Scaled Isotropic Results for Two-Dimensional Anisotropic Scattering Media

Abstract

The full anisotropic scattering solutions of the radiative equation of transfer are compared with the scaled isotropic scattering solutions. Square enclosures with a collimated incidence, a diffuse incidence, or an isothermal emission are considered for comparison. The isotropic scaling approximation is found to predict accurately the radiative flux and the average incident radiation for the isothermal emission problem and for most diffuse incidence problems. For the collimated incidence problem, the isotropic scaling solutions are acceptable only for weakly scattering media. For large scattering albedo the error in the isotropic scaling is appreciable for the diffuse incidence problem and unacceptably large for the collimated incidence problem. The largest error in the y-direction net flux is found at the side wall regions when the medium is purely scattering. The isothermal emission problem or problems with symmetric boundary conditions can be accurately modeled by a scaled isotropic phase function, since the effect of the phase function anisotropy is negligible in such problems.