A single–region Finite Volume framework for modeling discontinuous magnetic field distributions

Abstract

In this paper we present a novel method to model discontinuous distributions of magnetic fields. The method is based on a finite volume discretization of a divergence form of the magnetostatic equations. The theoretical framework is written in terms of the vector potential, therefore, the computational implementation is capable of predicting the magnetic field distribution in permeable, permanently magnetized, and current-carrying media. The use of a single-region meshing scheme simplifies the simulation set-up due to the fact that it avoids the use of interface boundary conditions. This renders it computationally more effective than the multi-region counterpart. In order to test the performance of the present approach we execute several numerical experiments and compare the results against a multi-region discontinuous method and a single-region boundary layerless method. The experiments demonstrate that provided the boundary layer complies with certain topological rules, the method gives accurate results of the magnitude and direction of the magnetic field, both near and far from the interfaces. We show that, for orthogonal meshes, the results obtained with a single-region approach using boundary layers are comparable to the results obtained with a multi-region framework that imposes the magnetic field gradient discontinuity as a boundary condition.