Hofmann, Tobias ; Müller, Ralf ; Andrä, Heiko (2017)
A fast immersed interface method for the Cahn–Hilliard equation with arbitrary boundary conditions in complex domains.
In: Computational Materials Science, 140
doi: 10.1016/j.commatsci.2017.08.025
Artikel, Bibliographie
Kurzbeschreibung (Abstract)
A fast immersed boundary method for the Cahn–Hilliard equation is introduced. The decomposition of the fourth-order non-linear Cahn–Hilliard equation into a system of linear parabolic second-order equations allows to pose arbitrary Neumann or surface wetting conditions on the boundary. In space a finitevolume discretization on a regular Cartesian voxel grid allows the use of fast parabolic solvers via Fourier transform of arbitrary convergence order. For the time discretization, a second-order Runge–Kutta scheme is applied. The polynomial approximation of the chemical potential results in a numerical scheme that is unconditionally gradient-stable and allows large time steps. With an additional pre-conditioner for the linear system, the condition of linear system is minimized. By this the convergence is independent of both spatial discretization and time step size. This allows for the simulation of phase separation in large porous complex domains with three dimensions and over hundred million degrees of freedom while applying arbitrary boundary conditions and using large time steps.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2017 |
| Autor(en): | Hofmann, Tobias ; Müller, Ralf ; Andrä, Heiko |
| Art des Eintrags: | Bibliographie |
| Titel: | A fast immersed interface method for the Cahn–Hilliard equation with arbitrary boundary conditions in complex domains |
| Sprache: | Englisch |
| Publikationsjahr: | Dezember 2017 |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Computational Materials Science |
| Jahrgang/Volume einer Zeitschrift: | 140 |
| DOI: | 10.1016/j.commatsci.2017.08.025 |
| URL / URN: | https://linkinghub.elsevier.com/retrieve/pii/S09270256173044... |
| Kurzbeschreibung (Abstract): | A fast immersed boundary method for the Cahn–Hilliard equation is introduced. The decomposition of the fourth-order non-linear Cahn–Hilliard equation into a system of linear parabolic second-order equations allows to pose arbitrary Neumann or surface wetting conditions on the boundary. In space a finitevolume discretization on a regular Cartesian voxel grid allows the use of fast parabolic solvers via Fourier transform of arbitrary convergence order. For the time discretization, a second-order Runge–Kutta scheme is applied. The polynomial approximation of the chemical potential results in a numerical scheme that is unconditionally gradient-stable and allows large time steps. With an additional pre-conditioner for the linear system, the condition of linear system is minimized. By this the convergence is independent of both spatial discretization and time step size. This allows for the simulation of phase separation in large porous complex domains with three dimensions and over hundred million degrees of freedom while applying arbitrary boundary conditions and using large time steps. |
| 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 13:33 |
| Letzte Änderung: | 04 Mai 2022 13:33 |
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