Abstract
A nodal formulation of a fixed-source two-dimensional neutron transport problem, in Cartesian geometry, defined in a heterogeneous medium, is solved by an analytical approach. Explicit expressions, in terms of the spatial variables, are derived for averaged fluxes in each region in which the domain is subdivided. The procedure is an extension of an analytical discrete ordinates method, the ADO method, for the solution of the two-dimensional homogeneous medium case. The scheme is developed from the discrete ordinates version of the two-dimensional transport equation along with the level symmetric quadrature scheme. As usual for nodal schemes, relations between the averaged fluxes and the unknown angular fluxes at the contours are introduced as auxiliary equations. Numerical results are in agreement with results available in the literature.
Kurzfassung
Die Knotenformulierung eines zweidimensionalen Neutronentransportproblems mit fester Quelle in kartesischer Geometrie in einem heterogenen Medium wird durch einen analytischen Ansatz gelöst. Explizite Ausdrücke werden in Form räumlicher Variablen abgeleitet für gemittelte Flüsse in allen unterteilten Bereichen. Das Verfahren ist eine Erweiterung der analytischen diskreten Ordinaten-Methode, der ADO-Methode, zur Lösung des zweidimensionalen Falls eines homogenen Mediums. Das Schema wird aus der diskreten Ordinaten Version der zweidimensionalen Transportgleichung zusammen mit der symmetrischen Quadraturformel entwickelt. Wie für Knotensysteme üblich, werden die Beziehungen zwischen den gemittelten Flüssen und den unbekannten Winkelflüssen an den Konturen als Hilfsgleichungen eingeführt. Die numerischen Ergebnisse stimmen überein mit den in der Literatur verfügbaren Ergebnissen.
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