Displaying similar documents to “The topological asymptotic for the Navier-Stokes equations”

The topological asymptotic for the Navier-Stokes equations

Samuel Amstutz (2010)

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...

The topological asymptotic expansion for the Quasi-Stokes problem

Maatoug Hassine, Mohamed Masmoudi (2004)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper, we propose a topological sensitivity analysis for the Quasi-Stokes equations. It consists in an asymptotic expansion of a cost function with respect to the creation of a small hole in the domain. The leading term of this expansion is related to the principal part of the operator. The theoretical part of this work is discussed in both two and three dimensional cases. In the numerical part, we use this approach to optimize the locations of a fixed number of air injectors...

Removing holes in topological shape optimization

Maatoug Hassine, Philippe Guillaume (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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The gradient based topological optimization tools introduced during the last ten years tend naturally to modify the topology of a domain by creating small holes inside the domain. Once these holes have been created, they usually remain unchanged, at least during the topological phase of the optimization algorithm. In this paper, a new asymptotic expansion is introduced which allows to decide whether an existing hole must be removed or not for improving the cost function. Then, two numerical...