A numerical method for multigroup slab-geometry eigenvalue problems in transport theory with no spatial truncation error

Abstract

Abstract A new numerical nodal method is developed for multigroup slab-geometry discrete ordinates (SN) eigenvalue problems with no spatial truncation error. The numerical results are exactly those of the dominant analytical solution of the multigroup SN eigenvalue problem on the grid points apart from finite arithmetic considerations and regardless of the spatial grid. We have implemented the option of using the multigroup albedo boundary condition, that is a measure of the reflective power of the neutron reflector, e.g., water or graphite. The Power method used in the outer iterations for convergence of the dominant numerical solution has been accelerated by a scheme based on Tchebycheff extrapolation of the fission source. Numerical results are given to illustrate the method's accuracy.