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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2024 Volume 64, Number 8, Pages 1517–1528 (Mi zvmmf11818)

Mathematical physics

Scheme for calculating unsteady flows of heat-conducting gas in the three-temperature approximation

V. T. Zhukov, O. B. Feodoritova

Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 125047, Moscow, Russia

Abstract: A technique for numerical modeling of unsteady flows of heat-conducting gas in a three-temperature approximation is presented. This technique was built using the fundamental principles of S.K. Godunov. For time integration, the calculation of each time step is carried out by splitting the governing equations into hyperbolic and parabolic subsystems. The first subsystem is solved using a generalization of the Godunov scheme, and the second, using an explicitly iterative Chebyshev scheme. For discretization, moving curvilinear adaptive grids are used; the discrete scheme is written in curvilinear coordinates with preserving the symmetries of the differential problem. The technique is implemented in the form of a parallel code for multiprocessor computers. The main objective is to provide computational studies on the problem of controlled thermonuclear fusion, but it can also be used in other applications of computational aero-gas-dynamics.

Key words: numerical modeling, high-temperature gas dynamics, multi-temperature models, difference schemes, Godunov scheme, Chebyshev iterations.

UDC: 519.635

Received: 10.03.2024
Revised: 10.03.2024
Accepted: 05.05.2024

DOI: 10.31857/S0044466924080153


 English version:
Computational Mathematics and Mathematical Physics, 2024, 64:8, 1840–1851

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© Steklov Math. Inst. of RAS, 2025