Assessment of 2 D-Transport / 1 D-Diffusion Approximations in a Pin Resolved Variational Nodal Method for PWR Calculations

An assessment of the approximation in a two-dimensional transport/one-dimensional diffusion (2D/1D) variational nodal method for pin-resolved pressurized water reactor (PWR) core calculations is presented. The derivation of the response matrices on which the solution algorithms are based is modified to include a more efficient inclusion of the quasi-reflected interface conditions that are essential to the method’s success. The accuracy of the angular approximations is summarized, and a series of test problems based on the C5G7 benchmarks is examined to determine the level of discretization error compared to multi-group Monte Carlo reference solutions. Errors resulting from finite element and orthogonal polynomial approximations to the spatial variables in the lateral plane as well as axial discretization are analyzed. Results for the twoand three-dimensional C5G7 benchmarks illustrate the resulting tradeoffs between accuracy and cost. Accuracy for two-dimensional problems proves to be excellent; while in three-dimensions the axial diffusion theory limits accuracy. It is found that removing the axial diffusion limitation will require abandoning the 2D/1D formulation and basing the method on the three-dimensional even-parity transport equation, in which cross derivatives between the lateral plane and axial direction are present. Preliminary theoretical work indicates no insurmountable impediments to the development of such a fully threedimensional pin-resolved variational nodal method.