A NEW INITIAL VALUE METHOD FOR INTERNAL INTENSITIES IN RADIATIVE TRANSFER

摘要

A classical problem in mathematical physics is determination of the intensity of the diffuse radiation field produced in a finite homogeneous slab which absorbs and scatters radiation iso-tropically, the incident radiation being uniform parallel rays Traditional approaches involve solving either an unstable linear two-point boundary-value problem or a singular integral equation Both of these have computational drawbacksnWe present a new method which has analytical and computational advantages First, we derive a decomposition formula which expresses the internal intensity function terms of Chandrasekhar's X and Y functions, the source function J, and two new functions, b and h, which represent the internal intensities due to isotropic sources at the top and bottom The effect of this is that the internal inten¬sity function is expressed in terms of functions of fewer independent variablesnSince adequate tables of X, Y and J are available, the remaining task is to devise an effective method for computing b and h This we do by deriving differential-Integral equations which they satisfy, and by employing Chandrasekhar's method of finite ordinates. This leads to the integration of an initial value problem for a system of ordinary differential equations, a task for which the modern digital computer is admirably suited We present some typical results and a comparison, where possible, against other calculations.