Garcke, Harald and Hecht, Claudia (2016) Shape and Topology Optimization in Stokes Flow with a Phase Field Approach. APPLIED MATHEMATICS AND OPTIMIZATION, 73 (1). pp. 23-70. ISSN 0095-4616, 1432-0606
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In this paper we introduce a new formulation for shape optimization problems in fluids in a diffuse interface setting that can in particular handle topological changes. By adding the Ginzburg-Landau energy as a regularization to the objective functional and relaxing the non-permeability outside the fluid region by introducing a porous medium approach we hence obtain a phase field problem where the existence of a minimizer can be guaranteed. This problem is additionally related to a sharp interface problem, where the permeability of the non-fluid region is zero. In both the sharp and the diffuse interface setting we can derive necessary optimality conditions using only the natural regularity of the minimizers. We also pass to the limit in the first order conditions.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | GRADIENT THEORY; DESIGN; TRANSITIONS; CRITERION; EQUATIONS; DOMAIN; FLUIDS; DRAG; Shape and topology optimization; Phase field method; Diffuse interfaces; Stokes flow; Fictitious domain |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 12 Mar 2019 13:05 |
| Last Modified: | 12 Mar 2019 13:05 |
| URI: | https://pred.uni-regensburg.de/id/eprint/2429 |
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