Implementation, validation and comparison of different algorithms to solve the Bateman equations for very large systems

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    Abstract

    Since 2004, SCK-CEN has been engaged in the development of the ALEPH code. The ALEPH code is used to determine the behaviour of nuclear reactor cores. In this code, two equations are important, namely the neutron transport equations and the Bateman equations. The neutron transport equations determine the
    neutron ux and the Bateman equations are used to describe the time evolution of the nuclide concentrations. The transport equations can be solved using stochastic methods, such as the Monte Carlo algorithms. In general, Monte Carlo methods can be used to look for numerical solutions equations with a probabilistic interpretation. A way of implementing Monte Carlo methods is through Monte Carlo N-particle code. The objective of this master thesis is to improve the way the Bateman equations are currently worked out. The
    Bateman equations will be solved with deterministic methods. This master thesis is organized as follows. First, the Bateman equations with their properties will be described. Thereafter, the different algorithms which could possibly be used to solve the Bateman equations, will be discussed. These algorithms are
    - Calculating the exponential of the system matrix using the scaling and squaring algorithm
    - Chebyshev Rational Approximation method
    - RadauIIA method.
    Finally, it will be examined which is the best algorithm to solve the Bateman equations.
    Original languageEnglish
    QualificationMaster of Science
    Awarding Institution
    • Universiteit Gent
    Supervisors/Advisors
    • Van Daele, Marnix, Supervisor, External person
    • Van den Eynde, Gert, SCK CEN Mentor
    StatePublished - 2016

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