Computation of POD basis functions for fluid flows with lanczos methods

The proper orthogonal decomposition (POD) approach allows us to construct low-order models for fluid flows. Supposing an ensemble of solutions of the time-dependent Navier-Stokes equations at fixed time instants (snapshots) is given, the aim is to compute a few global basis functions to represent the main dynamics of the flow. The POD basis functions can be computed via a truncated singular value decomposition of the data matrix given by the snapshots, where Lanczos methods can be used to calculate the POD basis functions efficiently.