Jacobi Polynomials Flux Moments Expansions and Factorized Kernel Approach to the Stationary Integral Anisotropic Transport in a Finite Cylinder

摘要

A transport method was developed in view of benchmark calculations of the eigenvalues and flux distributions for monoenergetic neutrons anisotropically colliding in a critical cylinder of finite radius and half-height. For the kernels appearing in the system of integral equations for spherical harmonic moments of the angular flux, we proposed a factorized form that accounted for the anisotropy of scattering and worked in the original Euclidean space, extending to cylinder geometry, of interest for pratical reactor calculations, a technique previously adopted for the simpler parallelepiped geometry. This treatment of the two-dimensional kernels allows representations typical in one dimensional problems for the matrix formulation to which the problem reduces by the introduction of a corresponding projectional technique. Optimal in view of an appropriate matrix formulation appears also the representation of the unknown spherical harmonics moments in terms of special jacobi polynomials, coinciding with a Legrendre polynomials expansion for the total flux in the case of isotropic scattering. The high accuracy of the results obtained in this case for both eigenvalues and fluxes is finally tested by internal convergence studies and heights as well as for the limiting cases or ratios of radius to height going to zero or to infinity. (Atomindex citation 17:011618)