Abstract.
In present paper we recall the canonical Taylor-Green vortex problem solved by in-house implementation of the novel CABARET numerical scheme in weakly compressible formulation. The simulations were carried out on the sequence of refined grids with \( 64^3\), \( 128^3\), \( 256^3\) cells at various Reynolds numbers corresponding to both laminar (\({\rm Re}=100, 280\)) and turbulent (\({\rm Re}=1600, 4000\)) vortex decay scenarios. The features of the numerical method are discussed in terms of the kinetic energy dissipation rate and integral enstrophy curves, temporal evolution of the spanwise vorticity, energy spectra and spatial correlation functions.
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References
G.I. Taylor, A.E. Green, Proc. R. Soc. London, Ser. A 158, 499 (1937)
S. Goldstein, Lond. Edinb. Dublin. Philos. Mag. 30, 85 (1940)
M. Brachet, D. Meiron, S. Orszag, B. Nickel, R. Morf, U. Frisch, J. Fluid Mech. 130, 411 (1983)
S. Orszag, Numerical simulation of the Taylor-Green vortex (Springer Berlin Heidelberg, Berlin, Heidelberg, 1974) pp. 50--64
L. Berselli, J. Math. Fluid Mech. 7, S164 (2005)
D. Drikakis, C. Fureby, F.F. Grinstein, D. Youngs, J. Turbul. 8, N20 (2007) DOI: https://doi.org/10.1080/14685240701250289
E.V. Koromyslov, M.V. Usanin, L.Y. Gomzikov, A.A. Siner, Comput. Contin. Mech. 8, 24 (2015) (Utilization of high order DRP-type schemes and large eddy simulation based on relaxation filtering for turbulent gas flow computations in the case of Taylor-Green vortex breakdown
V. Goloviznin, S. Karabasov, T. Kozubskaya, N. Maksimov, Comput. Math. Math. Phys. 49, 2168 (2009)
C. Tam, J. Webb, J. Comput. Phys. 107, 262 (1993)
N. Taguelmimt, L. Danaila, A. Hadjadj, Flow Turbul. Combust. 96, 163 (2016)
L.G. Margolin, W.J. Rider, F.F. Grinstein, J. Turbul. 7, N15 (2006)
I. Shirokov, T. Elizarova, J. Turbul. 15, 707 (2014)
Y. Kulikov, E. Son, J. Phys.: Conf. Ser. 774, 012094 (2016)
Y. Kulikov, E. Son, Comput. Res. Model. 9, 881 (2017) DOI: https://doi.org/10.20537/2076-7633-2017-9-6-881-903
Y. Kulikov, E. Son, J. Phys.: Conf. Ser. 946, 012075 (2017)
Y. Kulikov, E. Son, Thermophys. Aeromech. 24, 909 (2017)
V. Goloviznin, A. Samarskii, Matem. Mod. 10, 86 (1998)
V. Goloviznin, A. Samarskii, Matem. Mod. 10, 101 (1998)
A. Iserles, IMA J. Numer. Anal. 6, 381 (1986)
V. Goloviznin, S. Karabasov, I. Kobrinskiy, Math. Models Comput. Simul. 15, 29 (2003)
V. Goloviznin, Matem. Mod. 18, 14 (2006)
M. Ivanov, A. Kiverin, S. Pinevich, I. Yakovenko, J. Phys.: Conf. Ser. 754, 102003 (2016)
V. Ostapenko, Matem. Mod. 21, 29 (2009)
V. Ostapenko, Comput. Math. Math. Phys. 52, 387 (2012)
S. Karabasov, V. Goloviznin, AIAA J. 45, 2801 (2007)
V. Semiletov, S. Karabasov, J. Comput. Phys. 253, 157 (2013)
A.V. Danilin, A.V. Solovjev, A.M. Zaitsev, Numer. Methods Program. 18, 1 (2017) (A modification of the CABARET scheme for numerical simulation of one-dimensional detonation flows using a one-stage irreversible model of chemical kinetics
S. Karabasov, P. Berloff, V. Goloviznin, Ocean Model. 30, 155 (2009)
V. Glotov, V. Goloviznin, Math. Models Comput. Simul. 4, 144 (2012)
V. Glotov, V. Goloviznin, Comput. Math. Math. Phys. 53, 721 (2013)
O. Kovyrkina, V. Ostapenko, Math. Models Comput. Simul. 5, 180 (2013)
O. Kovyrkina, V. Ostapenko, Dokl. Math. 91, 323 (2015)
V. Goloviznin, M. Zaytsev, S. Karabasov, I. Korotkin, Novel Algorithms of Computational Hydrodynamics for Multicore Computing (Moscow University Press, 2013)
J. DeBonis, Solutions of the Taylor-Green Vortex Problem Using High-Resolution Explicit Finite Difference Methods, in Aerospace Sciences Meetings (American Institute of Aeronautics and Astronautics, 2013) p. 0382
M. Brachet, Fluid Dyn. Res. 8, 1 (1991)
K. Hillewaert, Direct Numerical Simulation of the Taylor-Green Vortex at Re = 1600, in 2nd International Workshop on High-Order CFD Methods (Sponsored by DLR, AIAA and AFOSR, 2013)
U. Frisch, Turbulence: The Legacy of A.N. Kolmogorov (Cambridge University Press, 1995)
S. Jammy, C. Jacobs, N. Sandham, Enstrophy and kinetic energy data from 3D Taylor-Green vortex simulations https://eprints.soton.ac.uk/401892/ (2016)
M. Lesieur, S. Ossia, J. Turbul. 1, N7 (2000)
L. Skrbek, S. Stalp, Phys. Fluids 12, 1997 (2000)
R. Stepanov, F. Plunian, M. Kessar, G. Balarac, Phys. Rev. E 90, 053309 (2014)
P. Davidson, Turbulence: An Introduction for Scientists and Engineers (OUP Oxford, 2004)
P.L. O’Neill, D. Nicolaides, D. Honnery, J. Soria, Autocorrelation Functions and the Determination of Integral Length with Reference to Experimental and Numerical Data, in Proceedings of 15th Australasian Fluid Mechanics Conference, 13--17 December 2004, The University of Sydney, edited by M. Behnia, W. Lin, G. D. McBain (The University of Sydney, Sydney NSW, Australia, 2006) ISBN: 1-864-87695-6 (CD-ROM)
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Kulikov, Y.M., Son, E.E. Taylor-Green vortex simulation using CABARET scheme in a weakly compressible formulation. Eur. Phys. J. E 41, 41 (2018). https://doi.org/10.1140/epje/i2018-11645-4
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DOI: https://doi.org/10.1140/epje/i2018-11645-4