Interpolatory Galerkin Models for the Navier-Stokes-Equations

In this work the framework of deriving interpolatory reduced order models for partial differential equations with use of basis interpolation and a subsequent Galerkin projection from the work in Pyta et al. (2015) is extended. Therefore two new methods are presented. The first method uses Bézier curves to enable a continuous differentiable interpolation. The second method combines the congruence transformation with a new generalized framework of straightforward interpolation and orthogonalizing afterward. Results are shown for an example from practice: a model reduction of the Navier-Stokes-Equations for a two-dimensional cross section of a flat plate, which is actuated by spanwise traveling waves transversal to the incoming inflow.