Finite Volume Magnetostatics

Abstract

This document presents an analysis of the Finite Volume Method applied to the resolution of discontinuous magnetic fi eld distributions, using spatial discretizations based on unstructured and non-orthogonal meshes. First, a specifi c mathematical formulation is developed to address magnetostatic systems, optimized to handle the inherent complexity of magnetic interactions in such discretizations. The formulation is implemented within the OpenFOAM simulation environment, known for its fl exibility and capability to solve complex problems. To validate the proposed method, detailed comparisons are made with results obtained from other established numerical methods, specifi cally the Finite Element Method using the COMSOL computational software. The results demonstrate that the fi nite volume method is eff ective in capturing variations in the magnetic fi eld, even in the presence of complex interactions between diff erent media. This study not only confi rms the robustness and accuracy of the method but also highlights its potential for application in magnetic scenarios with complex geometries.