Magnetohydrodynamics (MHD) numerical simulations on the interaction of the solar wind with the magnetosphere: A review

The magnetosphere is the outermost layer of the geospace, and the interaction of the solar wind with the magnetosphere is the key element of the space weather cause-and-effect chain process from the Sun to Earth, which is one of the most challenging scientific problems in the geospace weather study. The nonlinearity, multiple component, and time-dependent nature of the geospace make it very difficult to describe the physical process in geospace using traditional analytic analysis approach. Numerical simulations, a new research tool developed in recent decades, have a deep impact on the theory and application of the geospace. MHD simulations started at the end of the 1970s, and the initial study was limited to two-dimensional (2D) cases. Due to the intrinsic three-dimensional (3D) characteristics of the geospace, 3D MHD simulations emerged in the 1980s, in an attempt to model the large-scale structures and fundamental physical processes in the magnetosphere. They started to combine with the space exploration missions in the 1990s and make comparisons with observations. Physics-based space weather forecast models started to be developed in the 21st century. Currently only a few space-power countries such as USA and Japan have developed 3D magnetospheric MHD models. With the rapid advance of space science in China, we have developed a new global MHD model, namely PPMLR-MHD, which has high order spatial accuracy and low numerical dissipation. In this review, we will briefly introduce the global 3D MHD modeling, especially the PPMLR-MHD code, and summarize our recent work based on the PPMLR-MHD model, with an emphasis on the interaction of interplanetary shocks with the magnetosphere, large-scale current systems, reconnection voltage and transpolar potential drop, and Kelvin-Helmholtz (K-H) instability at the magnetopause.