Boundary layer structure in turbulent thermal convection and its consequences for the required numerical resolution
By O. Shishkina, Richard J.A.M. Stevens, S. Grossmann, Detlef Lohse. 2010
361 citations recorded by the source corpus.
Results on the Prandtl–Blasius-type kinetic and thermal boundary layer (BL) thicknesses in turbulent Rayleigh–Bénard (RB) convection in a broad range of Prandtl numbers are presented. By solving the laminar Prandtl–Blasius BL equations, we calculate the ratio between the thermal and kinetic BL thicknesses, which depends on the Prandtl number only. It is approximated as for and as for , with . Comparison of the Prandtl–Blasius velocity BL thickness with that evaluated in the direct numerical simulations by Stevens et al (2010 J. Fluid Mech. 643 495) shows very good agreement between them. Based on the Prandtl–Blasius-type considerations, we derive a lower-bound estimate for the minimum number of computational mesh nodes required to conduct accurate numerical simulations of moderately high (BL-dominated) turbulent RB convection, in the thermal and kinetic BLs close to the bottom and top plates. It is shown that the number of required nodes within each BL depends on and and grows with the Rayleigh number not slower than . This estimate is in excellent agreement with empirical results, which were based on the convergence of the Nusselt number in numerical simulations.
Subfields: Computational Mechanics, Environmental Engineering
View Paper: https://www.semanticscholar.org/paper/0770bb3ec26421969f5000f960d67277dd4f1dde
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In Computational Mechanics
- Detlef Lohse
- S. Grossmann
- Richard J.A.M. Stevens
- Erwin P. van der Poel
- Julien Aubert
- T. Gastine
- Johannes Wicht
- J. LaCasce
In Environmental Engineering
- Erwin P. van der Poel
- Detlef Lohse
- Richard J.A.M. Stevens
- S. Grossmann
- T. Gastine
- Julien Aubert
- Johannes Wicht
Citations in the corpus
- Scaling regimes in spherical shell rotating convection (2016, background): “Particular attention must be paid to the numerical resolution requirements for global models of convection (Shishkina et al. 2010; King et al. 2012), since under-resolution can significantly degrade the accuracy of the obtained exponents when deriving asymptotic scaling laws (Amati et al. 2005).”
- Comparison between two- and three-dimensional Rayleigh–Bénard convection (2013, methodology): “To ensure adequate accuracy of the simulations, we compare the number of points we placed in the thermal boundary layer with the minimum number that should be placed inside the boundary layer according to Shishkina et al. (2010). For each Pr number this criterion is satisfied for the highest resolut”
- The unifying theory of scaling in thermal convection: the updated prefactors (2013, methodology): “nding with further implications is that the value a, i.e. the amplitude parameter of the Prandtl BL thickness, is higher than found by Grossmann & Lohse (2002). This avalue is for example used by Shishkina et al. (2010) to determine the number of grid points that should be placed in the boundary”