Paper
Modified-gradient methods for exact divergence-free in meshless magnetohydrodynamics
Authors
Xiongbiao Tu, Qiao Wang, Liang Gao, Yifa Tang
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.
Metadata
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2603.04077v1</id>\n <title>Modified-gradient methods for exact divergence-free in meshless magnetohydrodynamics</title>\n <updated>2026-03-04T13:50:06Z</updated>\n <link href='https://arxiv.org/abs/2603.04077v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2603.04077v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>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.\n 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.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='astro-ph.IM'/>\n <category scheme='http://arxiv.org/schemas/atom' term='physics.comp-ph'/>\n <category scheme='http://arxiv.org/schemas/atom' term='physics.plasm-ph'/>\n <published>2026-03-04T13:50:06Z</published>\n <arxiv:comment>20 Pages, 11 figures, accepted for publication in Journal of Computational Physics</arxiv:comment>\n <arxiv:primary_category term='astro-ph.IM'/>\n <author>\n <name>Xiongbiao Tu</name>\n </author>\n <author>\n <name>Qiao Wang</name>\n </author>\n <author>\n <name>Liang Gao</name>\n </author>\n <author>\n <name>Yifa Tang</name>\n </author>\n </entry>"
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