An Efficient Eddy Current Model for Nonlinear Maxwell Equations with Laminated Conductors

Abstract

In this paper, we propose a new eddy current model for the nonlinear Maxwell equations with laminated conductors. Direct simulation of three-dimensional (3D) eddy currents in grain-oriented (GO) silicon steel laminations is very challenging since the coating film over each lamination is only several microns thick and the magnetic reluctivity is nonlinear and anisotropic. The system of GO silicon steel laminations has multiple sizes, and the ratio of the largest scale to the smallest scale can amount to $10^6$. The new model omits coating films and thus reduces the scale ratio by 2--3 orders of magnitude. It avoids very fine or very anisotropic mesh in coating films and can reduce computations greatly in computing 3D eddy currents. We establish the well-posedness of the new model and prove the convergence of the solution of the original problem to the solution of the new model as the thickness of coating films tends to zero. The new model is validated by finite element computations of an engineering benchmark problem---Team Workshop Problem $21^c$--M1.