The present paper is devoted for numerical analysis of interface phenomena of magnetic fluids in real space and time, when the Boundary Element Method (BEM) is employed. The BEM obtains not only the magnetic potential and the normal magnetic induction for static magnetic fields but also the fluid velocity potential and the normal fluid velocity for incompressible–irrotational fluids, on arbitrary-shaped interfaces. During the discretizing process, one of the problems is the multiplicity, that is, multi-valued physical quantities at the edges and corners of the domains, or sharp-pointed peaks on the interface. Another problem is the singularity in the diagonal discretization terms, which is inherent to the BEM. Discretization elements at the same position are grouped for the multiplicity. The sum rules for discretization coefficients are used to avoid the singularity, which is derived from the uniform vector field conditions as the extension from the conventional one. Based on the formulated equations, a computational code was produced, and applied for simplified and more general conditions. This code generates magnetic fields on the interface between the fluid and the vacuum as intended with the least numerical effects. It also generates the fluid velocity caused by ununiform distribution of the sum of interface stresses. The applicability for the stability analysis on the Rosensweig instability is also discussed.

中文翻译：

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考虑多重性和奇异性的磁流体界面分析


本文致力于采用边界元法（BEM）对真实时空中的磁性流体界面现象进行数值分析。边界元法不仅可以获得静磁场的磁势和法向磁感应强度，还可以获得任意形状界面上不可压缩-无旋流体的流体速度势和法向流体速度。在离散化过程中，问题之一是多重性，即域的边角处的多值物理量，或界面上的尖峰。另一个问题是对角离散化项中的奇异性，这是边界元法所固有的。同一位置的离散化元素根据重数进行分组。离散化系数的求和规则是为了避免奇点，它是由均匀矢量场条件作为常规条件的扩展推导出来的。根据公式化的方程，生成了计算代码，并将其应用于简化和更一般的条件。该代码按照预期在流体和真空之间的界面上生成磁场，并且数值影响最小。它还会产生由界面应力总和的不均匀分布引起的流体速度。还讨论了 Rosensweig 不稳定性稳定性分析的适用性。