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

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  • We consider the modifi ed 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.
    Mathematics Subject Classification: Primary: 65M12, 65M22, 68U20; Secondary: 74D10.

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