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Article information
2024 , Volume 29, ¹ 1, p.5-17
Erkaev N.V., Gorbunova K.D.
Hydrodynamic models of outflow of the planetary atmospheres
The compact McCormack-type difference scheme with the fourth order of accuracy and a nonuniform grid is adapted for solving the hydrodynamic problem of the escaping planet’s atmosphere in the presence of absorption of external extreme ultraviolet radiation, which is important for modelling of planetary evolution. This problem requires a high accuracy difference scheme. Two real recently discovered exoplanets TOI-421b,c, significantly differing in mass and orbit radius, were considered as simulation objects. A peculiarity of this problem is the nonlocal heating function, which integrally depends on the distribution of physical quantities over the radial distance and spherical angle. In particular, this function decreases very steeply when distance near the planet decreases. Therefore, an uneven difference grid is used with a decreasing step towards the planet. As a result of numerical integration of time dependent spherically symmetric hydrodynamic equations, radial distributions of density, temperature, pressure and velocity were obtained. The heating function was averaged over spherical angles. The model took into account such fundamentally important physical processes as ionization and recombination, as well as Lyman-alpha radiation cooling. When carrying out calculations, hydrodynamic equations were solved in a conservative form, ensuring conservation of mass, momentum and energy. In this case, Euler’s hydrodynamic equation, which takes into account the detailed balance of acting forces, was used to estimate the approximation error for the compact difference scheme, which was compared with a similar error for the classical McCormack scheme. The comparison shows a significant advantage of the compact difference scheme used in this research.
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Keywords: hydrodynamic model, compact finite difference scheme, atmosphere
doi: 10.25743/ICT.2024.29.1.002
Author(s):
Erkaev Nikolai Vasilievich
Dr. , Professor
Position: General Scientist
Office: Institut Computing Simulation of SB RAS
Address: 660036, Russia, Krasnoyarsk, Akademgorodok 50/44
Phone Office: (3912) 49 57 41
E-mail: erkaev@icm.krasn.ru
SPIN-code: 1471-5166Gorbunova Kseniya Dmitrievna
Position: engineer
Office: Institute of Computational Modelling Siberian Brabch of the Russian Academy of Sciences
Address: 660036, Russia, Krasnoyarsk, Akademgorodok 50/44
E-mail: gksu475@gmail.com
References:
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Bibliography link:
Erkaev N.V., Gorbunova K.D. Hydrodynamic models of outflow of the planetary atmospheres // Computational technologies. 2024. V. 29. ¹ 1. P. 5-17
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