SIP-IFVM: Efficient time-accurate magnetohydrodynamic model of the corona and coronal mass ejections

¹ Centre for Mathematical Plasma-Astrophysics, Department of Mathematics, KU Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium
² State Key Laboratory of Space Weather, Chinese Academy of Sciences, Beijing 100190, China
³ School of Astronomy and Space Science and Key Laboratory of Modern Astronomy and Astrophysics, Nanjing University, Nanjing 210023, China
⁴ Institute of Physics, University of Maria Curie-Skłodowska, ul. Radziszewskiego 10, 20-031 Lublin, Poland
⁵ Institute of Theoretical Astrophysics, University of Oslo, PO Box 1029 Blindern, 0315 Oslo, Norway
⁶ Rosseland Centre for Solar Physics, University of Oslo, PO Box 1029 Blindern, 0315 Oslo, Norway
⁷ Von Karman Institute For Fluid Dynamics, Waterloosesteenweg 72, 1640 Sint-Genesius-Rode, Brussels, Belgium
⁸ School of Earth and Space Sciences, Peking University, Beijing 100871, China

^★ Corresponding authors; haopeng.wang1@kuleuven.be; jinhan.guo@kuleuven.be; Stefaan.Poedts@kuleuven.be

Received: 17 May 2024
Accepted: 8 December 2024

Abstract

Context. Coronal mass ejections (CMEs) are one of the main drivers of space weather. However, robust and efficient numerical modelling applications of the initial stages of CME propagation and evolution process in the sub-Alfvénic corona are still lacking.

Aims. Magnetohydrodynamic (MHD) solar coronal models are critical in the Sun-to-Earth model chain, but they do sometimes encounter low-β (<10⁻⁴) problems near the solar surface. This paper aims to deal with these low-β problems and make MHD modelling suitable for practical space weather forecasting by developing an efficient and time-accurate MHD model of the solar corona and CMEs. 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.

Methods. 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, ~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.

Results. 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.