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Second-order energy stable schemes for the new model of the Cahn-Hilliard-MHD equations

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Abstract

To simulate the two-phase flow of conducting fluids, we propose a coupled model of the Cahn-Hilliard equations and the inductionless and incompressible magnetohydrodynamic (MHD) equations. The model describes the dynamic behavior of conducting fluid under the influence of magnetic field. Based on the “invariant energy quadratization” method, we propose two fully discrete time-marching schemes which are linear, decoupled, unconditionally energy stable, and of second order. The well-posedness and energy stability of the discrete problems are proven. By extensive numerical experiments, we verify the second-order convergence of the numerical methods and demonstrate the capability of the coupled model for simulating two-phase flows.

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Funding

R. Chen is supported in part from the National Natural Science Foundation of China (NSFC), grants 12001055 and 11971072. H. Zhang is supported in part by the grants NSFC-11471046 and 11571045.

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Authors and Affiliations

  1. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, People’s Republic of China

    Rui Chen

  2. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, 100875, People’s Republic of China

    Hui Zhang

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  1. Rui Chen
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  2. Hui Zhang
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Correspondence to Rui Chen.

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Communicated by: Aihui Zhou

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Chen, R., Zhang, H. Second-order energy stable schemes for the new model of the Cahn-Hilliard-MHD equations. Adv Comput Math 46, 79 (2020). https://doi.org/10.1007/s10444-020-09822-x

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