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A First-Order, Semi-Implicit, and Unconditionally Energy-Stable Scheme for an Incompressible Ferrohydrodynamics Flow
Xiaojing Dong, Huayi Huang and Yunqing Huang

J. Comp. Math. DOI: 10.4208/jcm.2402-m2023-0181

Publication Date : 2024-05-27

  • 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.

  • Copyright

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