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 , , in wide cylinders with the aspect ratios and (where R denotes the radius and H – the height of the cylinder).
@article{CRMECA_2005__333_1_17_0,
author = {Olga Shishkina and Claus Wagner},
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},
volume = {333},
number = {1},
year = {2005},
doi = {10.1016/j.crme.2004.09.020},
language = {en},
}
TY - JOUR AU - Olga Shishkina AU - Claus Wagner TI - A fourth order accurate finite volume scheme for numerical simulations of turbulent Rayleigh–Bénard convection in cylindrical containers JO - Comptes Rendus. Mécanique PY - 2005 SP - 17 EP - 28 VL - 333 IS - 1 PB - Elsevier DO - 10.1016/j.crme.2004.09.020 LA - en ID - CRMECA_2005__333_1_17_0 ER -
%0 Journal Article %A Olga Shishkina %A Claus Wagner %T A fourth order accurate finite volume scheme for numerical simulations of turbulent Rayleigh–Bénard convection in cylindrical containers %J Comptes Rendus. Mécanique %D 2005 %P 17-28 %V 333 %N 1 %I Elsevier %R 10.1016/j.crme.2004.09.020 %G en %F CRMECA_2005__333_1_17_0
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/
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