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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2024, Volume 64, Number 6, Pages 1042–1054
DOI: https://doi.org/10.31857/S0044466924060126
(Mi zvmmf11774)
 

Mathematical physics

Turbulent kinetic energy in an approximate Riemann solver

M. I. Boldyrev

Russian Federal Nuclear Center E. I. Zababakhin All-Russian Scientific Research Institute of Technical Physics, 456770, Snezhinsk, Chelyabinsk oblast, Russia
Abstract: Turbulent kinetic energy (TKE) is taken into account in the approximate HLLC Riemann solver. The Euler equations are supplemented with a hyperbolic equation for TKE, and turbulent pressure is taken into account in the momentum and energy balance equations. The Jacobian of this system of equations and its eigenvalues are found, which are used to modify the HLLC solver. The validity of TKE allowance in the modified HLLC Riemann solver is verified by solving Sod’s problem. It is shown that the scheme is unstable at high turbulent pressure if turbulence is ignored in the computation of characteristic velocities.
Key words: compressible gas dynamics, Euler equations, turbulent kinetic energy, approximate Riemann solver, HLLC, Richtmyer–Meshkov instability.
Received: 03.11.2023
Accepted: 06.03.2024
English version:
Computational Mathematics and Mathematical Physics, 2024, Volume 64, Issue 6, Pages 1306–1316
DOI: https://doi.org/10.1134/S0965542524700532
Bibliographic databases:
Document Type: Article
UDC: 519.635
Language: Russian
Citation: M. I. Boldyrev, “Turbulent kinetic energy in an approximate Riemann solver”, Zh. Vychisl. Mat. Mat. Fiz., 64:6 (2024), 1042–1054; Comput. Math. Math. Phys., 64:6 (2024), 1306–1316
Citation in format AMSBIB
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\by M.~I.~Boldyrev
\paper Turbulent kinetic energy in an approximate Riemann solver
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2024
\vol 64
\issue 6
\pages 1042--1054
\mathnet{http://mi.mathnet.ru/zvmmf11774}
\crossref{https://doi.org/10.31857/S0044466924060126}
\elib{https://elibrary.ru/item.asp?id=75171321}
\transl
\jour Comput. Math. Math. Phys.
\yr 2024
\vol 64
\issue 6
\pages 1306--1316
\crossref{https://doi.org/10.1134/S0965542524700532}
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