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 del center dot 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.

Publication:

JOURNAL OF COMPUTATIONAL PHYSICS

http://dx.doi.org/10.1016/j.jcp.2026.114823

Author:

Xiongbiao Tu

School of Mathematics and Statistics, Hubei Normal University, 435002, Huangshi, China

E-mail addresses: hbnutu@yeah.net

Qiao Wang

National Astronomical Observatories, Chinese Academy of Sciences, 100101, Beijing, China

School of Astronomy and Space Science, University of Chinese Academy of Sciences, 100048, Beijing, China

Corresponding author

E-mail addresses: qwang@nao.cas.cn.

Liang Gao

Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal University, 100875, Beijing, China

School of Physics and Laboratory of Zhongyuan Light, Zhengzhou University, 450001, Zhengzhou, China

mail addresses: lgao@bnu.edu.cn

Yifa Tang

Academy of Mathematics and Systems Science, State Key Laboratory of Mathematical Sciences, Chinese Academy of Sciences, 100190, Beijing, China

School of Mathematical Sciences, University of Chinese Academy of Sciences, 100049, Beijing, China

E-mail addresses: tyf@lsec.cc.ac.cn