On the Diffusion Coefficients for Reactor Physics Applications

The definition of the multigroup diffusion coefficient for reactor physics problems is not unique; rather, it is based on limiting approximations made to the Boltzmann transport equation. In this paper, we present several new diffusion closures in an attempt to gain increased accuracy over the standard P1-based diffusion theory. First, the Levermore-Pomraning flux-limited diffusion theory is applied to reactor physics problems both in its original form and in a new modified form that makes the methodology more robust with respect to the energy variable. Additionally, two novel definitions of the diffusion coefficient are introduced that permit a neutron flux that is greater than first order in angle. These various diffusion theories are completed by developing consistent boundary conditions for each case. Diffusion theory solutions are computed for each unique closure and are compared against transport theory analytically for a simple half-space problem and numerically for a suite of simplified one-dimensional reactor problems. Conclusions and observations are made for each diffusion method in terms of its underlying assumptions and accuracy of the benchmark solutions.