MHD modeling of magnetic flux evolution around solar maximum by the coronal model COCONUT

In this paper, we simulate the magnetic flux evolution at different heliocentric distances during two solar-maximum Carrington rotations (CRs) using the time-evolving coronal magnetohydrodynamic (MHD) model COCONUT to investigate the ``open flux problem". The simulated open magnetic flux (OMF) near the solar surface is comparable to that derived from \textit{in situ} observations by PSP and WIND satellites, and is about 5 times larger than that derived from SDO coronal hole (CH) observations, and the variation in the simulated radial solar wind speed is consistent with the evolution of the OMF evaluated around the corresponding solar disk center. We find that the OMF is reduced by up to $45\%$ from 1.01~$R_s$ to 0.1~AU and increases with a higher-resolution mesh. The OMF decreases mainly within 3~$R_s$, where the closed magnetic flux drops more rapidly, from about $60\%$ of the total magnetic flux at 1.01~$R_s$ to about $4\%$ at 3~$R_s$. Moderate adjustment of the heating source term can effectively regulate the simulated OMF. Preprocessing the photospheric magnetograms with a potential field solver that removes many high-order spherical harmonic components reduces the OMF in the low corona, while having little impact beyond 3~$R_s$. Additionally, the ratio of the maximum to the minimum OMF can reach 1.4 during a single solar maximum CR. These findings highlight the necessity of considering higher grid resolution, more realistic heating mechanisms, and the time-evolving regime of coronal MHD modeling when further addressing the ``open flux problem".