Applicability and performance analysis of the phase-field modelling based on the Cahn-Hilliard method for the binary alloy

Applicability and performance analysis of the phase-field modelling based on the Cahn-Hilliard method for the binary alloys

Kamil Dudek, Danuta Szeliga

AGH University of Science and Technology, Faculty of Metals Engineering and Industrial Computer Science, Mickiewicza 30, 30-059 Krakow, Poland.



The Cahn-Hilliard method descries the driving force of the process of phase separation. Considering a binary (two-phase) alloy of conserved composition variable, the C-H model makes it possible to trace the process at which the domain creates pure subdomains of each component. Gururajan et al. have offered a simplified reference implementation of the aforementioned model, using the C language and FFTW libraries. It allows to perform a reverse Fourier transform to acquire a domain composition profile at a given time. Being a proof-of-concept, this approach does not stress on performance and the dedicated tools, like OpenPhase might not provide the flexibility necessary for new implementations. The following work aims on analyzing the C-H algorithm with regards of optimization, taking the Gururajan, among others, as a reference problem. Utilizing the models accompanied by replicable results facilitates the analysis of FFTW and GSL libraries, answering whether to search the replacement implementations and where (if necessary) work on code performance and parallelization. Finally, the improved model is intended to be used on external (non-random) initial composition, taken from ongoing simulations, in hope of preparation of the pearlitic steel model in the future.

Cite as:

Dudek, K., Szeliga, D. (2016). Applicability and performance analysis of the phase-field modelling based on the Cahn-Hilliard method for the binary alloys. Computer Methods in Materials Science, 16(1), 37 – 46.

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Baldan, A., 2002, Review: Progress in Ostwald ripening theoriesand their applications to nickel-base superalloys,Part I: Ostwald ripening theories, Department ofMetallurgical and Materials Engineering, Mersin University.

Bhadeshia, H. K. D. H., 2004, Materials Science and Metallurgy,MP6, L15.

Boettinger, W. J., Warren, J. A., 2014, NIST Materials Scienceand Engineering Laboratory.

Cheng, M., Rutenberg, A. D., 2005, Maximally fast coarseningalgorithms, Physical Reviev E, 72, 055701R.

Elliott, C. M., 1989, The Cahn-Hilliard model for the kinetics ofphase separation, Mathematical Models for PhaseChange Problems, IS of Numerical Mathematics, 88, 2-3.

Gururajan, M. P., 2005, Phase field modelling of microstructuralevolution using the Cahn-Hilliard equation: A reportto accompany CH-muSE.Kalidindi, S. R., 2012, Computationally-Efficient Fully-CoupledMulti-Scale Modeling of Materials Phenomena UsingCalibrated Localization Linkages, ISRN Materials Science,2012, 305692.

Man, E., Kleijn, C. R., 2014, Numreical Studies on Phase FieldDiffusion and Flow Solvers, Resources of the TransportPhenomena Research Group, Delft University of Technology,Faculty of Applied Sciences.Moelans, N., Blanpain, B., Wollants, P., 2007, An introductionto phase-field modeling of microstructure evolution,Computer Coupling of Phase Diagrams and Thermochemistry,32, 268-294.

Pimpalgaonkar, H., 2011, Phase Field FOAM.Provatas, N., Elder, K., 2005, Phase-Field Methods in MaterialScience, Wiley-VCH.

Rapaport, D. C., 2002, The Art of Molecular Dynamics Simulation,Numerical Recipes: The Art of Scientific Computing,Cambridge University Press.

Wheeler, A. A., Boettinger, W. J., 1992, Phase-field model ofsolute trapping during solidification, Physical Review E,47, 3, 1893-1909.

Yamanaka, A., Takaki, T., 2007, Coupled simulation of microstructuralformation and deformation behavior of ferrite–pearlite steel by phase-field method and homogenizationmethod, Materials Science and Engineering A, 480, 1-2,244-252.