A New time Integration Scheme for Cahn-hilliard Equations

R. Schaefer, M. Smol-ka, Lisandro Dalcin, M. Paszyn'ski

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations

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.
Original languageEnglish (US)
Title of host publicationProcedia Computer Science
PublisherElsevier BV
Pages1003-1012
Number of pages10
DOIs
StatePublished - Jun 1 2015

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