Application of the dynamic mode decomposition approach to the dispersion of radioactive contaminants in air

Reduced order models exploit underlying low-dimensional patterns of large physical systems, with the aim of extracting the dominant dynamics and of achieving a significant computational speedup. The recently developed dynamic mode decomposition (DMD) method describes the time evolution of a dynamic system by means of a superposition of a small set of empirical modes computed from a sequence of ‘snapshots’, i.e. samples of the system state at given time instants. DMD provides a linear operator which best approximates the nonlinear dynamics of a large system, thus extracting both spatial modes and the spectrum of frequencies which govern time evolution. In the current work, the DMD approach is applied to the transport of a radioactive contaminant in air from a localised source in a complex geometry. The snapshots are obtained from an unsteady finite volume CFD simulation. The results show the capability of DMD in retrieving the dominant dynamics of the system, allowing an accurate description of the high-dimensional transport problem by using relatively few degrees of freedom. The reduced order approach we propose could find application in problems which are relevant to nuclear safety, including the fast propagation of the system state for near-range dispersion predictions, or the coupling with data assimilation techniques for radiation estimation and monitoring. Indeed, the surrogate models built by means of DMD are able to replicate accurately and efficiently dynamic patterns acting at short time scales in complex domains.