The Source Stabilized Galerkin Formulation for Linear Moving Conductor Problems with Edge Elements

TL;DR

This paper introduces a source stabilization technique for edge element finite element methods to accurately model linear moving conductor problems in electromagnetic devices, validated through analytical and simulation results.

Contribution

A novel, parameter-free stabilization scheme for edge elements in finite element analysis of moving conductors, improving accuracy without additional parameters.

Findings

Analytical proof of stability and accuracy

Successful 2D and 3D simulation demonstrations

Requires graded regular mesh along motion direction

Abstract

The phenomenon of linear motion of conductor in a magnetic field is commonly found in electric machineries such as, electromagnetic brakes, linear induction motor, electromagnetic flowmeter etc. The design and analysis of the same requires an accurate evaluation of induced currents and the associated reaction magnetic fields. The finite element method is a generally employed numerical technique for this purpose. However, it needs stabilization techniques to provide an accurate solution. In this work, such a stabilization technique is developed for the edge elements. The stability and hence the accuracy is brought in by a suitable representation of the source term. The stability and accuracy of the proposed scheme is first shown analytically and then demonstrated with the help of 2D and 3D simulations. The proposed scheme is parameter-free and it would require a graded regular mesh along the direction of motion.