A reduced transfer equation in one-dimensional spherical geometry with central symmetry

Abstract

The transfer equation in spherical geometry with central symmetry, which is a partial differential equation in two variables r and m, is reduced to a one-dimensional transfer equation in r parametric in m. This is done by dropping the angular derivative from the equation in conservation form without impeding the moments of the specific intensity. The justification for this reduction of the transfer equation is demonstrated analytically and numerically. The numerical demonstration is made by comparing the moments, zeroth to fourth, obtained using the analytic solutions in r of both the reduced equation and the transfer equation in conservation form using the discrete ordinates method. The agreement between the two sets of data is perfect within round-off errors.