Cumulative variable formulation for transient conductive and radiative transport in participating media

Abstract

A new mathematical formulation is proposed for transient conductive and radiative transport in a participating gray, isotropically scattering plane-parallel medium. The methodology can be easily extended to include numerous additional effects. A systematic and unified treatment is presented using cumulative variables that allows for high-order integration using standard initial-value methods in the temporal variable while allowing for an effective orthogonal collocation method to be implemented in the spatial variable. A spectral approach is incorporated in the present context where Chebyshev polynomials of the first kind are used as the basis functions. This article illustrates the methodology and presents some comparisons with previously reported works.