Reduced order models applied to unsteady incompressible fluid flows

Resumen

This Thesis focuses on the developing and concept proofing of a purely data-driven reduced order model (ROM) for its further application to very complex dynamical sys- tems. The ROM will be based on a recent mathematical algorithm, called higher order dynamical mode decomposition (HODMD), which decomposes data sets of unsteady sys- tem responses in a collection of spatial modes and their dynamical behaviour defined by their frequencies and growth rates. This decomposition allows for the description of the system response in a semi-analytical form, continuous in time, which can be used to extrapolate future values by direct evaluation. A first ROM concept is applied to the system response of fluid flow around a multi-body array of cylinders at low Reynolds numbers, extrapolating the solution from the early transient stage to the attractor region. A complementary fluid dynamic analysis of the different spatio-temporal modes is carried out by means of the HODMD algorithm to shed light into the highly intricate dynamical response of this unsteady fluid flow. The drawbacks of the primitive ROM version are corrected with the addition of truncation and consistency error estimates of the system response as well as an HODMD interval adaptive law that enforces preliminary checks for the consistency estimate. Ultimately, this improved version is conceptually proved with two different nonlinear dynamical systems such as the Lorenz system and the complex Ginzburg-Landau equation.