Higher order finite difference schemes for the magnetic induction equations

TL;DR

This paper develops high order finite difference schemes using SBP and SAT techniques for stable, accurate simulation of magnetic induction equations, validated through numerical experiments.

Contribution

It introduces a novel combination of SBP operators and SAT boundary conditions for high order stable discretization of magnetic induction equations.

Findings

Schemes achieve high order accuracy in numerical tests.

The methods demonstrate stability for initial-boundary value problems.

Numerical experiments confirm the effectiveness of the proposed schemes.

Abstract

We describe high order accurate and stable finite difference schemes for the initial-boundary value problem associated with the magnetic induction equations. These equations model the evolution of a magnetic field due to a given velocity field. The finite difference schemes are based on Summation by Parts (SBP) operators for spatial derivatives and a Simultaneous Approximation Term (SAT) technique for imposing boundary conditions. We present various numerical experiments that demonstrate both the stability as well as high order of accuracy of the schemes.