On Overcoming the Transverse Boundary Error of the SU/PG Scheme for Moving Conductor Problems

TL;DR

This paper addresses the transverse boundary error in the SU/PG scheme for moving conductor problems by removing Coulomb's gauge, improving solution accuracy while maintaining computational efficiency.

Contribution

It introduces a gauge removal technique to mitigate boundary errors in the SU/PG scheme for moving conductors, enhancing numerical stability.

Findings

Reduced boundary error in numerical simulations.

Maintained computational efficiency of GFEM.

Improved physical accuracy of solutions.

Abstract

Conductor moving in magnetic field is quite common in electrical equipment. The numerical simulation of such problem is vital in their design and analysis of electrical equipment. The Galerkin finite element method (GFEM) is a commonly employed simulation tool, nonetheless, due to its inherent numerical instability at higher velocities, the GFEM requires upwinding techniques to handle moving conductor problems. The Streamline Upwinding/Petrov-Galerkin (SU/PG) scheme is a widely acknowledged upwinding technique, despite its error-peaking at the transverse boundary. This error at the transverse-boundary, is found to be leading to non-physical solutions. Several remedies have been suggested in the allied fluid dynamics literature, which employs non-linear, iterative techniques. The present work attempts to address this issue, by retaining the computational efficiency of the GFEM. By suitable analysis, it is shown that the source of the problem can be attributed to the Coulomb's gauge. Therefore, to solve the problem, the Coulomb's gauge is taken out from the formulation and the associated weak form is derived. The effectiveness of this technique is demonstrated with pertinent numerical results.