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The extension of the 2-D finite element/boundary element hybrid method to general multigroup neutron diffusion theory

Die Erweiterung der zwei-dimensionalen Finite Elemente und Randelemente Hybridmethode zur allgemeinen Mehrgruppen-Neutrondiffusionstheorie
B. Ozgener, S. Cavdar and H. A. Ozgener
From the journal Kerntechnik

Abstract

The finite element-boundary element hybrid method developed previously for reflected systems and restricted to one or two group neutron diffusion theory has been extended to the general multigroup neutron diffusion theory by using the boundary integral equation of multigroup neutron diffusion theory. A linear or bilinear 2-D FEM formulation in the core combined with a 2-D linear BEM formulation in the reflector constitute the basic discretization procedure. Use of the boundary integral equation of multigroup diffusion theory transforms all group-to-group scattering domain integrals into surface integrals in the reflector. Hence the need for a reflector domain mesh is completely eliminated. Via comparisons with pure FEM and BEM solutions of the reflected systems within the context of three and four group diffusion theories, the present formulation is validated and assessed.

Kurzfassung

Die Finite Elemente und Randelemente Hybridmethode wurde für reflektierte Systeme entwickelt und blieb auf Ein- oder Zweigruppen Neutrondiffusionstheorie beschränkt. Diese Arbeit erweitert die obengenannte Methode mit Hilfe der Randintegralgleichung der Mehrgruppendiffusionstheorie zu Mehrgruppendiffusiongleichungen. Eine lineare oder bilineare zweidimensionale Finite Elemente Formulierung für den Reaktorkern, die mit einer linearen zwei-dimensionale Randelemente Formulierung für den Reflektor kombiniert wird, stellt das grundlegende Diskretisierungverfahren dar. Da die Benutzung der Randintegralgleichung der Mehrgruppendiffusionstheorie alle Streuungvolumenintegrale zu Oberflächeintegralen in dem Reflektor transformiert, wird eine Reflektorvolumenmasche überflüssig. Durch Vergleiche mit reinen Finite Elemente und Randelemente Lösungen für die reflektierten Systeme in Kontext der Drei- und Viergruppen Theorien wird die präsentierte Formulierung validiert und bewertet.

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Received: 2007-3-21
Published Online: 2013-04-05
Published in Print: 2007-11-01

© 2007, Carl Hanser Verlag, München