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 - <p style="text-align: justify;">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.</p>