Direkt zum Inhalt

Garcke, Harald ; Hecht, Claudia

Shape and topology optimization in Stokes flow with a phase field approach

Monograph

Garcke, Harald and Hecht, Claudia (2014) Shape and topology optimization in Stokes flow with a phase field approach. Preprintreihe der Fakultät Mathematik 10/2014, Working Paper.

DOI to cite this document: 10.5283/epub.33911


Abstract

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 ...

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.


Involved Institutions


Details

Item typeMonograph (Working Paper)
Series of the University of RegensburgPreprintreihe der Fakultät Mathematik
Volume10/2014
Date2014
Date of publication22 Jun 2016 09:58
InstitutionsMathematics > Prof. Dr. Harald Garcke
Classification
NotationType
35R35MSC
35Q35MSC
49Q10MSC
49Q20MSC
76D07MSC
KeywordsShape and topology optimization, phase field method, diffuse interfaces, Stokes flow, fictitious domain
Dewey Decimal Classification500 Science > 510 Mathematics
StatusUnknown
RefereedNo, this version has not been refereed yet (as with preprints)
Created at the University of RegensburgYes
URN of the UB Regensburgurn:nbn:de:bvb:355-epub-339110
Item ID33911

Export bibliographical data

Owner only: item control page

nach oben