An efficient, moments-based approximation for deviation propagators of recurrent flows

A simple, data-assisted and physics-based approach for recurrent fluid dynamics is presented, and approximations for the application to macroscopic problems are developed. Large-step predictions are built upon sufficiently similar reference states in a precomputed database around which the Navier–Stokes equations are linearized. Hence, the deviation of any flow field from its nearest reference state obeys a linear propagator, and its evolution over a large time step can be calculated by the convolution with this propagator. An efficient, Gaussian approximation for these operators is constructed from their leading-order moments, which can be obtained along with the set of reference states with little overhead costs. The methodology is applied to two- and three-dimensional vortex shedding after a cylinder at Re = 200. Validation is carried out via a comparison of field time series, temporal means and variances, autocorrelation functions at selected locations, and global balances of momentum and kinetic energy. Results for cases with boundary conditions outside the reference set are of mostly (very) good accuracy, with speed-ups of about two orders of magnitude compared to classical computational fluid dynamics simulations. While the propagator simulations do not reach real-time capability for large-scale, three-dimensional flows, they might serve as a data augmentation method in connection with machine learning approaches.