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- W2916171465 abstract "We study a space-fractional Allen-Cahn phase-field model in which the fractional Laplacian is defined to be an infinitesimal generator of an α-stable Lévy process with 0<α<2. Compared with the Allen-Cahn model using the Riemann-Liouville (R-L) fractional derivatives in the literature, the current model enjoys the following advantages: (1) it can control the sharpness and the decaying behavior of the interface via the tunable order parameter α as the Riemann-Liouville fractional model does; (2) it generates numerical solutions with sharper interfaces than the Riemann-Liouville fractional Allen-Cahn model with the same 1<α<2, and it can generate numerical solutions with even sharper interfaces as it also applies to the case for 0<α<1; (3) as α→2−, it provides good approximations to the classical Allen-Cahn model as the fractional Riemann-Liouville model does; (4) it is rotational invariant; and (5) it has a much slower mass decaying rate than the Riemann-Liouville fractional model. We also propose and analyze a first order in time and second order in space energy stable finite difference scheme." @default.
- W2916171465 created "2019-03-02" @default.
- W2916171465 creator A5033020983 @default.
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- W2916171465 date "2019-05-01" @default.
- W2916171465 modified "2023-10-06" @default.
- W2916171465 title "A fractional phase-field model using an infinitesimal generator of α stable Lévy process" @default.
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- W2916171465 doi "https://doi.org/10.1016/j.jcp.2019.01.042" @default.
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