Time-dependent boundary conditions for data-driven coronal global and spherical wedge-shaped models

The development of an efficient and accurate method for boundary condition treatments is of fundamental importance to data-driven magnetohydrodynamic (MHD) modelling of the global solar corona and solar active region. Particularly, in a 3D spherical wedge-shaped volume, suitable to the numerical study of solar active region, the transverse terms calls for a delicate treatment at the computational domain's edges and corners, and properly prescribed conditions for boundaries joining regions of different flow properties, so as to take account of the joint effect of incoming and outgoing waves. To provide a solution to the determination of boundary conditions, in this paper a systematic tactics is formulated for handling edges and corners and the prescribed conditions for inner/outer/edge/corner boundaries are proposed through the combination (CBC-ILW) of the time-dependent characteristic boundary conditions (CBCs) and the inverse Lax-Wendroff (ILW) procedure. First, a data-driven 3D MHD simulation has been carried out to study the dynamic evolution of the solar corona from 1R(s) to 6.7R(s) during the period between 2018 May 16 and August 6. The simulated results of the global coronal evolution provide a good comparison with observed coronal images during the period investigated. Then, the validity of 3D MHD-CBC-ILW is verified for a 3D spherical wedge model, by producing almost the same results as those taken out of the global model on a 3D spherical wedge-shaped volume.