The development of a three-dimensional nuclear reactor kinetics methodology based on the method of characteristics

The topic of this work is to develop the theoretical and practical foundations for a time-dependent method of characteristics, for use as an alternative to diffusion theory in a three-dimensional nuclear reactor kinetics computation. As a time-dependent method of characteristics has not been previously attempted, the goal is to demonstrate---affirmatively or negatively---the feasibility of such an approach and identify topics for future investigation. An explicit three-dimensional ray tracing methodology has been developed as a prerequisite task, combining various techniques that have been previously implemented into steady-state lattice physics code packages. In a reactor kinetics computation the problem geometry can be simplified beyond what would be appropriate for an assembly transport calculation, yielding a more efficient set of three-dimensional ray tracing procedures for the method of characteristics than has been previously achievable. Assessment of these spatial techniques is pursued via application to a series of steady state test problems that includes the OECD/NEA Neutron Transport Benchmark Problem. Results demonstrate that practical implementation of a three-dimensional method of characteristics will require a fine spatial discretization, which leads to longer computational runtimes.; Having successfully demonstrated the feasibility of a steady state method of characteristics in three-dimensional space, the primary task of this work is pursued: derivation and implementation of the fundamental equations for a time-dependent method of characteristics. Solutions to the time-dependent characteristic equation are sought initially via introduction of simple backward and forward time-differencing approximations and assessment is pursued via application to the two-dimensional TWIGL seed/blanket problem. Exorbitant runtimes preclude a complete analysis, however, and instead preliminary results have been generated for special cases of this problem. These results demonstrate that numerical instabilities are inherent to a time-differenced method of characteristics and, moreover, that one particular type of instability is unique to a Lagrangian transport formulation. While this observation suggests that a time-dependent method of characteristics may not be feasible, a more successful formulation could be pursued via future examination of alternative time-discretization methods. The problem of long runtimes, which limits applicability of the methods here described, could be resolved with the eventual introduction of computational acceleration and parallelization techniques.