COCONUT: A coronal model with an energy decomposition strategy

Abstract

In this paper, we propose an energy decomposition method combined with an HLL Riemann solver that includes an additional dissipation term in the energy equation to improve the numerical stability of the fully implicit, time-evolving coronal model COCONUT and extend its applicability to solar-maximum phases. In MHD simulations that evolve conservative variables in time, the thermal pressure is typically computed by subtracting the magnetic and kinetic energies from the total energy. In low-beta (the ratio of thermal to magnetic pressure; $< 10^{-3}$) regions, discretization errors of magnetic energy can be comparable to the thermal pressure, potentially leading to negative thermal pressure and causing the simulation to crash. Therefore, we update the decomposed energy, excluding the magnetic energy, at each time step. It avoids subtracting a large magnetic energy from the total energy to obtain a very small thermal pressure in low-$β$ regions, thereby improving the numerical stability of MHD models. We validate the algorithm using a time-evolving solar-maximum Carrington rotation simulation in 2025, which the previous code failed to run to completion. We also perform quasi-steady-state coronal simulations and 2D benchmark tests to further assess the algorithm's performance. The simulation results show that the algorithm produces results nearly identical to those obtained using the traditional full energy equation during solar minimum, while significantly improving COCONUT's ability to simulate coronal evolution under strong magnetic fields, even including fields exceeding 100 Gauss with $β<10^{-3}$. This method provides a promising approach for performing quasi-realistic coronal simulations during solar maxima.