Efficient IMEX and consistently energy-stable methods of diffuse-interface models for incompressible three-component flows

Junxiang Yang, Jian Wang, Zhijun Tan, Junseok Kim

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8 Citations (Scopus)

Abstract

In this study, we consider the numerical approximation of incompressible three-component fluids, in which the fluid interfaces are captured by ternary Cahn–Hilliard equations and the fluid flows are governed by Navier–Stokes equations. This system includes not only nonlinear effects but also coupling among phase-field variables, velocities, and pressure. The ternary Cahn–Hilliard–Navier–Stokes system also satisfies the energy dissipation law, which is a basic physical property. For the appropriate treatment of the nonlinear and coupling terms and preservation of the energy dissipation law in a discrete version, we develop second-order time-accurate, linearly implicit-explicit (IMEX) methods using a variation of the scalar auxiliary variable (SAV) method. To improve the consistency between the original and modified energies, a simple and effective energy relaxation technique is considered. We analytically proved the unique solvability and the relaxed energy dissipation law. The proposed schemes are highly efficient for implementation because only linear elliptic equations need to be solved separately. Extensive computational experiments are performed to validate the accuracy, energy stability, and performance of the proposed method. To facilitate further study, we provide the C codes for the typical numerical simulations at http://github.com/yang521.

Original languageEnglish
Article number108558
JournalComputer Physics Communications
Volume282
DOIs
Publication statusPublished - 2023 Jan

Bibliographical note

Funding Information:
The author J. Yang is supported by the China Postdoctoral Science Foundation (No. 2022M713639 ) and the 2022 International Postdoctoral Exchange Fellowship Program (Talent-Introduction Program) (No. YJ20220221 ). J. Yang is supported by the National Natural Science Foundation of China (No. 12201657 ), the China Postdoctoral Science Foundation (No. 2022M713639 ), and the 2022 International Postdoctoral Exchange Fellowship Program (Talent-Introduction Program) (No. YJ20220221 ). Jian Wang expresses thanks for the Startup Foundation for Introducing Talent of NUIST , and Jiangsu shuangchuang project ( JSSCBS20210473 ). Z. Tan is supported by the National Nature Science Foundation of China ( 11971502 ), Guangdong Natural Science Foundation ( 2022A1515010426 ), Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University ( 2020B1212060032 ), and Key-Area Research and Development Program of Guangdong Province ( 2021B0101190003 ). The corresponding author (J.S. Kim) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2022R1A2C1003844 ). The authors thank the reviewers for their constructive comments on this revision.

Publisher Copyright:
© 2022 Elsevier B.V.

Keywords

  • Energy stability
  • Linear method
  • Relaxation technique
  • Three-component fluids

ASJC Scopus subject areas

  • Hardware and Architecture
  • General Physics and Astronomy

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