Numerical approximation of the Chan-Hillard equation with memory effects in the dynamics of phase separation

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2011, 2011(Special): 953-962. doi: 10.3934/proc.2011.2011.953

Numerical approximation of the Chan-Hillard equation with memory effects in the dynamics of phase separation

Nicolas Lecoq ^1, , Helena Zapolsky ^1, and P.K. Galenko ^2,

1.	Groupe de Physique de Matériaux UMR CNRS6634, Université de Rouen, 1, Avenue de l'Université, 76801 Saint-Etienne du Rouvray, France
2.	Institut für Materialphysik im Weltraum, DLR- Deutsches Zentrum für Luft- und Raumfahrt, 51170 Köln

Received July 2010 Revised May 2011 Published October 2011

Abstract
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We consider the modified Cahn-Hilliard equation for phase separation suggested to account for spinodal decomposition in deeply supercooled binary alloy systems or glasses. This equation contains, as additional term, the second-order time derivative of the concentration multiplied by a positive coefficient $\Tau_d$ (time for relaxation). We consider a numerical approximation scheme based on Fourier spectral method and perform numerical analysis of the scheme. We present results of numerical simulations for three spatial dimensions, and examine the stability and convergence of the scheme.

Keywords: Cahn-Hilliard equation, Numerical analysis., Memory effects, Spinodal decomposition.

Mathematics Subject Classification: Primary: 65M12, 65M22, 68U20; Secondary: 74D1.

Citation: Nicolas Lecoq, Helena Zapolsky, P.K. Galenko. Numerical approximation of the Chan-Hillard equation with memory effects in the dynamics of phase separation. Conference Publications, 2011, 2011 (Special) : 953-962. doi: 10.3934/proc.2011.2011.953

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