PhD, University of Cincinnati, 2005, Engineering : Nuclear and Radiological Engineering
The Boltzmann equation, which is often used to describe neutral particle transport process, is impossible to solve analytically in most cases. Solving the equation by a numerically method could also be very time-consuming for some problems. Therefore, various approximation methods have been developed for particle transport calculations. In this dissertation, a new Flux-Limited diffusion method (DM) is investigated as a low-order approximation to the transport equation. Specifically, the new Flux-Limited diffusion method (DM) is derived based on the Minerbo maximum entropy Eddington factor and corresponding boundary conditions are developed. Performance of the DM method is tested for a variety of particle transport problems: including steady-state problems, transient problems, one-dimensional problems, two-dimensional problems, flux distribution problems, eigen-value problems, one-group problems, and two-group problems. The tests demonstrate that compared with other approximations, the DM method has the following good features. (1) The DM method is a low order approximation as the classic diffusion method but can improve the accuracy of classic diffusion method by a factor up to 10. (2) The DM method has relatively fast computing speed compared with other high order approximations and its computation cost is not too expensive compared with the classic diffusion method. (3) The DM method can predict proper traveling speed of particles in time-dependent problems. (4) The DM method is valid for neutral particle transport in systems containing strong absorbers, regions near particle sources or boundaries, and systems where strongly anisotropic scattering of particles occur. (5) The DM method is superior to other Flux-Limited diffusion methods available in the literature. (6) The solutions of the DM method are numerically stable in all the circumstances. Overall, the DM method is promising as a low-order approximation for particle transport calculations in some applicatio (open full item for complete abstract)
Committee: Bingjing Dr. Su (Advisor)
Subjects: Engineering, Nuclear