Second order convex splitting schemes for periodic nonlocal Cahn–Hilliard and Allen–Cahn equations

We devise second-order accurate, unconditionally uniquely solvable and unconditionally energy stable schemes for the nonlocal Cahn–Hilliard (nCH) and nonlocal Allen–Cahn (nAC) equations for a large class of interaction kernels. We present numerical evidence that both schemes are convergent. We solve...

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Bibliographic Details
Published in:Journal of computational physics 2014-11, Vol.277, p.48-71
Main Authors: Guan, Zhen, Lowengrub, John S., Wang, Cheng, Wise, Steven M.
Format: Article
Language:English
Subjects:
Energy stability
Multigrid
Nonlocal Cahn–Hilliard equation
Unique solvability
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Summary:We devise second-order accurate, unconditionally uniquely solvable and unconditionally energy stable schemes for the nonlocal Cahn–Hilliard (nCH) and nonlocal Allen–Cahn (nAC) equations for a large class of interaction kernels. We present numerical evidence that both schemes are convergent. We solve the nonlinear equations resulting from discretization using an efficient nonlinear multigrid method and demonstrate the performance of our algorithms by simulating nucleation and crystal growth for several different choices of interaction kernels.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2014.08.001