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Techniques de traçage pour la méthode des caractéristiques appliquée à la résolution de l'équation du transport des neutrons en domaines multi-dimensionnels

François Févotte 1 
1 LTSD - Laboratoire de Transport Stochastique et Déterministe
SERMA - Service des Réacteurs et de Mathématiques Appliquées : DEN/DM2S/SERMA
Abstract : In the past years, the Method of Characteristics (MOC) has become a popular tool for the numerical solution of the neutron transport equation. Among its most interesting advantages are its good precision over computing time ratio, as well as its ability to accurately describe complicated geometries using non structured meshes. In order to reduce the need for computing resources in the method of characteristics, we propose in this dissertation two lines of improvement. The first axis of development is based on an analysis of the transverse integration technique in the method of characteristics. Various limitations have been discerned in this regard, which we intend to correct by proposing a new variant of the method of characteristics. Through a better treatment of material discontinuities in the geometry, our aim is to increase the accuracy of the transverse integration formula in order to decrease the computing resources without sacrificing the quality of the results. This method has been numerically tested in order to show its interest. Analysing the numerical results obtained with this new method also allows better understanding of the transverse integration approximations. Another improvement comes from the observation that industrial reactor cores exhibit very complex structures, but are often partly composed of a lattice of geometrically identical cells or assemblies. We propose a systematic method taking advantage of repetitions in the geometry to reduce the storage requirements for geometric data. Based on the group theory, this method can be employed for all lattice geometries. We present some numerical results showing the interest of the method in industrial contexts.
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Submitted on : Tuesday, March 30, 2010 - 10:08:49 AM
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François Févotte. Techniques de traçage pour la méthode des caractéristiques appliquée à la résolution de l'équation du transport des neutrons en domaines multi-dimensionnels. Modélisation et simulation. Université Paris Sud - Paris XI, 2008. Français. ⟨tel-00468118⟩

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