Solution of the neutron group-diffusion equations by orthogonal collocation with cubic hermite interpolants

Abstract

Abstract The method of orthogonal collocation (OC) is used to find approximate solutions for the neutron group flux and precursor concentration equations of space-time nuclear reactor dynamics. In the OC method, the unknown solution is approximated by a finite linear combination U of local basis functions. The coefficients of this linear combination are determined by forcing the “defect”, LU - f, to zero at the Gaussian quadrature abscissae selected as collocation points for maximum accuracy. After discretizing the space variables by collocation using C1 cubic Hermite basis functions, the resulting system of ordinary differential equations is integrated in time by a version of the “θ-method”. A general group diffusion computer code COLFEM was developed and was applied in particular to the solution of a onedimensional two-energy group “benchmark” problem. Numerical results show excellent agreement with those obtained by the finite difference (FD) and the conventional finite element method (FEM) with an app...