A Finite Volume scheme for the solution of discontinuous magnetic field distributions on non-orthogonal meshes

TL;DR

This paper introduces a Finite Volume method for accurately computing discontinuous magnetic fields on complex non-orthogonal meshes, improving robustness and validation against established techniques.

Contribution

It develops a novel Finite Volume formulation for magnetic field distribution on non-orthogonal meshes, including a specialized solver and stabilization techniques.

Findings

Accurate magnetic field computation on complex meshes.

Effective solver with stabilization techniques.

Validation shows comparable or improved accuracy.

Abstract

We present a Finite Volume formulation for determining discontinuous distributions of magnetic fields within non-orthogonal and non-uniform meshes. The numerical approach is based on the discretization of the vector potential variant of the equations governing static magnetic field distribution in magnetized, permeable and current carrying media. After outlining the derivation of the magnetostatic balance equations and its associated boundary conditions, we propose a cell-centered Finite Volume framework for spatial discretization and a Block Gauss-Seidel multi-region scheme for solution. We discuss the structure of the solver, emphasizing its effectiveness and addressing stabilization and correction techniques to enhance computational robustness. We validate the accuracy and efficacy of the approach through numerical experiments and comparisons with the Finite Element method.