test cases. The predicted angular distribution of brightness temperature and Stokes vector by the LRBFM agree very well with the benchmark. It is demonstrated that the LRBFM is accurate to solve vector radiative transfer in participating media with randomly oriented axisymmetric particles.