A Stable Weighted Residual Finite Element Formulation for the Simulation of Linear Moving Conductor Problems

TL;DR

This paper introduces a parameter-free, stable weighted residual finite element formulation for simulating linear moving conductor problems, effectively reducing numerical oscillations and improving accuracy in 1D, 2D, and 3D cases.

Contribution

It develops a novel, parameter-free weighted residual formulation that enhances stability and accuracy in finite element simulations of moving conductors.

Findings

The formulation is analytically stable for 1D problems.

It achieves higher convergence rates and accuracy in test cases.

Stability is demonstrated in 3D simulations.

Abstract

The finite element method is one of the widely employed numerical techniques in electrical engineering for the study of electric and magnetic fields. When applied to the moving conductor problems, the finite element method is known to have numerical oscillations in the solution. To resolve this, the upwinding techniques, which are developed for the transport equation are borrowed and directly employed for the magnetic induction equation. In this work, an alternative weighted residual formulation is explored for the simulation of the linear moving conductor problems. The formulation is parameter-free and the stability of the formulation is analytically studied for the 1D version of the moving conductor problem. Then the rate of convergence and the accuracy are illustrated with the help of several test cases in 1D as well as 2D. Subsequently, the stability of the formulation is demonstrated with a 3D moving conductor simulation.