Efficient solution of 3D electromagnetic eddy-current problems within the finite volume framework of OpenFOAM

TL;DR

This paper introduces a novel finite volume method within OpenFOAM for efficiently solving 3D electromagnetic eddy-current problems, enabling coupled multi-physics simulations with complex geometries.

Contribution

It presents a semi-coupled multi-mesh approach using Coulomb gauge potentials and Biot-Savart law, along with a discretisation scheme for conductivity discontinuities, advancing electromagnetic modeling in OpenFOAM.

Findings

Validated the method with extensive numerical tests.

Achieved efficient modeling of complex 3D geometries.

Demonstrated potential for coupled multi-physics simulations.

Abstract

Eddy-current problems occur in a wide range of industrial and metallurgical applications where conducting material is processed inductively. Motivated by realising coupled multi-physics simulations, we present a new method for the solution of such problems in the finite volume framework of foam-extend, an extended version of the very popular OpenFOAM software. The numerical procedure involves a semi-coupled multi-mesh approach to solve Maxwell's equations for non-magnetic materials by means of the Coulomb gauged magnetic vector potential and the electric scalar potential. The concept is further extended on the basis of the impressed and reduced magnetic vector potential and its usage in accordance with Biot-Savart's law to achieve a very efficient overall modelling even for complex three-dimensional geometries. Moreover, we present a special discretisation scheme to account for possible discontinuities in the electrical conductivity. To complement our numerical method, an extensive validation is completing the paper, which provides insight into the behaviour and the potential of our approach.