Helicity-conservative finite element discretization for incompressible MHD systems

TL;DR

This paper introduces finite element methods for incompressible MHD systems that exactly preserve key physical invariants like magnetic helicity, cross helicity, energy, and magnetic divergence at the discrete level, ensuring physical fidelity.

Contribution

It develops a novel finite element discretization using discrete differential forms that conserves multiple invariants simultaneously for incompressible MHD systems.

Findings

Numerical tests demonstrate the method's effectiveness.

The scheme preserves invariants exactly at the discrete level.

Improved physical accuracy over traditional methods.

Abstract

We construct finite element methods for the incompressible magnetohydrodynamics (MHD) system that precisely preserve magnetic and cross helicity, the energy law and the magnetic Gauss law at the discrete level. The variables are discretized as discrete differential forms in a de Rham complex. We present numerical tests to show the performance of the algorithm.