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Investigating the stability of the phase field solution of equilibrium droplet configurations by eigenvalues and eigenvectors

Diewald, Felix ; Kuhn, Charlotte ; Heier, Michaela ; Langenbach, Kai ; Horsch, Martin ; Hasse, Hans ; Müller, Ralf (2018)
Investigating the stability of the phase field solution of equilibrium droplet configurations by eigenvalues and eigenvectors.
In: Computational Materials Science, 141
doi: 10.1016/j.commatsci.2017.08.029
Article, Bibliographie

Abstract

Phase field models have recently been used to investigate the physical behavior of droplets in static as well as dynamic situations. As those models are often driven by an Allen-Cahn evolution equation, their stationary solution is given by the first order optimality condition of an energy functional. This includes the possibility of computing saddle points and maxima rather than minima of the energy functional. The present work shows the post-processing of eigenvalues and eigenvectors of the system matrix of the phase field model in order to investigate the stability of equilibrium droplet configurations. This postprocessing can easily be ported to other evolution equations. The underlying phase field model is described and the resulting discrete finite element eigenvalue problem is stated. The investigation of eigenvalues and eigenvectors is illustrated by examples.

Item Type: Article
Erschienen: 2018
Creators: Diewald, Felix ; Kuhn, Charlotte ; Heier, Michaela ; Langenbach, Kai ; Horsch, Martin ; Hasse, Hans ; Müller, Ralf
Type of entry: Bibliographie
Title: Investigating the stability of the phase field solution of equilibrium droplet configurations by eigenvalues and eigenvectors
Language: English
Date: January 2018
Publisher: Elsevier
Journal or Publication Title: Computational Materials Science
Volume of the journal: 141
DOI: 10.1016/j.commatsci.2017.08.029
URL / URN: https://linkinghub.elsevier.com/retrieve/pii/S09270256173045...
Abstract:

Phase field models have recently been used to investigate the physical behavior of droplets in static as well as dynamic situations. As those models are often driven by an Allen-Cahn evolution equation, their stationary solution is given by the first order optimality condition of an energy functional. This includes the possibility of computing saddle points and maxima rather than minima of the energy functional. The present work shows the post-processing of eigenvalues and eigenvectors of the system matrix of the phase field model in order to investigate the stability of equilibrium droplet configurations. This postprocessing can easily be ported to other evolution equations. The underlying phase field model is described and the resulting discrete finite element eigenvalue problem is stated. The investigation of eigenvalues and eigenvectors is illustrated by examples.

Divisions: 13 Department of Civil and Environmental Engineering Sciences
13 Department of Civil and Environmental Engineering Sciences > Mechanics
13 Department of Civil and Environmental Engineering Sciences > Mechanics > Continuum Mechanics
Date Deposited: 04 May 2022 13:34
Last Modified: 04 May 2022 13:34
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