Use this URL to cite or link to this record in EThOS:
Title: Characteristic-based methods for modelling neutron transport
Author: Baker, David James
ISNI:       0000 0004 2747 7052
Awarding Body: University of Nottingham
Current Institution: University of Nottingham
Date of Award: 2012
Availability of Full Text:
Access from EThOS:
In this thesis we study techniques based on the method of characteristics applied to neutron transport problems. These methods have been widely used in the solution of such problems and have been implemented in a number of commercial and re- search codes, such as the CACTUS module of Serco Assurance's WIMS software. Since characteristics-based methods are widely used in the field of nuclear energy, where safety, reliability and predictability are of paramount importance, a rigorous analysis of the convergence properties of these methods is required; this topic represents the main focus of this thesis. We begin by using results from functional analysis to obtain an a priori bound on the error in the L [infinity] norm when employing the method of long characteristics (LC) in space in conjunction with a discrete ordinates (SN) method in angle. Our analysis applies to a source problem in 20 space with vacuum boundary conditions. We show that, with refinement in element diameter h, convergence of the LC method is at least O(h), and under certain assumptions, the SN scheme is also at least first order. These results are confirmed by numerical tests. Next we obtain a similar bound on the L[infinity]-error in the case when a variety of the short characteristic (SC) method, which approximates the neutron flux with an arbitrarily high-order piecewise polynomial approximation, is exploited. We prove that for a qth order polynomial approximation, we can expect at least O(hq) convergence in the SC solution. This result is again validated by numerical results. Finally, the SC method described above is implemented in a code and applied to a variety of standard theoretical benchmark problems as well as a number of realistic models, both from the literature and provided by Serco Assurance. Results from the code show close agreement with those from a variety of independent, external sources.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available