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

Zh. Vychisl. Mat. Mat. Fiz., 2023 Volume 63, Number 9, Pages 1554–1563 (Mi zvmmf11621)

Mathematical physics

Universal approach to analysis of dissipation properties of a numerical method for solving gas dynamic equations

P. V. Chuvakhovab, I. O. Pogorelovab, K. V. Shubinb

a Central Aerohydrodynamic Institute, 140180, Zhukovskii, Moscow oblast, Russia
b Moscow Institute of Physics and Technology (National Research University), 141701, Dolgoprudnyi, Moscow oblast, Russia

Abstract: A universal approach to the verification of a numerical method for solving the Navier–Stokes equations is proposed, through which the dissipation properties of the method can be reliably assessed. The approach is based on viscous damping of weak elementary perturbations propagating in uniform flow. The corresponding theoretical solution allows one to determine the order of convergence of the numerical method.

Key words: numerical dissipation, numerical viscosity, numerical method, Navier–Stokes equations, Euler equations, convergence.

UDC: 519.635

Received: 27.10.2022
Revised: 26.03.2023
Accepted: 28.04.2023

DOI: 10.31857/S0044466923090065


 English version:
Computational Mathematics and Mathematical Physics, 2023, 63:9, 1708–1716

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© Steklov Math. Inst. of RAS, 2024