01650nas a2200145   4500008004100000245007300041210006900114260001300183520112000196100001801316700002001334700002201354700002101376856010701397       2014                        en  d00aModel Order Reduction in Fluid Dynamics: Challenges and Perspectives0 aModel Order Reduction in Fluid Dynamics Challenges and Perspecti  bSpringer3 aThis 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.1 aLassila, Toni1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi  uhttps://www.math.sissa.it/publication/model-order-reduction-fluid-dynamics-challenges-and-perspectives