TY - JOUR
T1 - A 2D Fourth-Order CESE Scheme for Solving the Ideal MHD Equations
AU - Zhou , Yufen
AU - Feng , Xueshang
AU - Shen , Fang
AU - Yang , Liping
AU - Zhang , Man
JO - Communications in Computational Physics
VL - 2
SP - 348
EP - 374
PY - 2025
DA - 2025/08
SN - 38
DO - http://doi.org/10.4208/cicp.OA-2024-0259
UR - https://global-sci.org/intro/article_detail/cicp/24301.html
KW - CESE method, fourth-order accuracy, MHD.
AB - <p style="text-align: justify;">We construct a two-dimensional fourth-order space-time conservation element and solution element (CESE) schemes for solving the ideal magnetohydrodynamics (MHD) equations. In the CESE scheme, the flow variables are calculated by
using the same procedure as that of the original second-order CESE scheme. The
scheme preserves most favorable attributes of the original second-order CESE method.
Moreover, it is simple and easy to program. The numerical example for the smooth
Alfvén wave problem suggests that the scheme can achieve the fourth-order accuracy
for smooth solutions. In order to verify the efficiency of the schemes, we simulate several 2D MHD problems. We find that the fourth-order scheme can capture shocks and
details of complex flow structures very well, and control the magnetic divergence efficiently. Moreover, the scheme is essentially CFL number insensitive schemes. The last
several complex test problems further verify the performance of proposed scheme.</p>