A new method for the solution of the transport equation in slab geometry

Abstract

A new method, called the method of analytic angles, is developed for the solution of the transport equation (Boltzmann integro-differential equation) in slab geometry. The essence of the method is the discretization of the spatial variable accompanied by an analytic solution for the resulting difference equation with respect to the angular variable. This contrasts to other procedures, such as to the spherical harmonic, Wick-Chandrasekhar and Carlson's SN-method, which are restricted to a finite number of values of the angular variable. Two examples have been worked out. One is the phonon transport in solids with randomly distributed scattering centers. Here the numerical solution agrees very well with the asymptotic analytical solutions. The other example, a neutron transport problem, allows comparison with the S N -method, and indicates the excellence of the solution.