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Optimal control of Navier-Stokes equations using Lagrange-Galerkin methods

Gilles Fourestey 1 Marwan Moubachir
1 CAIMAN - Scientific computing, modeling and numerical analysis
CRISAM - Inria Sophia Antipolis - Méditerranée , ENPC - École des Ponts ParisTech, CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : In this report, we are investigating the numerical approximation of an optimal control problem involving the evolution of a newtonian viscous incompressible fluid described by the Navier-Stokes equations. This PDE system is discretized using a low order finite element in space coupled with a Lagrange-Galerkin scheme for the nonlinear advection operator. We introduce a full discrete linearized scheme that is used to compute the gradient of a given cost function by ensuring its consistency. Using gradient based optimization algorithms, we are able to deal with two fluid flow control problems : Drag reduction around a moving cylinder, an identification of far-field velocity using the knowledge of the fluid load on a rectangular bluff body, for both fixed and moving configuration.
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Submitted on : Tuesday, May 23, 2006 - 7:23:59 PM
Last modification on : Friday, February 4, 2022 - 3:18:52 AM
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  • HAL Id : inria-00071976, version 1



Gilles Fourestey, Marwan Moubachir. Optimal control of Navier-Stokes equations using Lagrange-Galerkin methods. RR-4609, INRIA. 2002. ⟨inria-00071976⟩



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