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

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 a≡H/R=0.2 and a=0.4 (where R denotes the radius and H - the height of the cylinder). To cite this article: O. Shishkina, C. Wagner, C. R. Mecanique 333 (2005).