Garcke, Harald and Hecht, Claudia (2016) APPLYING A PHASE FIELD APPROACH FOR SHAPE OPTIMIZATION OF A STATIONARY NAVIER-STOKES FLOW. ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 22 (2). pp. 309-337. ISSN 1292-8119, 1262-3377
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We apply a phase field approach for a general shape optimization problem of a stationary Navier-Stokes flow. To be precise we add a multiple of the Ginzburg-Landau energy as a regularization to the objective functional and relax the non- permeability of the medium outside the fluid region. The resulting diffuse interface problem can be shown to be well-posed and optimality conditions are derived. We state suitable assumptions on the problem in order to derive a sharp interface limit for the minimizers and the optimality conditions. Additionally, we can derive a necessary optimality system for the sharp interface problem by geometric variations without stating additional regularity assumptions on the minimizing set.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | TOPOLOGY OPTIMIZATION; CRITERION; Shape and topology optimization; phase field method; diffuse interfaces; stationary Navier-Stokes flow; fictitious domain |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 25 Mar 2019 09:19 |
| Last Modified: | 25 Mar 2019 09:19 |
| URI: | https://pred.uni-regensburg.de/id/eprint/3130 |
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