Comptes Rendus
A fourth order accurate finite volume scheme for numerical simulations of turbulent Rayleigh–Bénard convection in cylindrical containers
Comptes Rendus. Mécanique, Volume 333 (2005) no. 1, pp. 17-28.

A finite volume scheme, which is based on fourth order accurate central differences in spatial directions and on a hybrid explicit/semi-implicit time stepping scheme, was developed to solve the incompressible Navier–Stokes and energy equations on cylindrical staggered grids. This includes a new fourth order accurate discretization of the velocity and temperature fields at the singularity of the cylindrical coordinate system and a new stability condition [J. Appl. Numer. Anal. Comput. Math. 1 (2004) 315–326]. The method was applied in direct numerical simulations of turbulent Rayleigh–Bénard convection for different Rayleigh numbers Ra=10γ, γ=5,,8, in wide cylinders with the aspect ratios aH/R=0.2 and a=0.4 (where R denotes the radius and H – the height of the cylinder).

Published online:
DOI: 10.1016/j.crme.2004.09.020
Keywords: Computational fluid mechanics, Rayleigh–Bénard convection, Direct numerical simulation, High-order finite volume schemes

Olga Shishkina 1; Claus Wagner 1

1 DLR – Institute for Aerodynamics and Flow Technology, Bunsenstrasse 10, 37073 Göttingen, Germany
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Olga Shishkina; Claus Wagner. A fourth order accurate finite volume scheme for numerical simulations of turbulent Rayleigh–Bénard convection in cylindrical containers. Comptes Rendus. Mécanique, Volume 333 (2005) no. 1, pp. 17-28. doi : 10.1016/j.crme.2004.09.020. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2004.09.020/

[1] F. Heslot; B. Castaing; A. Libchaber A transition to turbulence in helium gas, Phys. Rev. A, Volume 36 (1987), pp. 5870-5873

[2] B.I. Shraiman; E.D. Siggia Heat transport in high-Rayleigh number convection, Phys. Rev. A, Volume 42 (1990), pp. 3650-3653

[3] E.D. Siggia High Rayleigh number convection, Annu. Rev. Fluid Mech., Volume 26 (1994), pp. 137-168

[4] X. Chavanne; F. Chillà; B. Chabaud; B. Castaing; B. Hebral Turbulent Rayleigh–Bénard convection in gaseous and liquid He, Phys. Fluids, Volume 13 (2001), pp. 1300-1320

[5] S. Grossmann; D. Lohse Scaling in thermal convection: a unifying theory, J. Fluid Mech., Volume 407 (2000), pp. 27-56

[6] S.J. Kimmel; J.A. Domaradzki Large Eddy Simulations of Rayleigh–Bénard convection using subgrid scale estimation model, Phys. Fluids, Volume 12 (2000), pp. 169-184

[7] G. Grötzbach Direct numerical simulation of laminar and turbulent Bénard convection, J. Fluid Mech., Volume 119 (1982), pp. 27-53

[8] R.M. Kerr Rayleigh number scaling in numerical convection, J. Fluid Mech., Volume 310 (1996), pp. 139-179

[9] R. Verzicco; R. Camussi Numerical experiments on strongly turbulent thermal convection in a slender cylindrical cell, J. Fluid Mech., Volume 477 (2003), pp. 19-49

[10] J.G.M. Eggels; F. Unger; M.H. Weiss; J. Westerweel; R.J. Adrian; R. Friedrich; F.T.M. Nieuwstadt Fully developed turbulent pipe flow: a comparison between direct numerical simulation and experiment, J. Fluid Mech., Volume 268 (1994), pp. 175-209

[11] F. Unger, Numerische Simulation turbulenter Rohrströmungen, Dissertation, Lehrstuhl fuer Fluidmechanik, TU Muenchen, 1994

[12] H. Choi, P. Moin, J. Kim, Turbulent drug reduction: studies of feedback control and flow over riblets, Thermoscience Division, Dept. of Mech. Eng., Stanford, Report TF-55, 1992

[13] A.G. Kravchenko; P. Moin On the effect of numerical errors in large eddy simulations of turbulent flows, J. Comput. Phys., Volume 131 (1997), pp. 310-322

[14] U. Schumann Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli, J. Comput. Phys., Volume 18 (1975), pp. 376-404

[15] U. Schumann Fast elliptic solvers and their application in fluid dynamics (W. Kollmann, ed.), Computational Fluid Dynamics, Hemishere, Washington, 1980, pp. 376-404

[16] A.J. Chorin Numerical solution of the Navier–Stokes equations, Math. Comput., Volume 22 (1968), pp. 745-762

[17] A.J. Chorin On the convergence of discrete approximations to the Navier–Stokes equations, Math. Comput., Volume 23 (1969), pp. 341-353

[18] O. Shishkina, C. Wagner, A fourth order finite volume scheme for turbulent flow simulations in cylindrical domains, Computers and Fluids, submitted for publication

[19] O. Shishkina; C. Wagner Stability conditions for the Leapfrog–Euler scheme with central spatial discretization of any order, J. Appl. Numer. Anal. Comput. Math., Volume 1 (2004), pp. 315-326

[20] O. Shishkina; C. Wagner Stability analysis of high-order finite volume schemes in turbulence simulations (G. Psihoyios, ed.), NACoM-2003 Extended Abstracts, APU, Cambridge, UK, 2003, pp. 158-161

[21] B.E. Mitchell; S.K. Lele; P. Moin Direct computation of the sound generated by an axisymmetric jet, AIAA J., Volume 35 (1997) no. 10, p. 1574

[22] K. Mohseni; T. Colonius Numerical treatment of polar coordinate singularities, J. Comput. Phys., Volume 157 (2000), pp. 787-795

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