A First-Order, Semi-Implicit, and Unconditionally Energy-Stable Scheme for an Incompressible Ferrohydrodynamics Flow
Year: 2025
Author: Xiaojing Dong, Huayi Huang, Yunqing Huang
Journal of Computational Mathematics, Vol. 43 (2025), Iss. 4 : pp. 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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2402-m2023-0181
Journal of Computational Mathematics, Vol. 43 (2025), Iss. 4 : pp. 866–897
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 32
Keywords: Unconditionally energy-stable scheme Ferrohydrodynamics Magnetic fluid Prior estimates Error analysis.
Author Details
-
A cost-efficient third-order upwind compact scheme with adjustable dissipation for entropically damped artificial compressibility model-based transient incompressible flows
Chen, Zhengxing | Shen, Rui | Tian, Zhenfu | Song, ZhenhuaPhysics of Fluids, Vol. 37 (2025), Iss. 3
https://doi.org/10.1063/5.0259769 [Citations: 0] -
A streamfunction-velocity formulation-based higher-order upwind compact difference method for solving unsteady natural convection
Wu, Shuang | Yan, Yaping | Chen, Zhengxing | Tian, ZhenfuPhysics of Fluids, Vol. 37 (2025), Iss. 6
https://doi.org/10.1063/5.0272570 [Citations: 0] -
An unconditionally stable variable time step scheme for two-phase ferrofluid flows
Keram, Aytura | Huang, Pengzhan | He, YinnianComputer Methods in Applied Mechanics and Engineering, Vol. 442 (2025), Iss. P.118018
https://doi.org/10.1016/j.cma.2025.118018 [Citations: 0]