an:06409991
Zbl 1306.65266
Lecoq, Nicolas; Zapolsky, Helena; Galenko, P. K.
Numerical approximation of the Cahn-Hillard equation with memory effects in the dynamics of phase separation
EN
Discrete Contin. Dyn. Syst. 2011, Suppl., 953-962 (2011).
00338613
2011
j
65M70 65M12 65M22 80A22
Cahn-Hilliard equation; spinodal decomposition; memory effects; numerical analysis
Summary: 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.