Efficient magnetohydrodynamic modelling of the time-evolving corona by COCONUT

Context. Magnetohydrodynamic (MHD) solar corona models are critical in the Sun-to-Earth modelling chain and are the most complex and computationally intensive component. Compared to quasi-steady-state corona models that are constrained by a time-invariant magnetogram over a Carrington rotation (CR) period, time-evolving corona models driven by time-varying photospheric magnetograms are more realistic and can maintain more useful information to accurately describe solar wind evolution and forecast coronal mass ejection propagation. Aims. Implicit methods have significantly improved the efficiency of quasi-steady MHD coronal modelling. However, developing efficient time-evolving corona models to improve space weather forecasting is also important. This paper aims to demonstrate that time-evolving corona simulations can be performed efficiently and accurately using an implicit method with relatively large time steps, thus reducing the overall computational cost. We also evaluate differences between coronal structures captured by time-evolving and quasi-steady simulations over a CR period during solar minimum. Methods. We extended the quasi-steady COCONUT model, a global MHD corona model that uses implicit methods to select large time steps, into a time-evolving corona model. Specifically, we used a series of hourly updated photospheric magnetograms to drive the evolution of coronal structures from the solar surface to 25 R s during two CRs around the 2019 eclipse in an inertial coordinate system. At each time step, the inner-boundary magnetic field was temporal-interpolated and updated from adjacent observation-based magnetograms. We compare the time-evolving and quasi-steady simulations to demonstrate that the differences in these two types of coronal modelling can be obvious even for a solar minimum. The relative differences in radial velocity and density can be over 15% and 25% at 20 R s during one CR period. We also evaluated the impact of time steps on the simulation results. Using a time step of approximately 10 minutes balances efficiency and necessary numerical stability and accuracy for time-evolving corona simulations around solar minima. The chosen 10-minute time step significantly exceeds the Courant-Friedrichs-Lewy stability condition needed for explicit corona modelling, and the time-evolving COCONUT can thus simulate the coronal evolution during a full CR within only 9 hours (using 1080 CPU cores for 1.5M grid cells). Results. The simulation results demonstrate that time-evolving MHD coronal simulations can be performed efficiently and accurately using an implicit method, offering a more realistic alternative to quasi-steady-state simulations. The fully implicit time-evolving corona model thus promises to simulate the time-evolving corona accurately in practical space weather forecasting.