Model Order Reduction in Fluid Dynamics: Challenges and Perspectives

  • Toni Lassila
  • Andrea Manzoni
  • Alfio Quarteroni
  • Gianluigi RozzaEmail author
Part of the MS&A - Modeling, Simulation and Applications book series (MS&A, volume 9)


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.


Proper Orthogonal Decomposition Proper Orthogonal Decomposition Mode Posteriori Error Estimation Reduce Basis Galerkin Projection 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Toni Lassila
    • 1
  • Andrea Manzoni
    • 2
  • Alfio Quarteroni
    • 1
    • 3
  • Gianluigi Rozza
    • 2
    Email author
  1. 1.MATHICSE-CMCS Modelling and Scientific ComputingEcole Polytechnique Fédérale de LausanneLausanneSwitzerland
  2. 2.SISSA Mathlab — International School for Advanced StudiesTriesteItaly
  3. 3.MOX — Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly

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