Higher order finite difference schemes for the magnetic induction equations with resistivity

TL;DR

This paper develops high-order, energy-stable finite difference schemes for the magnetic induction equations with resistivity, using SBP operators and SAT boundary conditions, validated through numerical experiments.

Contribution

It introduces a novel combination of SBP and SAT techniques to achieve stable, high-order accurate schemes for resistive magnetic induction equations.

Findings

Schemes are proven to be energy stable.

Numerical experiments confirm high-order accuracy.

Methods outperform lower-order schemes in stability and precision.

Abstract

In this paper, we design high order accurate and stable finite difference schemes for the initial-boundary value problem, associated with the magnetic induction equation with resistivity. We use Summation-By-Parts (SBP) finite difference operators to approximate spatial derivatives and a Simultaneous Approximation Term (SAT) technique for implementing boundary conditions. The resulting schemes are shown to be energy stable. Various numerical experiments demonstrating both the stability and the high order of accuracy of the schemes are presented.