This paper presents a novel second-order cell-centered Lagrangian method for 2D ideal magnetohydrodynamic (MHD) equations on unstructured meshes. It primarily consists of the following two parts: First, by revisiting the 1D HLLC-type Riemann solver, a discrimination approach based on the CAVEAT algorithm is redefined to assess the merits and disadvantages of the MHD Lagrangian algorithm, which is more stringent than traditional hydrodynamic methods. A 2D nodal Riemann solver is built on unstructured meshes to fulfill the aforementioned criteria, successfully maintaining the intrinsic compatibility between edge fluxes and the nodal flow. Meanwhile, in the Lagrangian approach, the finite volume scheme inherently preserves the solenoidal property of the magnetic field, which is a difficult challenge on triangular meshes. Second, the traditional reconstruction algorithm has only first-order volume accuracy on triangular meshes, as shown by theoretical analysis and numerical validation. As a result, an adaptive reconstruction technique is developed to identify the shock wave zones from the smooth flow field regions, improving the scheme's accuracy to second-order. Ultimately, a simple magnetic field reconstruction method that rigorously satisfies the magnetic field's nodal divergence constraint is developed. A variety of numerical experiments are carried out to illustrate the accuracy and robustness of the algorithm.

Publication:

JOURNAL OF COMPUTATIONAL PHYSICS

http://dx.doi.org/10.1016/j.jcp.2026.114897

Author:

Xun Wang

Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

E-mail addresses: s151025@muc.edu.cn

Chengdi Ma

School of Mathematical Sciences, Peking University, Beijing, 100871, China

Corresponding author.

E-mail addresses: mcd2020@stu.pku.edu.cn