In this study, the applicability of the Lattice Boltzmann Method to neutron transport is investigated.
The transport model used, is derived from the Boltzmann equation for neutral particles by inverting
the streaming operator and casting the integral transport equation into an operator form. From the
operator equation, an iterative solution to the transport problem is presented, with the first collision
source as the starting point for the iteration scheme. One of the main features of the method is the
simultaneous discretization of the phase space of the problem, whereby particles are restricted to
move on a lattice.
A full description of the discretization scheme is given along with the iterative procedure and
quadrature set used for the angular discretization. To mitigate lattice ray effects, an angular
refinement scheme is introduced to increase the angular coverage of the problem phase space.
The method is then applied to a model problem to investigate its applicability to neutron transport.
Three cases are considered where constant, linear and exponential interpolants are used to account
for the accumulation of flux due to the streaming of particles between nodes. The results obtained
are compared to a reference solution, that was calculated by using the MCNP code and to the values
calculated using a nodal SN method. Finally, areas of improvement are identified and possible
extensions to the algorithm are provided. / Thesis (MIng (Engineering Sciences in Nuclear Engineering))--North-West University, Potchefstroom Campus, 2013
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:nwu/oai:dspace.nwu.ac.za:10394/8691 |
| Date | January 2012 |
| Creators | Erasmus, Bernard |
| Publisher | North-West University |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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