Szczegóły publikacji
Opis bibliograficzny
A new time integration scheme for Cahn-hilliard equations / R. SCHAEFER, M. SMOŁKA, L. Dalcin, M. PASZYŃSKI // Procedia Computer Science [Dokument elektroniczny]. — Czasopismo elektroniczne ; ISSN 1877-0509. — 2015 — vol. 51, s. 1003–1012. — Wymagania systemowe: Adobe Reader. — Bibliogr. s. 1011–1012, Abstr. — ICCS 2015 : International Conference On Computational Science : Computational Science at the Gates of Nature : June 1–3, 2015 in Reykjavík, Iceland
Autorzy (4)
- AGHSchaefer Robert
- AGHSmołka Maciej
- Dalcin Lisandro
- AGHPaszyński Maciej
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 90705 |
|---|---|
| Data dodania do BaDAP | 2015-07-10 |
| Tekst źródłowy | URL |
| DOI | 10.1016/j.procs.2015.05.244 |
| Rok publikacji | 2015 |
| Typ publikacji | referat w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Procedia Computer Science |
Abstract
In this paper we present a new integration scheme that can be applied to solving difficult non-stationary non-linear problems. It is obtained by a successive linearization of the Crank-Nicolson scheme, that is unconditionally stable, but requires solving non-linear equation at each time step. We applied our linearized scheme for the time integration of the challenging Cahn-Hilliard equation, modeling the phase separation in fluids. At each time step the resulting variational equation is solved using higher-order isogeometric finite element method, with B-spline basis functions. The method was implemented in the PETIGA framework interfaced via the PETSc toolkit. The GMRES iterative solver was utilized for the solution of a resulting linear system at every time step. We also apply a simple adaptivity rule, which increases the time step size when the number of GMRES iterations is lower than 30. We compared our method with a non-linear, two stage predictor-multicorrector scheme, utilizing a sophisticated step length adaptivity. We controlled the stability of our simulations by monitoring the Ginzburg-Landau free energy functional. The proposed integration scheme outperforms the two-stage competitor in terms of the execution time, at the same time having a similar evolution of the free energy functional. © The Authors.
