Garcke, Harald and Hinze, Michael and Kahle, Christian and Lam, Kei Fong (2018) A phase field approach to shape optimization in Navier-Stokes flow with integral state constraints. ADVANCES IN COMPUTATIONAL MATHEMATICS, 44 (5). pp. 1345-1383. ISSN 1019-7168, 1572-9044
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We consider the shape optimization of an object in Navier-Stokes flow by employing a combined phase field and porous medium approach, along with additional perimeter regularization. By considering integral control and state constraints, we extend the results of earlier works concerning the existence of optimal shapes and the derivation of first order optimality conditions. The control variable is a phase field function that prescribes the shape and topology of the object, while the state variables are the velocity and the pressure of the fluid. In our analysis, we cover a multitude of constraints which include constraints on the center of mass, the volume of the fluid region, and the total potential power of the object. Finally, we present numerical results of the optimization problem that is solved using the variable metric projection type (VMPT) method proposed by Blank and Rupprecht, where we consider one example of topology optimization without constraints and one example of maximizing the lift of the object with a state constraint, as well as a comparison with earlier results for the drag minimization.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | TOPOLOGY OPTIMIZATION; DRAG; SPACES; FLUIDS; MODEL; Topology optimization; Shape optimization; Phase field approach; Navier-Stokes flow; Integral state constraints |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 09 Dec 2019 14:32 |
| Last Modified: | 09 Dec 2019 14:32 |
| URI: | https://pred.uni-regensburg.de/id/eprint/13752 |
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