Modeling neutronic transients with Galerkin projection onto a greedy-sampled, POD subspace

Presented here is an application of POD-Galerkin projection to develop a reduced-order-model (ROM) that approximates the solution of the multi-group, time-dependent, diffusion equation with a lower computational cost. Such reduced models are often sought in the context of parametric studies and uncertainty quantification, which require successive evaluation of the full-order model (FOM). To construct the ROM efficiently, greedy sampling was used to generate a reduced subspace that represents the entire parameter (here, cross-sections) domain. By using this subspace, the ROM is expected to yield accurate predictions when used in place of the FOM for uncertainty quantification conducted, e.g., with direct Monte-Carlo sampling. The TWIGL benchmark was used here for illustration. A ROM constructed with a POD basis of rank 10 was able to reproduce the core power with a maximum RMS error on the order of 10^–6, and for the precursors concentration it was 10^–9. Moreover, the statistical moments obtained from the ROM were in good agreement with those of the full-order-model. The mean relative error of the power sample mean prediction was about 4 ×10^–6 for both the ramp and the step perturbations. In terms of the computational efficiency, the ROM time, including the projection, is approximately four-times faster than the full-order-model.