Discrete Ordinates Numerical Integration Method for Neutron Transport Equation in Slab Geometry

Abstract

A method is presented for solving neutron transport problems in slab geometry with the application of discrete ordinates numerical integration to the Boltzmann transport equation.Neutron spectra for water, iron and carbon layers are calculated and compared with experimental data. Good agreement is obtained between computed and measured values for both angular distributions and the energy spectra of neutrons. The calculated neutron spectra in an iron-water layer are also presented as an example of solutions derivable for neutron transport problems in multi-layered shield.

A Numerical Method for Solving the Neutron Transport Equation in Finite Cylindrical Geometry

“…The evaluation of the integral equation (14) is performed by a procedure similar to that utilized for plane geometry< 9 l.…”

“…For hydrogen scatterer the derivation of the transfer function TuCmJ.m(r) is best done by applying the alternate procedure which was used for plane geometryc 9 '.…”

“…The application of the procedure yields Further, v and s. are defined in the same manner as described in the previous paperc 9 ', -5 …”

A Numerical Method for Solving the Neutron Transport Equation in Finite Cylindrical Geometry

“…( 8) can be reduced to an equation in matrix notation: (9) Here the flux r!> 11 (R,,E 1 ) and the quantity G'' (R,,E 1 ) …”

“…INTRODUCTION Calculations of neutron penetration through radiation shields inevitably require the use of numerical methods in which the Boltzmann transport equation must be solved. Several studies< 1 H 9 > have been reported in this connection, and the author & Kataoka have presented a numerical method< 9 > for slab geometry embodying the numerical integration of discrete ordinates. This numerical integration scheme is applied to the calculation of the scattering integral, and the Boltzmann equation is solved for a finite multilayered cylindrical configuration with the use of quasi-cartesian coordiates (2).…”