The response matrix discrete ordinates solution to the 1D radiative transfer equation

Sparse Discrete Ordinates Method in Radiative Transfer

The stationary monochromatic radiative transfer equation (RTE) is a partial differential transport equation stated on a five-dimensional phase space, the Cartesian product of physical and angular domain. We solve the RTE with a Galerkin FEM in physical space and collocation in angle, corresponding to a discrete ordinates method (DOM). To reduce the complexity of the problem and to avoid the “cu...

Two-dimensional Transient Radiative Heat Transfer Using Discrete Ordinates Method

The S-N discrete ordinates (DO) method is developed for the first time to solve transient radiative heat transfer in a two-dimensional rectangular enclosure with absorbing, emitting, and anisotropically scattering medium subject to diffuse and/or collimated laser irradiation. The transient DO method is used to solve several example problems and compared with the existing results and the Monte C...

On the Equivalence Between the Discrete Ordinates and the Spherical Harmonics Methods in Radiative Transfer

In this work concerning steady-state radiative-transfer calculations in plane-parallel media, the equivalence between the discrete ordinates method and the spherical harmonics method is proved. More specifically, it is shown that for standard radiative-transfer problems without the imposed restriction of azimuthal symmetry the two methods yield identical results for the radiation intensity when...

Solution of the Radiative Transfer Equation in the Separable Approximation

A method for the fast and accurate solution of the radiative transfer equation in plane-parallel media with coherent isotropic scattering is presented. This largely analytical approach uses the formalism of meromorphic functions in order to obtain the total solution, i.e. the angle and depth variation of the radiation field. A discretization of space and angle coordinates is not required. For t...

Phase-Function Normalization in the 3-D Discrete-Ordinates Solution of Radiative Transfer—PART II: Benchmark Comparisons