A multi-dimensional discrete-ordinates method for polarized radiative transfer. Part I: Validation for randomly oriented axisymmetric particles

Abstract

A polarized multi-dimensional radiative transfer model based on the discreteordinates method is presented. The model solves the monochromatic vector radiative transfer equation (VRTE) that considers polarization using the four Stokes parameters. For the VRTE, the intensity of the scalar radiative transfer equation is replaced by the Stokes intensity vector; the position-dependent scalar extinction coefficient is replaced by a direction- and position-dependent 4 × 4 extinction matrix; the position-dependent scalar absorption coefficient is replaced by a direction- and position-dependent emission (absorption) vector; and the scalar phase function is replaced by a scattering phase matrix. The model can solve the VRTE for anisotropically scattering one-, two-, or three-dimensional Cartesian geometries. Validation for one-dimensional polarized radiative transfer compares model results with benchmark cases available in the literature. For two- and three-dimensional geometries, the model is tested by using a one-dimensional system as input and running in three-dimensional mode. A validation for a three-dimensional geometry based on Kirchoff s law for an isothermal enclosure is also presented. The model uses a parallel computing paradigm where each Stokes parameter is assigned to a computer processing unit. In Part II, the model will be validated for systems containing oriented particles, and benchmark results for three-dimensional geometries will be given.