CESE Schemes for Solar Wind Plasma MHD Dynamics

Magnetohydrodynamic (MHD) numerical simulation has emerged as a pivotal tool in space physics research, witnessing significant advancements. This methodology offers invaluable insights into diverse space physical phenomena based on solving the fundamental MHD equations. Various numerical methods are utilized to approximate the MHD equations. Among these, the space-time conservation element and solution element (CESE) method stands out as an effective computational approach. Unlike traditional numerical schemes, the CESE method significantly enhances accuracy, even at the same base point. The concurrent discretization of space and time for conserved variables inherently achieves higher-order accuracy in both dimensions, without the need for intricate higher-order time discretization processes, which are often challenging in other methods. Additionally, this scheme can be readily extended to multidimensional cases, without relying on operator splitting or direction alternation. This paper primarily delves into the remarkable progress of CESE MHD models and their applications in studying solar wind, solar eruption activities, and the Earth's magnetosphere. We aim to illuminate potential avenues for future solar-interplanetary CESE MHD models and their applications. Furthermore, we hope that the discussions presented in this review will spark new research endeavors in this dynamic field.