Calculation of the eigenfunctions of the two-group neutron diffusion equation and application to modal decomposition of BWR instabilities

In this thesis, numerical methods aiming at determining the eigenfunctions, their adjoint and the corresponding eigenvalues of the two-group neutron diffusion equations representing any heterogeneous system are investigated. First, the classical power iteration method is modified so that the calculation of modes higher than the fundamental mode is possible. Thereafter, the Explicitly-Restarted Arnoldi method, belonging to the class of Krylov subspace methods, is touched upon. Although the modified power iteration method is a computationally-expensive algorithm, its main advantage is its robustness, i.e. the method always converges to the desired eigenfunctions without any need from the user to set up any parameter in the algorithm. On the other hand, the Arnoldi method, which requires some parameters to be defined by the user, is a very efficient method for calculating eigenfunctions of large sparse system of equations with a minimum computational effort. These methods are thereafter used for off-line analysis of the stability of Boiling Water Reactors. Since several oscillation modes are usually excited (global and regional oscillations) when unstable conditions are encountered, the characterization of the stability of the reactor using for instance the Decay Ratio as a stability indicator might be difficult if the contribution from each of the modes are not separated from each other. Such a modal decomposition is applied to a stability test performed at the Swedish Ringhals-1 unit in September 2002, after the use of the Arnoldi method for pre-calculating the different eigenmodes of the neutron flux throughout the reactor. The modal decomposition clearly demonstrates the excitation of both the global and regional oscillations. Furthermore, such oscillations are found to be intermittent with a time-varying phase shift between the first and second azimuthal modes.

Climatological analysis of temperature and salinity fields in the Mediterranean sea

A climatological field is a mean gridded field that represents the monthly or seasonal trend of an ocean parameter. This instrument allows to understand the physical conditions and physical processes of the ocean water and their impact on the world climate. To construct a climatological field, it is necessary to perform a climatological analysis on an historical dataset. In this dissertation, we have constructed the temperature and salinity fields on the Mediterranean Sea using the SeaDataNet 2 dataset. The dataset contains about 140000 CTD, bottles, XBT and MBT profiles, covering the period from 1900 to 2013. The temperature and salinity climatological fields are produced by the DIVA software using a Variational Inverse Method and a Finite Element numerical technique to interpolate data on a regular grid. Our results are also compared with a previous version of climatological fields and the goodness of our climatologies is assessed, according to the goodness criteria suggested by Murphy (1993). Finally the temperature and salinity seasonal cycle for the Mediterranean Sea is described.