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              <p>This paper deals with the numerical treatment of two additional terms in the Lmnc-system derived and studied in previous publications and modelling the coolant in a nuclear reactor core. On the one hand, we investigate the influence of the thermal conduction upon steady analytical solutions and upon numerical strategies designed in dimensions 1 and 2. On the other hand, we consider a time-varying thermodynamic pressure that enables to simulate a larger variety of physical situations. Taking into account the resulting terms in the equations lead us to adapt numerical methods to ensure accuracy.</p>
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              <p>Le système d'équations Lmnc étudié précédemment par les auteurs permet de modéliser l'eau dans le circuit primaire d'un réacteur nucléaire. Dans ce papier, nous nous intéressons à l'enrichissement du modèle par la prise en compte de deux phénomènes : d'une part la diffusion thermique qui influe sur les états stationnaires et sur les schémas numériques mis en oeuvre en dimensions 1 et 2, et d'autre part la dépendance en temps de la pression thermodynamique an de pouvoir simuler des situations physiques plus variées. Les nouveaux termes intervenant dans les équations nécessitent d'adapter les outils numériques an de maintenir la précision des résultats.</p>
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