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.


Editor(s):
Quarteroni, A
Rozza, G
Published in:
Reduced Order Methods For Modeling And Computational Reduction, 9, 235-273
Presented at:
Workshop on Reduced Basis, POD and Reduced Order Methods for Model and Computational Reduction: towards Real-time Computing and Visualization', u'Workshop on Reduced Basis, POD and Reduced Order Methods for Model and Computational Reduction: towards Real-time Computing and Visualization
Year:
2014
Publisher:
Springer International Publishing
ISSN:
2037-5255
ISBN:
978-3-319-02090-7
978-3-319-02089-1
Laboratories:




 Record created 2014-12-30, last modified 2018-05-03


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