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Efficient fully-decoupled and fully-discrete explicit-IEQ numerical algorithm for the two-phase incompressible flow-coupled Cahn-Hilliard phase-field model

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Abstract

In this paper, an efficient fully-decoupled and fully-discrete numerical scheme with second-order temporal accuracy is developed to solve the incompressible hydrodynamically coupled Cahn-Hilliard model for simulating the two-phase fluid flow system. The scheme is developed by combining the finite element method for spatial discretization and several effective time marching approaches, including the pressure-correction projection method for dealing with fluid equations and the explicit-invariant energy quadratization (explicit-IEQ) approach for dealing with coupled nonlinear terms. The obtained scheme is very efficient since it only needs to solve several decoupled, linear elliptic equations with constant coefficients at each time step. We also strictly prove the solvability and unconditional energy stability of the scheme, and verify the accuracy and stability of the scheme through plenty of numerical examples.

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Acknowledgements

Chuanjun Chen was supported by National Natural Science Foundation of China (Grant No. 12271468) and Shandong Province Natural Science Foundation (Grant Nos. ZR2021ZD03 and ZR2021MA010). Xiaofeng Yang was supported by National Science Foundation of USA (Grant No. DMS-2012490).

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Authors and Affiliations

  1. School of Mathematics and Information Sciences, Yantai University, Yantai, 264005, China

    Chuanjun Chen

  2. Department of Mathematics, University of South Carolina, Columbia, SC, 29208, USA

    Xiaofeng Yang

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  1. Chuanjun Chen
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  2. Xiaofeng Yang
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Correspondence to Xiaofeng Yang.

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Chen, C., Yang, X. Efficient fully-decoupled and fully-discrete explicit-IEQ numerical algorithm for the two-phase incompressible flow-coupled Cahn-Hilliard phase-field model. Sci. China Math. (2023). https://doi.org/10.1007/s11425-022-2096-x

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