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topological asymptotic

ESAIM: Control, Optimisation and Calculus of Variations (1)

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The topological asymptotic for the Navier-Stokes equations
Samuel Amstutz
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 11 / Issue 3 / July 2005

Published online by Cambridge University Press:

15 July 2005, pp. 401-425

Print publication:

July 2005
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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 of cost functional and a numerical application is presented.