A finite volume formulation for magnetostatics of discontinuous media within a multi-region OpenFOAM framework

Abstract

In this article we present a formulation for the numerical computation of static magnetic fields in discontinuous media. Focusing on solving magneto-fluid-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.