Theoretical and computational analysis of twogroup integral transport equation for finite spherical and cylindrical media
Abstract
A twogroup integral transport equation is reduced to a form which can be solved using the method of singular eigenfunction expansion. With application to both spherical and cylindrical geometries, this second order transform procedure is demonstrated to be equivalent to the more specialized firstorder transform procedure applicable only to spherical problems. A numerical algorithm for the spherical shellsource problem is incorporated in a computer code. The total neutron densities, angular flux, net current and macroscopic neutron balance can be obtained from this computation. The accuracy of the code is investigated by a comparison of the total flux with the values obtained using a discrete ordinates code. Agreement was achieved to within the numerical accuracy of the model. The contribution to the density from the discrete and continuous eigenfunctions is shown separately.
 Publication:

Ph.D. Thesis
 Pub Date:
 July 1976
 Bibcode:
 1976PhDT........45L
 Keywords:

 Integral Transformations;
 Spherical Shells;
 Transport Theory;
 Algorithms;
 Cylindrical Shells;
 Diffusion Theory;
 Mathematical Models;
 Neutron Distribution;
 Nuclear and HighEnergy Physics