Upwind 3-D Vector Potential Formulation for Electromagnetic Braking Simulations

The calculation of motion-induced eddy currents in massive conductors yields a 3-D convection-diffusion problem. Up-winding and SUPG formulations are well established methods to obtain stable discretizations of the scalar convection-diffusion equations in the case of singular perturbation, but there is very little reported experience with the stability of convection in the vector case, i.e., electromagnetism. Numerical experiments with the up-winding method proposed by Xu (Trans. on Mag., 2006; 42:667-670, 2006) has proven it to be insufficient. Building on the work of Heumann (Research report 2008-30, Seminar für Angewandte Mathematik, Eidgenssische Technische Hochschule, Oct. 2008), an alternative approach based on a finite-element discretization of the Lie derivative implied by the convection phenomenon is proposed.