SIP-IFVM: An efficient time-accurate implicit MHD model of corona and CME with strong magnetic field

Context. Coronal mass ejections (CME) are one of the main drivers of space weather. However, robust and efficient numerical\nmodelling of the initial stages of CME propagation and evolution process in the sub-Alfvénic corona is still lacking.\nAims. Magnetohydrodynamic (MHD) solar coronal models are critical in the Sun-to-Earth model chain but sometimes encounter low-\nβ (< 10−4) problems near the solar surface. This paper aims to deal with these low-β problems and make MHD modelling suitable for\npractical space weather forecasting by developing an efficient and time-accurate MHD model of the solar corona and CME launch. In\nthis paper, we develop an efficient and time-accurate three-dimensional (3D) single-fluid MHD solar coronal model and employ it to\nsimulate the CME’s evolution and propagation.\nMethods. Based on the quasi-steady-state implicit MHD coronal model (Feng et al. 2021; Wang et al. 2022a), we further develop an\nefficient time-accurate coronal model which can be used to speed up the CME simulation by selecting a large time-step size and call\nit the Solar Interplanetary Phenomena-Implicit Finite Volume Method (SIP-IFVM) coronal model. A pseudo-time marching method,\nwhere a pseudo time, τ, is introduced at each physical time step to update the solution by solving a steady-state problem on τ, is\ndevised to improve the temporal accuracy. A Regularised Biot-Savart Laws (RBSL) flux rope whose axis can be designed in an\narbitrary shape is inserted into the background corona to trigger the CME event. We perform a CME simulation on the background\ncorona of Carrington rotation (CR) 2219 and evaluate the impact of time-step sizes on simulation results. It demonstrates that this\nmodel can simulate the CME evolution and propagation process from the solar surface to 20 Rs in less than 0.5 hours (192 CPU cores,\n∼ 1 M cells). Compared to the explicit counterpart, this implicit coronal model is not only faster but also has greater numerical stability.\nWe also conduct an ad hoc simulation with initial magnetic fields artificially increased. It shows that this model can effectively deal\nwith time-dependent low-β problems (β < 10−4). Additionally, an Orszag-Tang MHD vortex flow simulation demonstrates that the\npseudo-time-marching method used in this coronal model can also simulate small-scale unsteady-state flows.\nResults. The simulation results show that this MHD coronal model is very efficient and numerically stable and is promising to timely\nand accurately simulate time-varying events in solar corona with low plasma β.