Email this article 
TURBULENT KINETIC ENERGY IN AN APPROXIMATE SOLVER OF THE RIEMANN GAS DYNAMICS PROBLEM
- Authors: Boldyrev M.I1
-
Affiliations:
- Russian Federal Nuclear Center—Zababakhin All-Russia Research Institute of Technical Physics
- Issue: Vol 64, No 6 (2024)
- Pages: 1042-1054
- Section: Mathematical physics
- URL: https://ogarev-online.ru/0044-4669/article/view/273769
- DOI: https://doi.org/10.31857/S0044466924060126
- EDN: https://elibrary.ru/XYEANH
- ID: 273769
Cite item
Open Access
Access granted
Subscription Access
Abstract
The paper describes the consideration of turbulent kinetic energy in solving the gas-dynamic problem of discontinuity decay (Riemann problem) using the HLLC approximate solver. The system of Euler equations is considered with the addition of the hyperbolic equation of turbulent kinetic energy and consideration of turbulent pressure in the momentum and energy balance equations. The Jacobian coefficient of the system of equations and its eigenvalues are found. Based on this, changes are made to the calculation scheme in the HLLC solver. Using the Sod problem as an example, the correctness of taking into account turbulent kinetic energy in solving the Riemann problem is verified, and the instability of the scheme at high turbulent pressure is shown in the case of not taking turbulence into account in calculating the characteristic velocities.
About the authors
M. I Boldyrev
Russian Federal Nuclear Center—Zababakhin All-Russia Research Institute of Technical Physics
Email: boldyrevmi@vniitf.ru
Snezhinsk, Chelyabinsk oblast, 456770 Russia
References
- Годунов С. К. Разностный метод численного расчета разрывных решений гидродинамики // Матем. сб. 1959. Т. 47. № 3. С. 271–306.
- Toro E. F., Spruce M., Speares W. Restoration of the contact surface in the HLL-Riemann solver // Shock Waves. 1994. V. 4. P. 25–34.
- Hu X., Adams N. A., Iaccarino G. On the HLLC Riemann solver for interface interaction in compressible multi-fluid flow // J. Comput. Phys. 2009. V. 228. P. 6572–6589.
- Garrick D. P., Owkes M., Regele J. D. A finite-volume HLLC-based scheme for compressible interfacial flows with surface tension // J. Comput. Phys. 2017. V. 339. P. 46–67.
- Taylor G. I. The instability of liquid surfaces when accelerated in a direction perpendicular to their planes // Proc. Royal. Soc. Ser. A. 1950. V. 201. P. 192.
- Мешков Е. Е. Неустойчивость границы раздела двух газов, ускоряемой ударной волной // Изв. АН СССР. Мех. жидкости и газа. 1969. № 5. С. 151–157.
- Zhou Y. Rayleigh-Taylor and Richtmyer-Meshkov instability induced flow, turbulence, and mixing. II // Phys. Rep. 2017. V. 723–725. P. 1–160.
- Jakobsen H. A. Chemical reactor modeling. Multiphase reactive flows. Berlin: Springer-Verlag, 2008.
- Declercq E., Forestier A., Hérard J.-C., Louis X., Poissant G. An exact Riemann solver for multicomponent turbulent flow // Inter. J. Comput. Fluid Dyn. 2001. V. 14. P. 117–131.
- Toro E. F. Riemann solvers and numerical methods for fluid dynamics. Berlin: Springer–Verlag, 2009.
- Mohammadi B., Pironneau O. Analysis of the k-ε turbulence model. New York: John Wiley & Sons, 1994.
- Davis S. F. Simplified second–order Godunov–tType methods // SIAM J. Sci. Stat. Comput. 1988. V. 9. P. 445–473.
- Pelanti M., Shyue K.-M. A numerical model for multiphase liquid-vapor-gas flows with interfaces and cavitation // Inter. J. Mul. Flow. 2019. V. 113. P. 208–230.
- Sod G. A. A survey of several finite difference methods for systems of nonlinear hyperbolic conservation Laws // J. Comput. Phys. 1978. V. 27. P. 1–31.
- Kamm J. R. An exact, compressible one-dimensional Riemann solver for general, Convex Equations of State. Los Alamos National Laboratory. 2015. https://permalink.lanl.gov/object/tr?what=info:lanl-repo/lareport/LA-UR-15-21616
- van Leer B. On the relation between the upwind–differencing schemes of Godunov, Enguist-Osher and Roe // SIAM J. Sci. Stat. Comput. 1985. V. 5. P. 1–20.
- Vetter M., Sturtevant B. Experiments on the Richtmyere–Meshkov instability of an air/𝑆𝐹6 interface // Shock Waves. 1995. V. 4. P. 247–252.
- Morán-López J. T., Schilling O. Multicomponent Reynolds-averaged Naviere-Stokes simulations of reshocked RichtmyereMeshkov instability-induced mixing // High Energy Den. Phys. 2013. V. 9. P. 112–121.
Supplementary files
