Author(s) :
Thomas Slawig
Preprint series :
to appear in SIAM Contr. Opt.
MSC 2000
- 49Q10 Optimization of shapes other than minimal surfaces
-
76D05 Navier-Stokes equations
Abstract :
Fr\'echet differentiability and a formula for the derivative with respect to dom
ain variation of a general class of cost functionals
under the constraint of the two-dimensional stationary incompressible Navier-Sto
kes equations are shown.
An embedding domain technique provides an
equivalent formulation of the problem on a fixed domain and
leads to a simple and computationally cheap line integral formula for the deriva
tive of the
cost functional with respect to domain variation.
Existence of a solution to the corresponding domain optimization
problems is proved.
A numerical example shows the effectivity of the derivative formula.
Keywords :
domain optimization, Navier-Stokes equations, embedding domain technique