An unconditionally energy-stable second-order time-accurate numerical scheme for the coupled Cahn–Hilliard system in copolymer/homopolymer mixtures

Li, Yibao; Lujing, Zhang; Qin, Xia; Yu, Qin; Kim, Junseok

doi:10.1016/j.commatsci.2021.110809

Cited by 12 publications

(1 citation statement)

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“…For example, Yang and Kim [31] proposed a coupled scheme by using the Lagrange multiplier approach and the second-order backward difference formula (BDF2) method. Li et al [24] presented a linearized implicit and coupled scheme by using the Crank-Nicolson-type method and a nonlinearly stabilized splitting approach. Li and Mei [20] developed a family of coupled schemes by using the BDF2 method and the SAV approach.…”

Section: Introductionmentioning

confidence: 99%

A Decoupled, Linearly Implicit and Unconditionally Energy Stable Scheme for the Coupled Cahn-Hilliard Systems

Zhao,

Li,

Wen

2024

JCM

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We present a decoupled, linearly implicit numerical scheme with energy stability and mass conservation for solving the coupled Cahn-Hilliard system. The time-discretization is done by leap-frog method with the scalar auxiliary variable (SAV) approach. It only needs to solve three linear equations at each time step, where each unknown variable can be solved independently. It is shown that the semi-discrete scheme has second-order accuracy in the temporal direction. Such convergence results are proved by a rigorous analysis of the boundedness of the numerical solution and the error estimates at different time-level. Numerical examples are presented to further confirm the validity of the methods.

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Section: Introductionmentioning

confidence: 99%