Model order reduction in fluid dynamics: challenges and perspectives

This chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit strong nonlinearities – which are mainly related either to nonlinear convection terms and/or some geometric variability – that often cannot be treated by simple linearization. Additional difficulties arise when attempting model reduction of unsteady flows, especially when long-term transient behavior needs to be accurately predicted using reduced order models and more complex features, such as turbulence or multiphysics phenomena, have to be taken into consideration. We first discuss some general principles that apply to many parametric model order reduction problems, then we apply them on steady and unsteady viscous flows modelled by the incompressible Navier-Stokes equations. We address questions of inf-sup stability, certification through error estimation, computational issues and – in the unsteady case – long-time stability of the reduced model. Moreover, we provide an extensive list of literature references. Toni Lassila and Alfio Quarteroni MATHICSE-CMCS Modelling and Scientific Computing, Ecole Polytechnique Fédérale de Lausanne, Station 8, CH-1015 Lausanne, Switzerland. e-mail: [email protected],[email protected] Alfio Quarteroni MOX Dipartimento di Matematica, Politecnico di Milano, P.za Leonardo da Vinci 32, I-20133 Milano, Italy. Andrea Manzoni and Gianluigi Rozza SISSA Mathlab International School for Advanced Studies, Santorio A, Via Bonomea 265, I-34136 Trieste, Italy. e-mail: [email protected],[email protected]