Geodesic
Shape optimization for surface functionals in Navier-Stokes flow using a phase field approach
Harald Garcke1 ; Claudia Hecht1 ; Michael Hinze2 ; Christian Kahle2 ; Kei Fong Lam1 orcid
1Universität Regensburg, Germany
2Universität Hamburg, Germany
Interfaces and free boundaries, Tome 18 (2016) no. 2, pp. 219-261

Voir la notice de l'article provenant de la source EMS Press

DOI

We consider shape and topology optimization of an object in fluid flow governed by the Navier–Stokes equations. Shapes are modelled with the help of a phase field approach and the solid body is relaxed to be a porous medium. The phase field method uses a Ginzburg–Landau functional in order to approximate a perimeter penalization. We focus on surface functionals and carefully introduce a new modelling variant, show existence of minimizers and derive first order necessary conditions. These conditions are related to classical shape derivatives by identifying the sharp interface limit with the help of formally matched asymptotic expansions. Finally, we present numerical computations based on a Cahn–Hilliard type gradient descent which demonstrate that the method can be used to solve shape optimization problems for fluids with the help of the new approach.
DOI : 10.4171/ifb/363
Classification : 49-XX, 35-XX
Mots-clés : Shape optimization, phase-field method, lift, drag, Navier–Stokes equations

Harald Garcke  1   ; Claudia Hecht  1   ; Michael Hinze  2   ; Christian Kahle  2   ; Kei Fong Lam  1

1 Universität Regensburg, Germany
2 Universität Hamburg, Germany 
Harald Garcke; Claudia Hecht; Michael Hinze; Christian Kahle; Kei Fong Lam. Shape optimization for surface functionals in Navier-Stokes flow using a phase field approach. Interfaces and free boundaries, Tome 18 (2016) no. 2, pp. 219-261. doi: 10.4171/ifb/363
@article{10_4171_ifb_363,
     author = {Harald Garcke and Claudia Hecht and Michael Hinze and Christian Kahle and Kei Fong Lam},
     title = {Shape optimization for surface functionals in {Navier-Stokes} flow using a phase field approach},
     journal = {Interfaces and free boundaries},
     pages = {219--261},
     year = {2016},
     volume = {18},
     number = {2},
     doi = {10.4171/ifb/363},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/363/}
}
TY  - JOUR
AU  - Harald Garcke
AU  - Claudia Hecht
AU  - Michael Hinze
AU  - Christian Kahle
AU  - Kei Fong Lam
TI  - Shape optimization for surface functionals in Navier-Stokes flow using a phase field approach
JO  - Interfaces and free boundaries
PY  - 2016
SP  - 219
EP  - 261
VL  - 18
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4171/ifb/363/
DO  - 10.4171/ifb/363
ID  - 10_4171_ifb_363
ER  - 
%0 Journal Article
%A Harald Garcke
%A Claudia Hecht
%A Michael Hinze
%A Christian Kahle
%A Kei Fong Lam
%T Shape optimization for surface functionals in Navier-Stokes flow using a phase field approach
%J Interfaces and free boundaries
%D 2016
%P 219-261
%V 18
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/363/
%R 10.4171/ifb/363
%F 10_4171_ifb_363

Cité par Sources :