CDS/CIMMS Lunchtime Seminar: Reduced-order models for fluids, using approximate balanced truncation and dynamically scaling modes

Dr. Clancy Rowley, Mechanical & Aerospace Engineering, Princeton University

This work addresses model-reduction techniques for fluids, using several variants of the standard Proper Orthogonal Decomposition (POD) method. In the first variant, we use POD as an approximation of balanced truncation, using adjoint simulations to quantify the dynamical importance of different flow states. We illustrate the method on a number of examples, including a 3D linearized channel flow, and  the separating flow over an airfoil at large angles of attack, and we show that this method significantly outperforms standard POD, producing low-order models that have much greater accuracy for a given number of modes. In the second variant, we present reduced-order models of a temporally evolving shear layer, using POD modes that scale in space as the shear layer spreads. Using this approach, very low-order models (4 complex modes) capture much of the relevant nonlinear behavior over a wide range of shear layer thicknesses. We conclude with some open questions and challenges for POD-based reduced order models.