• Citer

Numerical solution of neutron kinetics equations using A-stable algorithms

par Devooght, Jacques ;Mund, Ernest
Référence Progress in nuclear energy, 16, 2, page (97-126)
Publication Publié, 1985

Article révisé par les pairs

• Accès en ligne
• Détails
• Contenu
• Statistiques

Résumé :

This paper gives a detailed account of both theoretical and numerical investigations which have been conducted in the application of A-stable algorithms to neutron kinetics problems. It is broadly divided into three sections. General considerations on desirable features of a reactor dynamics code are followed by the theoretical background. In order to be self-contained, the stability properties of one-step methods are recalled with emphasis on the A-stability concept introduced by Dahlquist. An algorithm is described, based on the interpolation of exp(z) in the unit disc of the complex plane, which generates A-stable schemes wnn(z), (n= 1,...) with so-called 'spectral matching' properties. Practical reasons limit to w11 (z) its use for the integration of the kinetics equations and the analytical properties of this first order rational approximation to the exponential function are studied. A second class of suitable integration schemes is made of the implicit Runge-Kutta (IRK) family, particularly the subclass of diagonally implicit Runge-Kutta (DIRK) methods which are factorizable. Finally, the numerical results obtained with these algorithms are discussed on a set of four point kinetics problems for both fast and thermal-type reactors. © 1985.