TY - JOUR
T1 - Linear, Second-Order Accurate, and Energy Stable Scheme for a Ternary Cahn–Hilliard Model by Using Lagrange Multiplier Approach
AU - Yang, Junxiang
AU - Kim, Junseok
N1 - Funding Information:
J. Yang is supported by China Scholarship Council (201908260060). The corresponding author (J.S. Kim) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2019R1A2C1003053).
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature B.V.
PY - 2021/4
Y1 - 2021/4
N2 - We develop a second-order accurate, energy stable, and linear numerical method for a ternary Cahn–Hilliard (CH) model. The proposed scheme is an extension of typical Lagrange multiplier approach for binary CH system. The second-order backward difference formula (BDF2) is applied to construct time discretization. We theoretically prove the mass conservation, unique solvability, and energy stability of the proposed scheme. We efficiently solve the resulting discrete linear system by using a multigrid algorithm. The numerical solutions demonstrate that the proposed scheme is practically stable and second-order accurate in time and space. Moreover, we can use the proposed scheme as an effective solver to calculate the ternary CH equations in ternary phase-field fluid systems.
AB - We develop a second-order accurate, energy stable, and linear numerical method for a ternary Cahn–Hilliard (CH) model. The proposed scheme is an extension of typical Lagrange multiplier approach for binary CH system. The second-order backward difference formula (BDF2) is applied to construct time discretization. We theoretically prove the mass conservation, unique solvability, and energy stability of the proposed scheme. We efficiently solve the resulting discrete linear system by using a multigrid algorithm. The numerical solutions demonstrate that the proposed scheme is practically stable and second-order accurate in time and space. Moreover, we can use the proposed scheme as an effective solver to calculate the ternary CH equations in ternary phase-field fluid systems.
KW - Energy stable scheme
KW - Multigrid method
KW - Second-order accuracy
KW - Ternary Cahn–Hilliard model
UR - http://www.scopus.com/inward/record.url?scp=85103413016&partnerID=8YFLogxK
U2 - 10.1007/s10440-021-00405-6
DO - 10.1007/s10440-021-00405-6
M3 - Article
AN - SCOPUS:85103413016
SN - 0167-8019
VL - 172
JO - Acta Applicandae Mathematicae
JF - Acta Applicandae Mathematicae
IS - 1
M1 - 10
ER -