In this work, we present a stable proper orthogonal decomposition–Galerkin approximation for parametrized steady incompressible Navier–Stokes equations with low Reynolds number. Supremizer solutions are addedto the reduced velocity space in order to obtain a stable reduced-order system, considering in particular thefulfillment of an inf-sup condition. The stability analysis is first carried out from a theoretical standpoint andthen confirmed by numerical tests performed on a parametrized two-dimensional backward-facing step flow.

Supremizer stabilization of POD-Galerkin approximation of parametrized steady incompressible Navier-Stokes equations

Ballarin, Francesco;Manzoni, Andrea;Quarteroni, Alfio;Rozza, Gianluigi
2015-01-01

Abstract

In this work, we present a stable proper orthogonal decomposition–Galerkin approximation for parametrized steady incompressible Navier–Stokes equations with low Reynolds number. Supremizer solutions are addedto the reduced velocity space in order to obtain a stable reduced-order system, considering in particular thefulfillment of an inf-sup condition. The stability analysis is first carried out from a theoretical standpoint andthen confirmed by numerical tests performed on a parametrized two-dimensional backward-facing step flow.
2015
Equivalent inf-sup condition; Parametrized Navier-Stokes equations; Pressure stabilization; Proper orthogonal decomposition; Reduced basis method; Engineering (all); Applied Mathematics; Numerical Analysis
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1038536
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