This work presents a whole-core benchmark problem based on a 2-loop pressurized water reactor with both UO₂and MOX fuel assemblies. The specification includes heterogeneity at both the assembly and core level. The geometry and material compositions are fully described and multi-group cross section libraries are provided in 2, 4, and 8 group formats. Simplifications made to the benchmark specification include a Cartesian boundary, to facilitate the use of transport codes that may have trouble with cylindrical boundaries, and control rod homogenization, to reduce the geometric complexity of the problem. These modifications were carefully chosen to preserve the physics of the problem and a justification of these modifications is given. Detailed Monte Carlo reference solutions including core eigenvalue, assembly averaged fission densities and selected fuel pin fission densities are presented for benchmarking diffusion and transport methods. Three different core configurations are presented in the paper namely all-rods-out, all-rods-in, and some-rods-in.

A new whole-core transport method is described for 3-D hexagonal geometry. This is an extension of a stochastic-deterministic hybrid method which has previously been shown highly accurate and efficient for eigenvalue problems. Via Monte Carlo, it determines the solution to the transport equation in sub-regions of reactor cores, such as individual fuel elements or sections thereof, and uses those solutions to compose a library of response expansion coefficients. The information acquired allows the deterministic solution procedure to arrive at the whole core solution for the eigenvalue and the explicit fuel pin fission density distribution more quickly than other transport methods. Because it solves the transport equation stochastically, complicated geometry may be modeled exactly and therefore heterogeneity even at the most detailed level does not challenge the method. In this dissertation, the method is evaluated using comparisons with full core Monte Carlo reference solutions of benchmark problems based on gas-cooled, graphite-moderated reactor core designs. Solutions are given for core eigenvalue problems, the calculation of fuel pin fission densities throughout the core, and the determination of incremental control rod worth. Using a single processor, results are found in minutes for small cores, and in no more than a few hours for a realistically large core. Typical eigenvalues calculated by the method differ from reference solutions by less than 0.1%, and pin fission density calculations have average accuracy of well within 1%, even for unrealistically challenging core configuration problems. This new method enables the accurate determination of core eigenvalues and flux shapes in hexagonal cores with efficiency far exceeding that of other transport methods.