Étude tridimensionnelle du transfert radiatif dans un milieu semi-transparent diffusant anisotrope par la méthode des transferts discrets modifiée

Solution of the Integrated Radiative Transfer Equation for Gray and Nongray Media

“…The radiative energy fluxes are determined using the discrete transfer method in conjugation with the discrete ordinate method, which uses the radiative transfer equation in integral form. This article shows the nearly analytical solution of the RTE in integral form, using a stepwise zeroth-order temperature profile (zeroth-order method) and a continuous first-order temperature profile (first-order method), as was previously done by Cumber [30] for a gray nonscattering medium and extended by Farhat and Radhouani [31] for a scattering medium. In this article the RTE is solved for a nongray and nonscattering medium with a bandlike absorption coefficient.…”

“…This leads to a nonconstant source term in the integrated RTE. This source term has been determined for a gray nonscattering medium by Cumber [30], and has been extended for a scattering medium and tested in a threedimensional domain by Farhat and Radhouani [31]. Cumber [30] evaluated and improved the discrete transfer method in this way and postulated that the method is numerically exact, geometrically flexible, and easily coupled to a computational fluid dynamics solver.…”

Comparison between Kim, Wiscombe and least squares scattering phase function renormalization methods

“…The Cumber linear profile caused negative radiant intensities when this condition is satisfied. This negativity was not observed when considering a 3-D rectangular enclosure [8]. A bi-linear interpolation method (Fig.…”

“…Among the solution methods of the radiation transport equation is the modified discrete transfer (MDT) method performed by Farhat and Radhouani and successfully applied to the case of a parallelepipedic enclosure [8]. In the present investigation, an improved MDT method is proposed in order to solve the radiative transfer equation (RTE) in a two-dimensional rectangular enclosure where anisotropic scattering in a STM is taken into account.…”

“…In the present investigation, an improved MDT method is proposed in order to solve the radiative transfer equation (RTE) in a two-dimensional rectangular enclosure where anisotropic scattering in a STM is taken into account. In [8] we have adopted the Cumber linear profile [9] which has been applied to temperature (anisothermal grid cells) and scattered radiation, in the same direction of propagation, in each grid cell. The accuracy of the MDT solutions increases when using a coarser first netting near the walls.…”