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.
Keywords: shape optimization, topological asymptotic, Navier-Stokes equations
@article{COCV_2005__11_3_401_0,
author = {Amstutz, Samuel},
title = {The topological asymptotic for the {Navier-Stokes} equations},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {401--425},
year = {2005},
publisher = {EDP Sciences},
volume = {11},
number = {3},
doi = {10.1051/cocv:2005012},
mrnumber = {2148851},
zbl = {1123.35040},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv:2005012/}
}
TY - JOUR AU - Amstutz, Samuel TI - The topological asymptotic for the Navier-Stokes equations JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2005 SP - 401 EP - 425 VL - 11 IS - 3 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv:2005012/ DO - 10.1051/cocv:2005012 LA - en ID - COCV_2005__11_3_401_0 ER -
%0 Journal Article %A Amstutz, Samuel %T The topological asymptotic for the Navier-Stokes equations %J ESAIM: Control, Optimisation and Calculus of Variations %D 2005 %P 401-425 %V 11 %N 3 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv:2005012/ %R 10.1051/cocv:2005012 %G en %F COCV_2005__11_3_401_0
Amstutz, Samuel. The topological asymptotic for the Navier-Stokes equations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 3, pp. 401-425. doi: 10.1051/cocv:2005012
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