Scalar and vector potentials' coupling on nonmatching grids for the simulation of an electromagnetic brake
Purpose - We present a method for the simulation of the dynamical behavior of a coupled magneto-mechanical system given in terms of a conductor moving through an electromagnetic field. Design/methodology/approach - For the magnetic part, we consider a model based on an electric vector and a magnetic scalar potential, whereas the mechanical part is modelled by the equation of a rigid body motion. A weak coupling is employed: at each time step the resulting forces are calculated yielding the new displacement of the conductor. Findings - Numerical results are given for the simulation of an electromagnetic brake with axisymmetric geometry. They indicate that the proposed method is especially well suited for eddy current problems involving moving conductors. Research limitations/implications - Further research should be undertaken toward the application of the proposed method to real 3D problems. Originality/value - The spatial discretization of the problem relies on the use of two independent triangulations to approximate the two involved potentials. Whereas the scalar magnetic potential is discretized by means of nodal H-1-conforming finite elements on a grid covering the global computational domain, the vector electric potential is approximated by H-curl-conforming edge elements on another grid only covering the conductor. The coupling between the two grids is accomplished via the mortar finite element method. At each time step, only the coupling matrix has to be reassembled, all other involved matrices remain the same. Moreover, no remeshing is necessary when the conductor changes its position. The paper should be valuable for any researcher interested in the numerical simulation of eddy current problems.
electromagnetism eddy currents mathematical modelling