In this article we present a formulation for the numerical computation of static magnetic fields in discontinuous media. Focusing on solving magneto-fuid-structure interaction problems, we developed a finite volume multi-region framework capable of treating an arbitrary number of magnetized, permeable and current carrying bodies. The balance equations are written in terms of the magnetic vector potential leading to a formulation with discontinuous boundary conditions at interfaces between regions. We derived a consistent formulation of the discrete interface boundary conditions which guarantee accurate results for the magnetic field. The computational framework is based on a multi-region implementation that relies on non-conformal field mapping between and an implicit-explicit iterative solution procedure. Several numerical experiments show that the formulation gives good results for orthogonal meshes in terms of magnitude and direction of the magnetic field. We executed a numerical uncertainty analysis for a test case where a volumetric current, a permanent magnet and a ferromagnetic material interact between each other; we report apparent orders of accuracy, grid convergence indexes and grid convergence curves for several points of the computational domain.

在本文中，我们提出了一种用于非连续介质中静磁场数值计算的公式。着重解决磁流体结构相互作用问题，我们开发了一种能够处理任意数量的磁化，可渗透和载流体的有限体积多区域框架。根据磁矢量势来写平衡方程，从而导致公式在区域之间的界面处具有不连续的边界条件。我们得出了离散界面边界条件的一致表述，以保证磁场的精确结果。该计算框架基于多区域实现，该实现依赖于非保形字段之间的映射以及隐式-显式迭代求解过程。几个数值实验表明，该公式对于正交网格在磁场的大小和方向上都给出了良好的结果。我们对一个测试案例进行了数值不确定性分析，在该案例中，体积电流，永磁体和铁磁材料之间相互作用；我们报告了计算域几个点的准确性，网格收敛指数和网格收敛曲线的明显顺序。