PHYSOR 2012 Advances in Reactor Physics Linking Research, Industry, and Education Knoxville, Tennessee, USA, April 15-20, 2012, on CD-ROM, American Nuclear Society, LaGrange Park, IL (2012) FLUX STABILIZATION IN NEUTRON PROBLEMS WITH FIXED SOURCES Daniele Tomatis ∗ and Aldo Dall’Osso AREVA NP Tour AREVA, 92084 Paris La D´ efense Cedex, France daniele.tomatis@areva.com; aldo.dallosso@areva.com ABSTRACT Although critical core calculations are the most common in design and safety analysis, fixed source calculations are needed for specific applications, e.g. to compute ex-core detector response functions, to develop new methodologies for dilution and reload error accidents and more in general for all situations involving sub-critical shut-down states. It is well known that the source problem becomes difficult to be solved with core configuration close to criticality, i.e. with the multiplication factor approaching unity, for the occurrence of numerical ill-conditioning and very high number of iterations, possibly leading to failure in the flux convergence. In this work, the Wielandt eigenshift technique used in iterative methods of critical problems is developed for source problems too, in order to stabilize the solution. The mathematical basis and the proof of the convergence are discussed. Compared to the existing methods, this technique allows also for more control to avoid singular behavior at inner iterations. Numerical tests with a 1D analytical benchmark are reported to prove the robustness of the technique. Key Words: Subcritical core calculations, Wielandt eigenshift, power method 1. INTRODUCTION Determining the neutron flux distribution with the highest accuracy in all possible confi gurations of the nuclear reactor is one of the most important steps in core-related safety studies. This means in short treating both critical and subcritical confi gurations of the neutron system. Critical problems are certainly more common in practical applications for reproducing the typical working conditions of power reactors. Mathematically, they are eigenvalue problems where the introduction of an arbitrary constant plays the role of eigenvalue, making singular the global operator characterizing the neutron balance equation. At least four kinds of eigenvalue are accounted in literature, but the neutron multiplication factor k eff has become the most known and used of all [1, 2]. For a given eigenvalue, the indetermination of the eigenmode (fundamental flux), which is accurate up to an arbitrary constant, is interpreted as possible infi nite power levels in the reactor. In a real reactor, this is prevented by thermal-hydraulic feedback effects. Concerning homogeneous equations, only one eigenmode is proved to be fully positive everywhere, and so only an eigenpair is of interest, that is the critical eigenpair [1]. In particular, ∗ Corresponding author.