An efficient, time-evolving, global MHD coronal model based on COCONUT

MHD coronal models are critical in the Sun-to-Earth model chain and the most complex and computationally intensive component, particularly the time-evolving coronal models, typically driven by a series of time-evolving photospheric magnetograms. There is an urgent need to develop efficient and reliable time-evolving MHD coronal models to further improve our ability to predict space weather. COCONUT is a rapidly developing MHD coronal model. Adopting the efficient implicit algorithm makes it suitable for performing computationally intensive time-evolving coronal simulations. This paper aims to extend COCONUT to an efficient time-evolving MHD coronal model. In this MHD model, as usual, an implicit temporal integration algorithm is adopted to avoid the CFL stability restriction and increase computational efficiency by large time steps. The Newton iteration method is applied within each time step to enhance the temporal accuracy. The unstructured geodesic mesh is used for flexibility in mesh division and to avoid degeneracy at the poles. Furthermore, an HLL Riemann solver with a self-adjustable dissipation term accommodates both low- and high-speed flows. A series of time-evolving photospheric magnetograms are utilized to drive the evolution of coronal structures from the solar surface to 25Rs during two Carrington rotations (CRs) around the 2019 eclipse in an inertial coordinate system. It shows that COCONUT can mimic the coronal evolution during a full CR within 9 hours (1080 CPU cores, 1.5M cells). We also compare the simulation results of time-evolving versus quasi-steady-state coronal simulations in the thermodynamic MHD model to validate the time-evolving approach. Additionally, we evaluate the effect of time steps on the simulation results to find an optimal time step that simultaneously maintains high efficiency and necessary numerical stability and accuracy.