A fourth order accurate finite volume scheme for numerical simulations of turbulent Rayleigh–Bénard convection in cylindrical containers

Olga Shishkina; Claus Wagner

doi:10.1016/j.crme.2004.09.020

A fourth order accurate finite volume scheme for numerical simulations of turbulent Rayleigh–Bénard convection in cylindrical containers

Olga Shishkina ¹ ; Claus Wagner ¹

¹ DLR – Institute for Aerodynamics and Flow Technology, Bunsenstrasse 10, 37073 Göttingen, Germany

Comptes Rendus. Mécanique, High-order methods for the numerical simulation of vortical and turbulent flows , Volume 333 (2005) no. 1, pp. 17-28.

Abstract

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 $Ra = 10^{γ}$ , $γ = 5, \dots, 8$ , in wide cylinders with the aspect ratios $a \equiv H / R = 0.2$ and $a = 0.4$ (where R denotes the radius and H – the height of the cylinder).

Published online: 2005-01-01

DOI: 10.1016/j.crme.2004.09.020

Keywords: Computational fluid mechanics, Rayleigh–Bénard convection, Direct numerical simulation, High-order finite volume schemes

Author's affiliations:

Olga Shishkina ¹; Claus Wagner ¹

¹ DLR – Institute for Aerodynamics and Flow Technology, Bunsenstrasse 10, 37073 Göttingen, Germany

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     title = {A fourth order accurate finite volume scheme for numerical simulations of turbulent {Rayleigh{\textendash}B\'enard} convection in cylindrical containers},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {17--28},
     publisher = {Elsevier},
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     year = {2005},
     doi = {10.1016/j.crme.2004.09.020},
     language = {en},
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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, High-order methods for the numerical simulation of vortical and turbulent flows , 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/

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