Numerical Solution of a Transient Three-Dimensional Eddy Current Model with Moving Conductors

Abstract

The aim of this paper is to propose and analyze a numerical method to solve a time-dependent eddy current problem in a domain containing moving non magnetic conductors. To this end, we choose a formulation in terms of the magnetic field, what leads to a parabolic problem for which we prove an existence result. For space discretization, we propose a finite element method based on N\u00e9d\u00e9lec edge elements on a mesh that remains fixed over the time. The curl-free constraint in the dielectric domain is relaxed by means of a penalty strategy that can be easily implemented, without the need that the mesh fits the moving conducting and dielectric domains. For time discretization, we use a backward Euler scheme. We report some numerical results. First, we solve a test problem with a known analytical solution, which allows us to assess the convergence of the method as the penalization and discretization parameters go to zero. Finally, we solve a problem with cylindrical symmetry, which allows us to compare the results with those obtained with an axisymmetric code.