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A High-Order Convex Splitting Method for a Non-Additive Cahn-Hilliard Energy Functional
- A High-Order Convex Splitting Method for a Non-Additive Cahn-Hilliard Energy Functional
- Lee, Hyun Geun; Shin, Jaemin; Lee, June-Yub
- Ewha Authors
- 이준엽; 신재민
- SCOPUS Author ID
- 이준엽; 신재민
- Issue Date
- Journal Title
- MATHEMATICS vol. 7, no. 12
- multi-component Cahn-Hilliard system; constrained convex splitting; unconditional unique solvability; unconditional energy stability; high-order time accuracy
- SCIE; SCOPUS
- Document Type
- 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.
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