Displaying similar documents to “On a shape control problem for the stationary Navier-Stokes equations”

On a shape control problem for the stationary Navier-Stokes equations

Max D. Gunzburger, Hongchul Kim, Sandro Manservisi (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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An optimal shape control problem for the stationary Navier-Stokes system is considered. An incompressible, viscous flow in a two-dimensional channel is studied to determine the shape of part of the boundary that minimizes the viscous drag. The adjoint method and the Lagrangian multiplier method are used to derive the optimality system for the shape gradient of the design functional.

Optimal control of linearized compressible Navier–Stokes equations

Shirshendu Chowdhury, Mythily Ramaswamy (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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We study an optimal boundary control problem for the two dimensional unsteady linearized compressible Navier–Stokes equations in a rectangle. The control acts through the Dirichlet boundary condition. We first establish the existence and uniqueness of the solution for the two-dimensional unsteady linearized compressible Navier–Stokes equations in a rectangle with inhomogeneous Dirichlet boundary data, not necessarily smooth. Then, we prove the existence and uniqueness of the optimal...

Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty

Toni Lassila, Andrea Manzoni, Alfio Quarteroni, Gianluigi Rozza (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We review the optimal design of an arterial bypass graft following either a (i) boundary optimal control approach, or a (ii) shape optimization formulation. The main focus is quantifying and treating the uncertainty in the residual flow when the hosting artery is not completely occluded, for which the worst-case in terms of recirculation effects is inferred to correspond to a strong orifice flow through near-complete occlusion.A worst-case optimal control approach is applied to the steady...

Distributed control for multistate modified Navier-Stokes equations

Nadir Arada (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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The aim of this paper is to establish necessary optimality conditions for optimal control problems governed by steady, incompressible Navier-Stokes equations with shear-dependent viscosity. The main difficulty derives from the fact that equations of this type may exhibit non-uniqueness of weak solutions, and is overcome by introducing a family of approximate control problems governed by well posed generalized Stokes systems and by passing to the limit in the corresponding optimality...

The topological asymptotic for the Navier-Stokes equations

Samuel Amstutz (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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The aim of the topological asymptotic analysis is to provide an asymptotic expansion of a shape functional with respect to the size of a small inclusion inserted inside the domain. The main field of application is shape optimization. This paper addresses the case of the steady-state Navier-Stokes equations for an incompressible fluid and a no-slip condition prescribed on the boundary of an arbitrary shaped obstacle. The two and three dimensional cases are treated for several examples...

Second-order sufficient optimality conditions for the optimal control of Navier-Stokes equations

Fredi Tröltzsch, Daniel Wachsmuth (2006)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper sufficient optimality conditions are established for optimal control of both steady-state and instationary Navier-Stokes equations. The second-order condition requires coercivity of the Lagrange function on a suitable subspace together with first-order necessary conditions. It ensures local optimality of a reference function in a L s -neighborhood, whereby the underlying analysis allows to use weaker norms than L ∞ .