CUMULATIVE VARIABLE FORMULATION FOR TRANSIENT CONDUCTIVE AND RADIATIVE TRANSPORT IN PARTICIPATING MEDIA

A new mathematical formulation is proposed for transient conductive an d radiative transport in a participating gray, isotropically scatterin g plane-parallel medium, The methodology can he easily extended to inc lude numerous additional effects. A systematic and unified treatment i s presented using cumulative variables that allows for high-order inte gration using standard initial-value methods in the temporal variable while allowing for an effective orthogonal collocation method to be im plemented 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 methodol ogy and presents some comparisons with previously reported works.