### Abstract:

The subject of this thesis is the development of a nodal discretization of the
low-order quasi-diffusion (QDLO) equations for global reactor core calculations.
The advantage of quasi-diffusion (QD) is that it is able to capture transport effects
at the surface between unlike fuel assemblies better than the diffusion
approximation. We discretize QDLO equations with the advanced nodal
methodology described by Palmtag (Pal 1997) for diffusion. The fast and thermal
neutron fluxes are presented as 2-D, non-separable expansions of polynomial and
hyperbolic functions.
The fast flux expansion consists of polynomial functions, while the thermal
flux is expanded in a combination of polynomial and hyperbolic functions. The
advantage of using hyperbolic functions in the thermal flux expansion lies in the
accuracy with which hyperbolic functions can represent the large gradients at the
interface between unlike fuel assemblies. The hyperbolic expansion functions
proposed in (Pal 1997) are the analytic solutions of the zero-source diffusion
equation for the thermal flux. The specific form of the QDLO equations requires
the derivation of new hyperbolic basis functions which are different from those
proposed for the diffusion equation.
We have developed a discretization of the QDLO equations with node-averaged
cross-sections and Eddington tensor components, solving the 2-D
equations using the weighted residual method (Ame 1992). These node-averaged
data are assumed known from single assembly transport calculations. We wrote a
code in "Mathematica" that solves k-eigenvalue problems and calculates neutron
fluxes in 2-D Cartesian coordinates.
Numerical test problems show that the model proposed here can reproduce
the results of both the simple diffusion problems presented in (Pal 1997) and those
with analytic solutions. While the QDLO calculations performed on one-node,
zero-current, boundary condition diffusion problems and two-node, zero-current
boundary condition problems with UO₂-UO₂ assemblies are in excellent agreement
with the benchmark and analytic solutions, UO₂-MOX configurations show more
important discrepancies that are due to the single-assembly homogenized cross-sections
used in the calculations. The results of the multiple-node problems show
similar discrepancies in power distribution with the results reported in (Pal 1997).
Multiple-node k-eigenvalue problems exhibit larger discrepancies, but these can be
diminished by using adjusted diffusion coefficients (Pal 1997). The results of
several "transport" problems demonstrate the influence of Eddington functionals on
homogenized flux, power distribution, and multiplication factor k.