In this paper, we propose an energy decomposition method to improve the numerical stability of time-evolving magnetohydrodynamic (MHD) coronal models, enabling them to resolve the stronger magnetic field during solar maxima without significantly filtering out small-scale structures from the observed magnetograms.We advance the decomposed energy that excludes the magnetic energy, instead of the total energy, in time. It avoids the operation of subtracting a large magnetic energy from the total energy to obtain a very small thermal pressure in low-beta regions, thereby improving the numerical stability of MHD models. We implemented this method in COCONUT and validated the model by performing a time-evolving coronal simulation during Carrington Rotation (CR) 2296, a solar maximum CR. We also compare quasi-steady-state simulation results during the solar minimum and the increasing phase, calculated using both versions of COCONUT adopting the decomposed energy equation and the traditional full energy equation to further validate the reliability of the energy decomposition method. The simulation results show that the energy decomposition method yields results nearly identical to those of the traditional full energy equation during solar minimum, while significantly enhancing COCONUT's ability to simulate coronal evolution under strong magnetic fields, even those exceeding 100 Gauss. This method is well suited for performing quasi-realistic time-evolving coronal simulations around solar maxima without excessively filtering out the observed strong magnetic fields.
Wang et al. (Thu,) studied this question.