Mathematical modeling and simulation of two-phase magnetohydrodynamic flows at low magnetic Reynolds numbers
Jiancheng Wang, Maojun Li, Zeyu Xia, Liwei Xu
我们提出了一种用于模拟不可压缩两相磁流体动力学(MHD)问题的新型数学框架。针对低磁雷诺数体系（其中感应磁场相对于外加磁场可忽略不计），首先建立了本征的锐界面系统。随后，我们采用相场方法表征界面，并通过昂萨格变分原理推导出热力学一致的相场模型。所得系统将两相流动的Abels–Garcke–Grün(AGG)模型与描述电磁现象的准静态公式相耦合。理论上，通过渐近分析研究了锐界面极限，推导出在界面厚度趋近于零时可恢复锐界面系统，从而证明了相场方法作为近似求解方法的可靠性。此外，我们展示了磁场对气泡动力学阻尼效应的三维数值实验，观测结果验证了所提框架在捕捉复杂MHD现象方面的有效性。
We propose a novel mathematical framework for simulating the two-phase incompressible magnetohydrodynamic (MHD) problems. Focusing on low magnetic Reynolds number regimes, where induced magnetic fields are negligible compared to applied fields, an intrinsic sharp-interface system is first formulated. Subsequently, we utilize the phase-field approach to characterize the interface and derive a thermodynamically consistent phase-field model through the Onsager's variational principle. The resulting...