  A novel approach to simulate dynamic, recurrent flows with very large time
steps is presented. Data-driven forecasts based on the method of analogues are
made employing a set of precomputed time series segments of flow fields. These
predictions are then corrected with the evolved deviation between initial flow
state and its nearest neighbor in the database. The evolution of these
deviations is obtained from the convolution with the propagator of the
linearized Navier-Stokes equations, where linearization takes place around the
most similar state in the database. The error $E_{\textrm{lin}}$ due to this
approximation implies the appropriate distance function to determine
nearest-neighbor fields. We tested the method on the simple case of 2D vortex
shedding behind a cylinder at Reynolds numbers in the range of 200 with step
sizes of up to 200 times larger than those used to generate the underlying data
with the PISO algorithm. Short-term forecasts showed a high degree of accuracy
with errors correlating well with $E_{\textrm{lin}}$ for a number of case
variations. But also after many steps, the predicted flow fields remained in
close agreement with high-fidelity CFD calculations with relative errors on the
order of 1% for the temporal averages. Furthermore, excellent conservation
behavior of global properties like total momentum and kinetic energy was
observed.
