Garcke, Harald and Hecht, Claudia and Hinze, Michael and Kahle, Christian and Lam, Kei Fong (2016) Shape optimization for surface functionals in Navier-Stokes flow using a phase field approach. INTERFACES AND FREE BOUNDARIES, 18 (2). pp. 219-261. ISSN 1463-9963, 1463-9971
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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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | TOPOLOGY OPTIMIZATION; DRAG; EQUATION; DESIGN; FLUIDS; Shape optimization; phase-field method; lift; drag; Navier-Stokes equations |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 21 Mar 2019 11:46 |
| Last Modified: | 21 Mar 2019 11:46 |
| URI: | https://pred.uni-regensburg.de/id/eprint/2615 |
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