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A High-Order Convex Splitting Method for a Non-Additive Cahn-Hilliard Energy Functional

Title
A High-Order Convex Splitting Method for a Non-Additive Cahn-Hilliard Energy Functional
Authors
Lee, Hyun GeunShin, JaeminLee, June-Yub
Ewha Authors
이준엽신재민
SCOPUS Author ID
이준엽scopus; 신재민scopus
Issue Date
2019
Journal Title
MATHEMATICS
ISSN
2227-7390JCR Link
Citation
MATHEMATICS vol. 7, no. 12
Keywords
multi-component Cahn-Hilliard systemconstrained convex splittingunconditional unique solvabilityunconditional energy stabilityhigh-order time accuracy
Publisher
MDPI
Indexed
SCIE; SCOPUS WOS
Document Type
Article
Abstract
Various Cahn-Hilliard (CH) energy functionals have been introduced to model phase separation in multi-component system. Mathematically consistent models have highly nonlinear terms linked together, thus it is not well-known how to split this type of energy. In this paper, we propose a new convex splitting and a constrained Convex Splitting (cCS) scheme based on the splitting. We show analytically that the cCS scheme is mass conserving and satisfies the partition of unity constraint at the next time level. It is uniquely solvable and energy stable. Furthermore, we combine the convex splitting with the specially designed implicit-explicit Runge-Kutta method to develop a high-order (up to third-order) cCS scheme for the multi-component CH system. We also show analytically that the high-order cCS scheme is unconditionally energy stable. Numerical experiments with ternary and quaternary systems are presented, demonstrating the accuracy, energy stability, and capability of the proposed high-order cCS scheme.
DOI
10.3390/math7121242
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자연과학대학 > 수학전공 > Journal papers
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