A high-order convex splitting method for a non-additive Cahn-Hilliard energy functional

Hyun Geun Lee, Jaemin Shin, June Yub Lee

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish
Article number1242
Issue number12
StatePublished - 1 Dec 2019

Bibliographical note

Publisher Copyright:
© 2019 by the authors.


  • Constrained convex splitting
  • High-order time accuracy
  • Multi-component Cahn-Hilliard system
  • Unconditional energy stability
  • Unconditional unique solvability


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