Reduced-order modeling of neutron transport separated in axial and radial space by Proper Generalized Decomposition with applications to nuclear reactor physics (2404.18016v2)

Abstract: In this article, we demonstrate the novel use of Proper Generalized Decomposition (PGD) to separate the axial and, optionally, polar dimensions of neutron transport. Doing so, the resulting Reduced-Order Models (ROMs) can exploit the fact that nuclear reactors tend to be tall, but geometrically simple, in the axial direction $z$, and so the 3D neutron flux distribution often admits a low-rank "2D/1D" approximation. Through PGD, this approximation is computed by alternately solving 2D and 1D sub-models, like in existing 2D/1D models of reactor physics. However, the present methodology is more general in that the decomposition is arbitrary-rank, rather than rank-one, and no simplifying approximations of the transverse leakage are made. To begin, we derive two original models: that of axial PGD -- which separates only $z$ and the sign of the polar angle $\alpha\in{-1,+1}$ -- and axial-polar PGD -- which separates both $z$ and the full polar angle $\mu$ from the radial domain. Additionally, we grant that the energy dependence $E$ may be ascribed to either radial or axial modes, or both, bringing the total number of candidate 2D/1D ROMs to six. To assess performance, these PGD ROMs are applied to two few-group benchmarks characteristic of Light Water Reactors. Therein, we find both the axial and axial-polar ROMs are convergent and that the latter are often more economical than the former. Ultimately, given the popularity of 2D/1D methods in reactor physics, we expect a PGD ROM which achieves a similar effect, but perhaps with superior accuracy, a quicker runtime, and/or broader applicability, would be eminently useful, especially for full-core problems.