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Volume 43, Issue 4
A First-Order, Semi-Implicit, and Unconditionally Energy-Stable Scheme for an Incompressible Ferrohydrodynamics Flow

Xiaojing Dong, Huayi Huang & Yunqing Huang

DOI: 10.4208/jcm.2402-m2023-0181

J. Comp. Math., 43 (2025), pp. 866-897.

Published online: 2025-07

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  • Abstract

In this paper, we propose and analyze a first-order, semi-implicit, and unconditionally energy-stable scheme for an incompressible ferrohydrodynamics flow. We consider the constitutive equation describing the behavior of magnetic fluid provided by Shliomis, which consists of the Navier-Stokes equation, the magnetization equation, and the magnetostatics equation. By using an existing regularization method, we derive some prior estimates for the solutions. We then bring up a rigorous error analysis of the temporal semi-discretization scheme based on these prior estimates. Through a series of experiments, we verify the convergence and energy stability of the proposed scheme and simulate the behavior of ferrohydrodynamics flow in the background of practical applications.

  • Keywords

Unconditionally energy-stable scheme, Ferrohydrodynamics, Magnetic fluid, Prior estimates, Error analysis.

  • AMS Subject Headings

65N30, 65N12, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-43-866, author = {Dong , XiaojingHuang , Huayi and Huang , Yunqing}, title = {A First-Order, Semi-Implicit, and Unconditionally Energy-Stable Scheme for an Incompressible Ferrohydrodynamics Flow}, journal = {Journal of Computational Mathematics}, year = {2025}, volume = {43}, number = {4}, pages = {866--897}, abstract = {

In this paper, we propose and analyze a first-order, semi-implicit, and unconditionally energy-stable scheme for an incompressible ferrohydrodynamics flow. We consider the constitutive equation describing the behavior of magnetic fluid provided by Shliomis, which consists of the Navier-Stokes equation, the magnetization equation, and the magnetostatics equation. By using an existing regularization method, we derive some prior estimates for the solutions. We then bring up a rigorous error analysis of the temporal semi-discretization scheme based on these prior estimates. Through a series of experiments, we verify the convergence and energy stability of the proposed scheme and simulate the behavior of ferrohydrodynamics flow in the background of practical applications.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2402-m2023-0181}, url = {http://global-sci.org/intro/article_detail/jcm/24264.html} }
TY - JOUR T1 - A First-Order, Semi-Implicit, and Unconditionally Energy-Stable Scheme for an Incompressible Ferrohydrodynamics Flow AU - Dong , Xiaojing AU - Huang , Huayi AU - Huang , Yunqing JO - Journal of Computational Mathematics VL - 4 SP - 866 EP - 897 PY - 2025 DA - 2025/07 SN - 43 DO - http://doi.org/10.4208/jcm.2402-m2023-0181 UR - https://global-sci.org/intro/article_detail/jcm/24264.html KW - Unconditionally energy-stable scheme, Ferrohydrodynamics, Magnetic fluid, Prior estimates, Error analysis. AB -

In this paper, we propose and analyze a first-order, semi-implicit, and unconditionally energy-stable scheme for an incompressible ferrohydrodynamics flow. We consider the constitutive equation describing the behavior of magnetic fluid provided by Shliomis, which consists of the Navier-Stokes equation, the magnetization equation, and the magnetostatics equation. By using an existing regularization method, we derive some prior estimates for the solutions. We then bring up a rigorous error analysis of the temporal semi-discretization scheme based on these prior estimates. Through a series of experiments, we verify the convergence and energy stability of the proposed scheme and simulate the behavior of ferrohydrodynamics flow in the background of practical applications.

Dong , XiaojingHuang , Huayi and Huang , Yunqing. (2025). A First-Order, Semi-Implicit, and Unconditionally Energy-Stable Scheme for an Incompressible Ferrohydrodynamics Flow. Journal of Computational Mathematics. 43 (4). 866-897. doi:10.4208/jcm.2402-m2023-0181
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