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A Fully-Decoupled Artificial Compressible Crank–Nicolson–Leapfrog Time Stepping Scheme for the Phase Field Model of Two-Phase Incompressible Flows

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Abstract

In this paper, we consider efficient numerical approximations for the phase field model of two-phase incompressible flows. To develop easy-to-implement time stepping scheme, we introduce two types of nonlocal auxiliary variables to achieve highly efficient and fully-decoupled scheme based on the Crank–Nicolson–Leapfrog (CNLF) formula and artificial compression method. We prove that the scheme is linear and unconditionally energy stable. Ample numerical experiments are performed to demonstrate the accuracy, stability and efficiency.

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Funding

This work is in part supported by the NSF of China (No. 11861054), Natural Science Foundation of Guangxi, China (No. 2020GXNSFAA297223), the Science and technology project of Guangxi, China (No. Guike AD21220114), State Key Laboratory of High Temperature Gas Dynamics (No.2021KF02), the NSF of China (Nos. 12071406, U19A2079), Natural Science Foundation of Xinjiang (NO.2021D01C114).

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Authors and Affiliations

  1. College of Mathematics and Statistics in Guangxi Normal University, Guilin, 541006, People’s Republic of China

    Lingzhi Qian, Chunya Wu & Huiping Cai

  2. Department of Mathematics, College of Sciences, Shihezi University, Shihezi, 832003, People’s Republic of China

    Huiping Cai

  3. College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, People’s Republic of China

    Xinlong Feng & Yuanyang Qiao

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  1. Lingzhi Qian
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Correspondence to Yuanyang Qiao.

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This work is in part supported by the NSF of China (No. 11861054), Natural Science Foundation of Guangxi, China (No. 2020GXNSFAA297223), the Science and technology project of Guangxi, China (No. Guike AD21220114), State Key Laboratory of High Temperature Gas Dynamics (No.2021KF02), the NSF of China (Nos. 12071406, U19A2079), Natural Science Foundation of Xinjiang (No. 2021D01C114).

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Qian, L., Wu, C., Cai, H. et al. A Fully-Decoupled Artificial Compressible Crank–Nicolson–Leapfrog Time Stepping Scheme for the Phase Field Model of Two-Phase Incompressible Flows. J Sci Comput 94, 50 (2023). https://doi.org/10.1007/s10915-022-02048-7

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