Discrete ordinates solution of radiative transfer across a slab with variable refractive index

Detection of Abnormalities in a Biological Tissue by Diffuse Optical Tomography: A Computational Study

“…The numerical treatment of the angular redistribution terms can be done by using the classical angular differencing scheme [23,28]. …”

“…However, it is important to note that in a varying refractive index medium, the rays are not straight lines but curves. So even in a rectangular geometry, the varying refractive index radiative transfer equation displays angular derivative terms [23][24][25]. In this paper, these terms are treated with finite differencing scheme.…”

Transient Combined Radiative–Conductive Heat Transfer in Two-Dimensional Complex Geometries with Variable Gas Properties

“…Some typical numerical methods used for the solution of radiative transfer equation are the spherical harmonic method (Menguc and Viskata 1986), the Monte Carlo method (MCM) (Modest 2003), Hottel and Sarofim's zonal method (Hottel and Sarofim 1967), eigen function method (Frankel 1995), F-N method (Siewert et al 1980), the discrete ordinates method (DOM) (Lemonnier and Le Dez 2002), the discrete transfer method (DTM) (Mishra et al 2003), and P-N method (Benassi et al 1983).…”

Discrete ordinate solutions associated with the finite Legendre transform for radiative transfer in a slab with sinusoidal refractive index

“…A number of studies interested in analyzing radiative transfer in a medium with continuously varying refractive index have been conducted. They include integral formulation [7], discrete curved ray tracing (DCRT) [8], Monte Carlo method (MCM) [9,10], the discrete ordinate method (DOM) [11][12][13], discrete transfer method [14] and differential approximation methods [15].…”