In this paper, we consider numerical approximation of an electrically conductive ferrofluid model, which consists of Navier-Stokes equations, magnetization equation, and magnetic induction equation. To solve this highly coupled, nonlinear, and multiphysics system efficiently, we develop a decoupled, linear, second-order in time, and unconditionally energy stable finite element scheme. We incorporate several distinct numerical techniques, including reformulations of the equations and a scalar auxiliary variable to handle the coupled nonlinear terms,a symmetric implicit-explicit treatment for the symmetric positive definite nonlinearity, and stable finite element approximations. We also prove that the numerical scheme is provably uniquely solvable and unconditionally energy stable rigorously. A series of numerical examples are presented to illustrate the accuracy and performance of our scheme.

翻译：本文研究了一种导电铁磁流体模型的数值逼近问题，该模型由纳维-斯托克斯方程、磁化方程和磁感应方程构成。为高效求解这一高度耦合、非线性且涉及多物理场的系统，我们提出了一种解耦、线性、时间二阶精度且无条件能量稳定的有限元格式。我们整合了多种独特的数值技术，包括：通过方程重构与标量辅助变量处理耦合非线性项，对对称正定非线性项采用对称隐式-显式处理，以及稳定的有限元逼近方法。我们严格证明了该数值格式具有可证明的唯一可解性与无条件能量稳定性。通过一系列数值算例，验证了所提格式的精度与性能。