A finite volume scheme for the solution of discontinuous magnetic field distributions on non-orthogonal meshes

We present a finite volume method for solving discontinuous magnetostatics on general non-orthogonal meshes. The proposed scheme captures field discontinuities across material interfaces by enforcing local conservation of the magnetic vector potential. Second-order spatial accuracy is achieved on highly skewed grids through the use of non-orthogonal correction schemes and gradient reconstruction techniques. A Block Gauss–Seidel iterative solver with under-relaxation is employed to ensure stable convergence even in strongly magnetized, high-permeability regions. A multi-region formulation guarantees conservative magnetic flux continuity at interfaces, eliminating the spurious flux leakage and field smearing that can plague conventional finite-element solutions. Verification against finite element solutions demonstrates that the method attains comparable accuracy while reducing computational cost. Grid Convergence Index studies indicate design-order (second-order) convergence in smooth-field regions. Furthermore, rigorous manufactured solution tests confirm near second-order convergence globally, validating the scheme’s theoretical order of accuracy across both homogeneous and discontinuous media. These results highlight the robustness, efficiency, and accuracy of the proposed framework. By synthesizing high-order finite volume discretization techniques, conservative interface coupling, and thorough verification practices, this work establishes FVM as a compelling, scalable alternative to classical FEM approaches for industrial-scale magnetostatic applications.