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
Artikel, Bibliographie
Kurzbeschreibung (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.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2018 |
| Autor(en): | Diewald, Felix ; Kuhn, Charlotte ; Heier, Michaela ; Langenbach, Kai ; Horsch, Martin ; Hasse, Hans ; Müller, Ralf |
| Art des Eintrags: | Bibliographie |
| Titel: | Investigating the stability of the phase field solution of equilibrium droplet configurations by eigenvalues and eigenvectors |
| Sprache: | Englisch |
| Publikationsjahr: | Januar 2018 |
| Verlag: | Elsevier |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Computational Materials Science |
| Jahrgang/Volume einer Zeitschrift: | 141 |
| DOI: | 10.1016/j.commatsci.2017.08.029 |
| URL / URN: | https://linkinghub.elsevier.com/retrieve/pii/S09270256173045... |
| Kurzbeschreibung (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. |
| Fachbereich(e)/-gebiet(e): | 13 Fachbereich Bau- und Umweltingenieurwissenschaften 13 Fachbereich Bau- und Umweltingenieurwissenschaften > Fachgebiete der Mechanik 13 Fachbereich Bau- und Umweltingenieurwissenschaften > Fachgebiete der Mechanik > Fachgebiet Kontinuumsmechanik |
| Hinterlegungsdatum: | 04 Mai 2022 13:34 |
| Letzte Änderung: | 04 Mai 2022 13:34 |
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