An analytic and numerical solution with spectral Green's function method for transport equation in spherical geometry

Abstract

Since in many cases curvilinear geometry is more appropriate than cartesian geometry for precise modeling of the complex systems for reactor calculation, we have developed the spectral Green's function (SGF) method which is employed to obtain angular and scalar flux distributions in heterogeneous sphere geometry with isotropic scattering. In this study, we showed that the neutron transport problems of homogeneous spheres could be reduced to the solution of plane geometry equation. Finally, some results are discussed and compared with those already obtained by diamond difference scheme to test the accuracy of the results. The agreement is satisfactory. SGF method is very suitable for the numerical solution of the neutron transport equation with isotropic scattering.