Implementation and Formulation of a Multi-Region, Electromagnetic Solver for Discontinuous Media

  • Bogaers, Alfred (Ex Mente Technologies)
  • Roos, Willem (Ex Mente Technologies)
  • Reynolds, Quinn (Mintek)
  • Zietsman, Johan (Ex Mente Technologies)

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In this paper we present the formulation and implementation of a multi-region, electromagnetic solver into OpenFOAM, coupled using preCICE [2]. The electromagnetic solver was developed for application to electric smelting furnaces, within the field of pyrometallurgy. In these class of problems, material discontinuities typically exist between various regions within a furnace, often differing by several orders of magnitude. To facilitate solving Maxwell’s equations using the finite volume method (FVM), the equations were formulated in terms of Coulomb gauged magnetic vector potentials and scalar electric potentials. When posed in this form, the material discontinuities feature in both Laplace and divergence operators, leading to numerical instabilities when solved using standard, continuous, FVM discretisation schemes. The distinct material interfaces further lead to jump discontinuities in both the electric and magnetic fields when current interacts with a time varying magnetic field, as well as when magnetic fields interact with ferro-magnetic materials. Beckstein et al. [1] proposed resolving these discontinuities using embedded FVM discretisation schemes, similar to those used in free surface flow modelling. More recently, Saravia [3] presented a multi-region approach, where the discontinuities within the magnetic potential field were treated with appropriate boundary conditions. In the current work we extend on the multi-region idea of Saravia [3], by further posing appropriate jump conditions for the electric potential field interacting with time varying magnetic fields. The jump conditions for both the electric and magnetic potential fields are implemented as Robin transmission conditions using preCICE, and solved using iterative subcycling. We will demonstrate the robustness and accuracy of the solution procedure on a number of appropriate numerical test cases.