SIP-IFVM: Efficient time-accurate magnetohydrodynamic model of the corona and coronal mass ejections
In this paper, we present an efficient and time-accurate three-dimensional (3D) single-fluid MHD solar coronal model and employ it to simulate CME evolution and propagation. Based on a quasi-steady-state implicit MHD coronal model, we developed an efficient time-accurate coronal model that can be used to speed up the CME simulation by selecting a large time-step size. We have called it the Solar Interplanetary Phenomena-Implicit Finite Volume Method (SIP-IFVM) coronal model. A pseudo-time marching method was implemented to improve temporal accuracy. A regularised Biot-Savart Laws (RBSL) flux rope, whose axis can be designed into an arbitrary shape, was inserted into the background corona to trigger the CME event. We performed a CME simulation on the background corona of Carrington rotation (CR) 2219 and evaluated the impact of time-step sizes on simulation results. Our study demonstrates that this model is able to simulate the CME evolution and propagation process from the solar surface to $20\; R_s$ in less than 0.5 hours (192 CPU cores, $\sim$ 1 M cells). Compared to the explicit counterpart, this implicit coronal model is not only faster, but it also has improved numerical stability. We also conducted an ad hoc simulation with initial magnetic fields artificially increased. It shows that this model can effectively deal with time-dependent low-$β$ problems ($β<10^{-4}$). Additionally, an Orszag-Tang MHD vortex flow simulation demonstrates that the pseudo-time-marching method used in this coronal model can simulate small-scale unsteady-state flows. The simulation results show that this MHD coronal model is very efficient and numerically stable. It is a promising approach to simulating time-varying events in the solar corona with low plasma $β$ in a timely and accurate manner.