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

Abstract

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.