Modified-gradient methods for exact divergence-free in meshless magnetohydrodynamics

TL;DR

This paper introduces a modified-gradient method for meshless magnetohydrodynamics that achieves exact divergence-free magnetic fields with high accuracy, improving simulation fidelity and reducing numerical errors compared to existing techniques.

Contribution

The paper proposes a novel implicit projection-based gradient regularization method that eliminates magnetic divergence errors in meshless MHD simulations, enhancing accuracy and conservation.

Findings

Achieves exact divergence-free magnetic fields with round-off precision.

Significantly improves magnetic field pattern and reduces numerical dissipation.

Outperforms the constrained-gradient method and GIZMO code in tests.

Abstract

We present a novel gradient regularization to completely eliminate the magnetic divergence error in meshless magnetohydrodynamics (MHD), which offers a high spatial resolution and conservative advantage, due to its Lagrangian nature. Comparing with the counterpart of constrained-gradient (CG) technique, we reform $\nabla \cdot \mathbf{B}=0$ by an implicit projection method to modify the magnetic-field gradients. The accuracy of modified-gradient (MG) method is verified and it achieves exact divergence-free results with round-off precision, by using tests of shock tube, 2D and 3D vortex, magneto-rotational instability, and especially, advection experiment, compared with CG method and the GIZMO code. It leads to noticeable improvement in pattern, amplitude and numerical dissipation of divergence error of magnetic field.