A finite volume method for ferrohydrodynamic problems coupled with microscopic magnetization dynamics
A finite volume method for ferrohydrodynamic problems coupled with microscopic magnetization dynamics
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DOI：
10.1016/j.amc.2022.127704
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发表时间：
2023-03
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影响因子：
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通讯作者：
Wenming Yang
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作者：
Wenming Yang
为铁磁流体动力学 (FHD) 开发了一种有限体积方法，用于处理受强磁极化力影响的流体运动力学。采用由连续性方程、动量方程、角动量方程、磁化方程和静磁泊松方程组成的Shliomis模型来描述流体动力学与磁化动力学强耦合的FHD问题。与之前大多数 FHD 模拟不同的是，我们经常使用类德拜磁化方程，而我们采用微观推导的磁化方程来描述铁磁流体磁化的演化，以便在各种流速、磁场强度和振荡频率下都有效。在所提出的方法中，每个控制方程都采用有限体积格式进行离散化，并且 FHD 中的变量（包括磁场、速度、压力和磁化强度）通过使用迭代解耦策略进行解耦。通过在内迭代循环中使用牛顿法迭代求解朗之万方程和使用有限体积法求解微观磁化方程来获得磁化场。将所提出的方法获得的结果与无磁场或有磁场下铁磁流体的库埃特-泊肃叶流的相应解析解或渐近解进行比较，验证了该方法在解决纯流体动力学、纯磁化动力学以及具有流体动磁耦合效应的一般 FHD 问题方面的可行性。
A finite volume method is developed for the ferrohydrodynamics (FHD) dealing with the mechanics of fluid motion influenced by strong forces of magnetic polarization. The Shliomis model consisting of the continuity equation, the momentum equation, the angular momentum equation, the magnetization equations, and the Poisson's equation of magnetostatics is adopted to describe the FHD problems, where the hydrodynamics are strongly coupled with the magnetization dynamics. Unlike most of the previous FHD simulations, where the Debye-like magnetization equation was frequently used, we employ the microscopically derived magnetization equation to describe the evolution of ferrofluid magnetization in order to be valid in a wide range of flow rates, magnetic field strengths and oscillating frequencies. In the proposed method, each governing equation is discretized by employing the finite-volume scheme, and the variables in FHD, including the magnetic field, velocity, pressure, and magnetization are uncoupled by using an iteratively uncoupled strategy. The magnetization field is obtained by iteratively solving a Langevin equation using Newton method and the microscopical magnetization equation employing finite volume method in an inner iterative loop. Comparisons of the results obtained by the proposed method with the corresponding analytic or asymptotic solutions for the Couette–Poiseuille flows of ferrofluids in the absence or subjected to magnetic fields validate its feasibility in solving the pure hydrodynamics, pure magnetization dynamics, and the general FHD problems with hydrodynamic-magnetic coupling effects.