Resolution Requirements for Accurate Reactor Calculations Using the Linear Discontinuous Finite Element Method

This work seeks to ascertain the accuracy of the Linear Discontinuous Finite Element Method (LD) for the spatial variable in realistic neutron-transport calculations for nuclear reactors. Our results have shown that LD is an excellent alternative to other methods, such as the Method of Characteristics, for computing these types of problems. We have implemented the Linear Discontinuous Finite Element Method (LD) in the massively parallel transport code PDT. We ran problems with a range of spatial, angular, and energy discretization choices. We then analyzed the spatial accuracy in these problems. From this analysis, we have determined spatial resolution requirements necessary when calculating accurate solutions using LD. For a typical 2D PWR reactor assembly, using 76 spatial cells per pin cell, we achieve an accuracy of 3 pcm in k-effective. Also we achieve an accuracy of 3 pcm in the pin power we see in the 4 fuel pins we looked at. We have also developed an error model that accurately predicts quantities of interest at infinite resolution. This model treats both spatial and angular discretization error for a given energy discretization. The model is ‘trained’ using a series of training points - a range of spatial and angular discretization choices and the corresponding QOI. The model then uses a least squares approach to fit the QOIs as a function of our discretization choices. The model quantifies the error in our computations when the mesh is not infinitely refined. This is important for not only predicting solutions to large scale problems that cannot be run but also for quantifying the accuracy of solutions to problems that can. We have also compared to the Method of Characteristics (MOC) for a range of problems in 2D and 3D. Through our collaboration with researchers from the University of Michigan and their MOC code MPACT, we have determined that for problems with geometric features or boundary layers that are extremely small relative to the problem domain, LD achieves higher accuracy with similar meshes when compared to MOC. This is due to the fact that the Method of Characteristics must use small track spacing to accurately resolve fine mesh attributes. This leads to large numbers of unknowns, compared to DFEMs, to compute solutions to problems with similar levels of accuracy. Finally we have observed the phenomenon of unphysical oscillations that appear in LD solutions to k-eigenvalue problems in which both the problem domain and the spatial cells have high aspect ratios. We have explained why and for what types of meshes these oscillations occur. We can now predict, for simple problems, both the scalar flux shape and the k-eigenvalue for problems with and without unphysical oscillations