Numerical approximation of the Cahn−Hilliard equation with memory effects in the dynamics of phase separation

N. Lecoq (1) , Helena Zapolsky (1) , Peter Galenko (2)

1 GPM - Groupe de physique des matériaux
2 DLR Institut für Materialphysik im Weltraum

We consider the modifified 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.

Domains: Physics [physics]

N. Lecoq, Helena Zapolsky, Peter Galenko. Numerical approximation of the Cahn−Hilliard equation with memory effects in the dynamics of phase separation. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS SUPPLEMENT, 2011, 31, pp.953-962. ⟨10.3934/proc.2011.2011.953⟩. ⟨hal-01777456⟩