A1 Refereed original research article in a scientific journal
COCONUT: A Coronal Model with an Energy Decomposition Strategy; 
Authors: Wang, Hao P.; Poedts, S.; Lani, A.; Dhib, R.; Linan, L.; Baratashvili, T.; Jeong, H. -j.; Zhou, Yu H.; Li, Yu C.; Najafi-Ziyazi, M.; Wang, J.; Schmieder, B.; Wang, W. S.; Husidic, E.
Publisher: Institute of Physics Publishing
Publication year: 2026
Journal: Astrophysical Journal Supplement
Article number: 40
Volume: 283
Issue: 1
ISSN: 0067-0049
eISSN: 1538-4365
DOI: https://doi.org/10.3847/1538-4365/ae40b1
Publication's open availability at the time of reporting: Open Access
Publication channel's open availability : Open Access publication channel
Web address : https://iopscience.iop.org/article/10.3847/1538-4365/ae40b1
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/523522913
Self-archived copy's licence: CC BY
Self-archived copy's version: Publisher`s PDF
In this paper, we propose an energy decomposition method combined with a Harten–Lax–van Leer 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 COolfluid COroNal UnsTructured (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-β (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 G with β < 10−3. This method provides a promising approach for performing quasi-realistic coronal simulations during solar maxima.
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Funding information in the publication:
This project has received funding from the European Research Council Executive Agency (ERCEA) under the ERC-AdG agreement No. 101141362 (Open SESAME). Neither the European Union nor the granting authority can be held responsible for them. These results were also obtained in the framework of the projects FA9550-18-1-0093 (AFOSR), C16/24/010 (C1 project Internal Funds KU Leuven), G0B5823N and G002523N (WEAVE) (FWO-Vlaanderen), and 4000145223 (SIDC Data Exploitation (SIDEX), ESA Prodex). This work is also supported by the National Natural Science Foundation of China (grant No. 42030204) and the BK21 FOUR program of the Graduate School, Kyung Hee University (GS-1-JO-NON-20242364). E.H. is grateful to the Space Weather Awareness Training Network (SWATNet), funded by the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No. 955620. The resources and services used in this work were provided by the VSC (Flemish Supercomputer Centre), funded by the Research Foundation—Flanders (FWO) and the Flemish Government.
