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Title: Shape and Topology Optimization in Stokes Flow with a Phase Field Approach

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.
Authors:
;  [1]
  1. Universität Regensburg, Fakultät für Mathematik (Germany)
Publication Date:
OSTI Identifier:
22469616
Resource Type:
Journal Article
Resource Relation:
Journal Name: Applied Mathematics and Optimization; Journal Volume: 73; Journal Issue: 1; Other Information: Copyright (c) 2016 Springer Science+Business Media New York; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; FLUIDS; GINZBURG-LANDAU THEORY; INTERFACES; MATHEMATICAL SOLUTIONS; OPTIMIZATION; PERMEABILITY; POROUS MATERIALS; TOPOLOGY