TY - JOUR
T1 - Numerical study of the ternary Cahn–Hilliard fluids by using an efficient modified scalar auxiliary variable 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 ). The authors thank the reviewers for the constructive comments on the revision of this article.
Publisher Copyright:
© 2021 Elsevier B.V.
PY - 2021/11
Y1 - 2021/11
N2 - Herein, we propose linear, decoupled, and energy dissipation-preserving schemes for the ternary Cahn–Hilliard (CH) fluid models by using a modified scalar auxiliary variable (MSAV) approach. The ternary CH model has extensive applications in material and fluid fields. When the classical scalar auxiliary variable (SAV) method is used for the ternary CH problem, extra computational costs are needed because of the decoupling between local and non-local variables. The MSAV method considered in this study not only inherits the merits of classical SAV method, i.e., linear scheme and energy stability, but also allows simpler calculations. In one time iteration, we only need to solve a set of linear equations by a step-by-step procedure, thus the computation is highly efficient. To accelerate the convergence, a fast linear multigrid algorithm is adopted to solve the resulting discrete systems. Various numerical tests without and with fluid flows are performed to verify the good performance of the proposed methods.
AB - Herein, we propose linear, decoupled, and energy dissipation-preserving schemes for the ternary Cahn–Hilliard (CH) fluid models by using a modified scalar auxiliary variable (MSAV) approach. The ternary CH model has extensive applications in material and fluid fields. When the classical scalar auxiliary variable (SAV) method is used for the ternary CH problem, extra computational costs are needed because of the decoupling between local and non-local variables. The MSAV method considered in this study not only inherits the merits of classical SAV method, i.e., linear scheme and energy stability, but also allows simpler calculations. In one time iteration, we only need to solve a set of linear equations by a step-by-step procedure, thus the computation is highly efficient. To accelerate the convergence, a fast linear multigrid algorithm is adopted to solve the resulting discrete systems. Various numerical tests without and with fluid flows are performed to verify the good performance of the proposed methods.
KW - Efficient algorithm
KW - Energy dissipation
KW - Multigrid method
KW - Ternary Cahn–Hilliard fluids
UR - http://www.scopus.com/inward/record.url?scp=85108422958&partnerID=8YFLogxK
U2 - 10.1016/j.cnsns.2021.105923
DO - 10.1016/j.cnsns.2021.105923
M3 - Article
AN - SCOPUS:85108422958
VL - 102
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
SN - 1007-5704
M1 - 105923
ER -