Efficient magnetohydrodynamic modelling of the time-evolving corona by COCONUT

Compared to quasi-steady-state corona models that are constrained by a time-invariant magnetogram over a 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 CME propagation. This paper demonstrate that time-evolving corona simulations can be performed efficiently and accurately using an implicit method with relatively large time steps. We also evaluate differences between coronal structures captured by time-evolving and quasi-steady simulations over a CR period during solar minimum. 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. 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, with coronal evolution during a full CR simulated within only 9 hours (using 1080 CPU cores for 1.5M grid cells). 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.