S. J. Wilson

Generalized eddington approximation method for radiative transfer problems in slab medium

Abstract A generalized Eddington approximation method is proposed to solve radiative transfer problems in an anisotropic scattering slab medium. The method, which was developed earlier to tackle transfer problems with asymmetric radiation fields in spherical geometry, proves to be equally useful in a planar geometry. The main feature of the method is to divide the radiation field into subregions identified by some angular parameters which, in turn, are determined from the transfer equation. The results are compared with existing data.

On the moment method for radiative transfer in spherical dust shells with a core

A two-shell moment method with three stream division of the radiation field has been suggested for solving radiative transfer problems in a non-grey extended dust shell surrounding a central star. The results computed are found to be of comparable accuracy with those of Unno and Kondo, obtained by generalized Eddington approximation. A more simplified approximation has been put forward for an optically thin medium.

Radiative transfer in absorbing, emitting and linearly anisotropically scattering inhomogeneous solid spheres

Abstract Radiative transfer in absorbing, emitting, linearly anisotropically scattering, inhomogeneous solid spheres with reflecting boundaries is considered. Thynell and Ozisik have reformulated this problem as a set of coupled integral equations and Thynell has solved the homogeneous case using Galerkins method. A collocation method is proposed by us to solve the coupled integral equations. This procedure may also be used to handle the inhomogeneous case. The results for the homogeneous case with isotropic scattering are compared with exact values by El-Wakil et al. The results for the homogeneous case with anisotropic scattering are compared with those obtained by Thynell. The results for the inhomogeneous case with isotropic scattering are compared with those of El-Wakil et al.

Modified spherical harmonic method in radiative transfer in linearly anisotropic scattering planar medium

Mengüç, and Viskanta (1983) examined the scope of some approximate methods for solving transfer problems in plane medium scattering anisotropically. His aim was to focus attention on methods capable of extension to multidimensional geometry. In the present paper, it is demonstrated that modified double-interval spherical harmonic method admirably suits that role. The transfer problem of Mengüç and Viskantas model has been solved by this method. The results computed are found to be in good agreement with those obtained by other methods.

Generalised Eddington approximation for radiative transfer problems in spherically-symmetric moving media

A moment method with three stream division of the radiation field was suggested by Wilson, Wan and Sen (1980) for solving radiative transfer problems in stationary, non-grey extended shells surrounding a central star. Use was made of the generalised Eddington relations as the closure conditions of the moment equations. In the present paper the same method has been utilised to study the radiative transfer problems in a non-grey, expanding gaseous spherical shells surrounding a central star. The transfer equation has been set in comoving frame in spherical geometry. The radiation and material quantities, angles and frequencies have been expressed in comoving frame. The mean intensity, flux and K-integrals have been calculated for extensive atmospheres in the presence of different velocity fields.

Moment Method for the Inverse Radiative Transfer in Inhomogeneous Media

In the present paper, an inverse problem of radiative transfer in an inhomogeneous plane medium of scattering albedo ω = ω 0 exp(− τ/s) is solved by a moment method. The results are compared with those obtained by Dunn (1983) using Monte Carlo method.

Radiative transfer in an isothermal slab with anisotropic scattering

Abstract The paper demonstrates that in solving the problem of radiative transfer in an isothermal slab with Rayleigh scattering, the modified double-interval method gives the first iterates of intensity moments of accuracy comparable with the kernel approximation method.

On the resolvent kernel for the transfer problem in an homogeneous sphere

Abstract A scheme for obtaining the resolvent kernel of the integral equation for radiative transfer problems in an isotropically scattering sphere is proposed. Unlike the earlier attempts, the spherical problem is not transformed to its plane-parallel analogue.

A collocation method for radiative transfer in a linearly anisotropically-scattering slab media with internal sources, space-dependent albedo and reflecting boundaries

A collocation method is used to obtain numerical values for the radiative transfer in absorbing, emitting, linearly anisotropically-scattering-inhomogeneous finite slab media. The results for the isotropic scattering are compared with those obtained by Thynell and Özisik (1986) for the homogeneous slab and with those obtained by Garcia and Siewert (1981) for the inhomogeneous slab.

Probabilistic model for the resolvent kernel in diffusion problems in spherical-shell media

A probabilistic model of the resolvent kernel for the integral equation arising in diffusion problems in nonhomogeneous, isotropically scattering, spherical-shell media is proposed. An analogue of the X and Y functions of Chandrasekhar is given for the spherical-shell geometry.