Displaying similar documents to “The topological asymptotic expansion for the Quasi-Stokes problem”

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...

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...

The effective boundary conditions for vector fields on domains with rough boundaries: Applications to fluid mechanics

Eduard Feireisl, Šárka Matušů-Nečasová (2011)

Applications of Mathematics

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The Navier-Stokes system is studied on a family of domains with rough boundaries formed by oscillating riblets. Assuming the complete slip boundary conditions we identify the limit system, in particular, we show that the limit velocity field satisfies boundary conditions of a mixed type depending on the characteristic direction of the riblets.

A multiscale correction method for local singular perturbations of the boundary

Marc Dambrine, Grégory Vial (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this work, we consider singular perturbations of the boundary of a smooth domain. We describe the asymptotic behavior of the solution u of a second order elliptic equation posed in the perturbed domain with respect to the size parameter of the deformation. We are also interested in the variations of the energy functional. We propose a numerical method for the approximation of u based on a multiscale superposition of the unperturbed solution and a profile defined...