Parametric reduced order dynamical model construction of a fluid flow control problem*

The problem of approximating a given fluid flow control problem, governed by the Navier-Stokes equations at varying Reynolds number, with a low-order parametric linear dynamical model, is presented. To this aim, a three steps approach is proposed: first, (i) the original Reynolds number dependent fluid flow problem is spatially and parametrically discretized, then (ii) each resulting local very large-scale Linear Time Invariant (LTI) Differential Algebraic Equations (DAE) models are approximated using the IRKA approach proposed by Gugercin et al. (2008), and finally (iii), the reduced order models are interpolated and transformed into a low-complexity Linear Fractional Representation (LFR). The overall process is illustrated in a top down framework using a generic flow configuration, namely, an open cavity flow. Numerical simulations assess the validity of the approach.