Time-fractional Allen-Cahn and Cahn-Hilliard phase-field models and their numerical investigation

摘要

We study (time) fractional Allen-Cahn and Cahn-Hilliard phase-field models to account for the anomalously subdiffusive transport behavior in heterogeneous porous materials or memory effect of certain materials. We develop an efficient finite difference scheme and a Fourier spectral scheme to effectively treat the significantly increased memory requirement and computational complexity, which arise due to the nonlocal behavior of the time-fractional models.