The neutron flux of accelerator driven subcritical systems (ADSs) may significantly differ from the fundamental alpha mode of these reactors, therefore developing computational methods for determining higher alpha eigenmodes of the neutron transport operator could be beneficial for the analysis of such systems. During the past decades various numerical methods have been devised to solve the time-eigenvalue equation, ranging from simple dual iteration schemes to elaborate Krylov methods. These are extremely resource intensive algorithms both in terms of CPU and memory usage and thus their application for real-life ADSs still can not provide engineering quality solutions.
Despite their extreme computational cost, however, no one tried to improve these calculations by applying some form of physical preconditioning, e.g. diffusion synthetic acceleration (DSA), although DSA has a long history in reactor physics and radiation transport calculations and it is a proven tool for acceleration of fixed source and lambda eigenvalue problems. The candidate will investigate the possible exploitation of DSA in multiple alpha eigenvalue calculations, including the choice and details of the underlying iterative method and the architecture of the possibly multi-layered preconditioning scheme.
Some modern numerical schemes solve the fixed source neutron transport equations in factorised form, that is, the angular flux is eliminated in favour of the flux moments of the scatter source expansion or some other projection of the flux, vastly reducing the memory footprint of the associated Krylov solvers. This approach can not trivially be applied to the time eigenvalue equation. However, it might be possible to separate the time scales such that an approximate factorisation could be introduced, based either on the flux moments or the fission source intensity. This approach could hopefully preserve the most important eigenmodes of the reactor while relieving the memory consumption of the method. The candidate will investigate the theoretical possibilities of deriving such factorised equations and, if succeeded, will implement and test their practical viability.
Reactor physics, numerical methods, strong software development skills, English anguage