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Deformation and coalescence of ferrodroplets in Rosensweig model using the phase field and modified level set approaches under uniform magnetic fields
Communications in Nonlinear Science and Numerical Simulation ( IF 3.9 ) Pub Date : 2020-02-05 , DOI: 10.1016/j.cnsns.2020.105213
Feng Bai , Daozhi Han , Xiaoming He , Xiaofeng Yang

By using both a phase field approach and a modified level set approach, two multiphase numerical models are proposed and compared in this paper to investigate the ferrodroplet deformation and merging process in a non-magnetic viscous medium under the influence of uniform magnetic fields. The finite element method is utilized for the spatial discretization of both numerical models. The numerical results show excellent agreement with the analytical solutions in the simple axisymmetric setting. The effects of different magnetic bond numbers and magnetic susceptibility on the deformation of ferrodroplets are systematically investigated. The coalescence process, in which two small ferrodroplets merge into a single larger droplet under uniform magnetic fields, is also studied by using both the phase field approach and the modified level set approach. Moreover the attraction phenomenon between two ferrodroplets, which was previously discovered in numerical experiments, is observed in our numerical tests. By comparing with analytical solutions, our study demonstrates that the diffuse interface (phase field) approach performs better than the modified level set approach when there is large topological deformation of the ferrodroplet. Several other important aspects, including the evolution of the flow field, the magnetic energy distribution, the spurious flows near the interfaces, and conservation of mass in both approaches, are studied as well.



中文翻译:

在均匀磁场下使用相场和改进的能级集方法在Rosensweig模型中铁滴的变形和合并

通过使用相场方法和改进的水平集方法,提出了两个多相数值模型并进行了比较,以研究均匀磁场影响下非磁性粘性介质中的铁滴形变和合并过程。有限元方法被用于两个数值模型的空间离散化。数值结果表明,在简单的轴对称设置中,解析解与解析解非常吻合。系统地研究了不同的磁键数和磁化率对铁滴变形的影响。还通过使用相场方法和改进的能级集方法研究了凝聚过程,在凝聚过程中,两个小的铁滴在均匀的磁场下合并为一个较大的液滴。此外,在我们的数值测试中观察到了两个铁滴之间的吸引现象,这是先前在数值实验中发现的。通过与解析解进行比较,我们的研究表明,当铁滴具有较大的拓扑变形时,扩散界面(相场)方法的性能优于改进的水平集方法。还研究了其他几个重要方面,包括流场的演化,磁能分布,界面附近的杂散流以及两种方法中的质量守恒。我们的研究表明,当铁滴具有较大的拓扑变形时,扩散界面(相场)方法的性能优于改进的水平集方法。还研究了其他几个重要方面,包括流场的演化,磁能分布,界面附近的杂散流以及两种方法中的质量守恒。我们的研究表明,当铁滴具有较大的拓扑变形时,扩散界面(相场)方法的性能优于改进的水平集方法。还研究了其他几个重要方面,包括流场的演化,磁能分布,界面附近的杂散流以及两种方法中的质量守恒。

更新日期:2020-02-05
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