THE SOURCE APPROXIMATION METHOD FOR MULTIDIMENSIONAL MEDIA USING THE SURFACE-INTEGRAL FORM OF THE RADIATIVE-TRANSFER EQUATION

A radiation source approximation of linear and quadratic interpolation over an optical length is constructed to simplify surface-integral equations of radiative transfer for an absorbing, emitting and linear anisotropic scattering medium. The expressions formulated here for incident radiation and radiative heat flux can be applied easily to various coordinate systems. Test cases of radiation in participating media with two-dimensional cylindrical and three-dimensional rectangular geometries are solved by the new technique. The numerical solutions are compared with other results obtained by the product-integration method (PIM). For all the cases considered the radiative transfer results predicted by the quadratic source approximation is in good agreement with the benchmark PIM solution and is more accurate than those obtained with the linear approximation. Since only integration at the bounding surface is involved in the equations of radiative transfer, the solution method is computationally efficient.