Discrete-ordinates solution for radiative-transfer problems

On the solution of multislab atmospheric radiation problems with an arbitrary number and type of stationary layers

“…the methods described by Stamnes et al (1988), Siewert (2000), and Chalhoub (2003). This can be accomplished as follows: for stationary boundary layers, the discrete bidirectional functions (10-11) and/or (12-13), where appropriate, can be used to replace the corresponding boundary layers at the bottom and/or top, while the discrete bidirectional functions (6-7) can be used to replace corresponding stationary internal layers, playing the role of nonstandard discontinuous conditions for the diffuse intensity.…”

Evaluation of radiances generated by solving the radiative-transfer equation with different approaches

“…In recent years it has been observed a growing interest towards the stochastic Monte Carlo method for the solution of the direct problem (Maurente et al, 2007;Chen and Liou, 2006;Battaglia and Mantovani, 2005;Postylyakov, 2004Postylyakov, , 2004a, as well as towards variations of the Discrete Ordinates Method (Çayan and Selçuk, 2007;Chalhoub, 2003Chalhoub, , 2005 which was originally proposed by Wick (1943) and Chandrasekhar (1944Chandrasekhar ( , 1950. Moreover, some researchers have performed comparisons of different solution strategies in order to identify accurate and fast methods to be used both in the direct and inverse radiative transfer problems (Jensen et al, 2007;Bulgarelli and Doyle, 2004;Chalhoub et al, 2003).…”

Multilayer differential discrete ordinate method for inhomogeneous participating media

“…Several techniques for solving the radiative transfer equation are currently available, as for example Monte Carlo method [2], F N method [3], spherical harmonics method [4], two-flux methods [5], finite volume method [6], discrete ordinates methods [7][8][9]. These techniques employ complicated mathematics and they generally require extensive programming effort.…”

“…Chandrasekhar [7] proposed the discrete ordinates method in his work on stellar and atmospheric radiation. The numerical analysis of the method for multiple scattering inhomogeneous media is discussed in detail by Stamnes et al [8] and Chalhoub [9]. Fiveland [10] demonstrated various quadrature schemes for the discrete ordinates method and verified the stability of solution under each scheme.…”