Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-24T07:17:27.015Z Has data issue: false hasContentIssue false

Parallel Direct Method of DNS for Two-Dimensional Turbulent Rayleigh-Bénard Convection

Published online by Cambridge University Press:  17 July 2017

Y. Bao*
Affiliation:
Department of MechanicsSun Yat-sen UniversityGuangzhou, China
J. Luo
Affiliation:
Department of MechanicsSun Yat-sen UniversityGuangzhou, China
M. Ye
Affiliation:
Department of MechanicsSun Yat-sen UniversityGuangzhou, China
*
*Corresponding author (stsby@mail.sysu.edu.cn)
Get access

Abstract

A highly efficient parallelization scheme of direct numerical simulation (DNS) for two-dimensional Rayleigh-Bénard convection is presented. By introducing the parallel diagonal dominant (PDD) algorithm to solve the pressure Poisson equation and adjusting the domain decomposition accordingly, all-to-all communication as the usual obstacle to parallel computing can be eliminated. Excellent strong scaling and weak scaling for the parallel efficiency are achieved. Numerical results show that very complex structures in flow exist at very high Ra numbers. The required high resolution both in space and in time can be obtained by the present method at low parallel overhead.

Type
Research Article
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Ahlers, G., Grossmann, S. and Lohse, D., “Heat Transfer and Large Scale Dynamics in Turbulent Rayleigh-Bénard Convection,” Reviews of Modern Physics, 81, pp. 503537 (2009).Google Scholar
2. Heslot, F., Castaing, B. and Libchaber, A., “Transitions to Turbulence in Helium Gas,” Physical Review A, 36, pp. 58705873 (1987).CrossRefGoogle ScholarPubMed
3. Grossmann, S. and Lohse, D., “Scaling in Thermal Convection: A Unifying Theory,” Journal of Fluid Mechanics, 407, pp. 2756 (2000).Google Scholar
4. Grossmann, S. and Lohse, D., “Thermal Convection for Large Prandtl Numbers,” Physical Review Letters, 86, pp. 33163319 (2001).Google Scholar
5. Grossmann, S. and Lohse, D., “Prandtl and Rayleigh Number Dependence of the Reynolds Number in Turbulent Thermal Convection,” Physical Review E, 66, pp. 16 (2002).Google Scholar
6. Grossmann, S. and Lohse, D., “Fluctuations in Turbulent Rayleigh–Bénard Convection: The Role of Plumes,” Physics of Fluids, 16, pp. 44624472 (2004).Google Scholar
7. Kraichnan, R., “Turbulent Thermal Convection at Arbitrary Prandtl Number,” Physics of Fluids, 5, pp. 13741389 (1962).Google Scholar
8. Stevens, R., van der Poel, E., Grossmann, S. and Lohse, D., “The Unifying Theory of Scaling in Thermal Convection: the Updated Prefactors,” Journal of Fluid Mechanics, 730, pp. 295308 (2013).Google Scholar
9. Verzicco, R. and Orlandi, P., “A Finite-Difference Scheme for Three-Dimensional Incompressible Flows in Cylindrical Coordinates,” Journal of Computational Physics, 123, pp. 402414 (1996).CrossRefGoogle Scholar
10. Shishkina, O. and Wagner, C., “A Fourth Order Accurate Finite Volume Scheme for Numerical Simulations of Turbulent Rayleigh–Bénard Convection in Cylindrical Containers,” Comptes Rendus Mécanique, 333, pp. 1728 (2005).Google Scholar
11. Xia, K.-Q., “Current Trends and Future Directions in Turbulent Thermal Convection,” Theoretical and Applied Mechanics Letters, 3, 52001 (2013).Google Scholar
12. Kaczorowski, M., Shishkin, A., Shishkina, O. and Wagner, C., “Developement of a Numerical Procedure for Direct Simulations of Turbulent Convection in a Closed Rectangular Cell,” New Results in Numerical and Experimental Fluid Mechanics VI, 96, pp. 381388 (2007).CrossRefGoogle Scholar
13. Daya, Z. and Ecke, R., “Does Turbulent Convection Feel the Shape of the Container?,” Physics Review Letters, 87, 184501 (2001).Google Scholar
14. Chong, K.-L., Huang, S.-D., Kaczorowski, M. and Xia, K.-Q., “Condensation of Coherent Structures in Turbulent Flows,” Physics Review Letters, 115, 264503 (2015).Google Scholar
15. Huang, S.-D., Kaczorowski, M., Ni, R. and Xia, K.-Q., “Confinement-Induced Heat-Transport Enhancement in Turbulent Thermal Convection,” Physics Review Letters, 111, 104501 (2013).Google Scholar
16. Chong, K.-L. and Xia, K.-Q., “Exploring the Severely Confined Regime in Rayleigh–Bénard Convection,” Journal of Fluid Mechanics, 805, R4 (2016).CrossRefGoogle Scholar
17. Ostilla-Monico, R., Yang, Y., van der Poel, E., Lohse, D. and Verzicco, R., “A Multiple-Resolution Strategy for Direct Numerical Simulation of Scalar Turbulence,” Journal of Computational Physics, 301, pp. 308321 (2015).Google Scholar
18. van der Poel, E., Ostilla-Mónico, R., Donners, J. and Verzicco, R., “A Pencil Distributed Finite Difference Code for Strongly Turbulent Wall-Bounded Flows,” Computers & Fluids, 116, pp. 1016 (2015).Google Scholar
19. Moin, P. and Verzicco, R., “On the Suitability of Second-Order Accurate Discretizations for Turbulent Flow Simulations,” European Journal of Mechanics - B/Fluids, 55, pp. 242245 (2016).Google Scholar
20. Mohan Rai, M. and Moin, P., “Direct Simulations of Turbulent Flow Using Finite-Difference Schemes,” Journal of Computational Physics, 96, pp. 1553 (1991).Google Scholar
21. Chorin, A., “On the Convergence of Discrete Approximations to the Navier-Stokes Equations,” Mathematics of Computation, 23, pp. 341353 (1969).Google Scholar
22. Chorin, A., “Numerical Solution of the Navier-Stokes Equations,” Mathematics of Computation, 22, pp. 745762 (1968).Google Scholar
23. Sun, X.-H., Sun, H.-Z. and Ni, L. M., “Parallel Algorithms for Solution of Tridiagonal Systems on Multicomputers,” Proceedings of the 3rd International Conference on Supercomputing - ICS ’89, pp. 303312 (1989).Google Scholar
24. Zhang, H., “On the Accuracy of the Parallel Diagonal Dominant Algorithm,” Parallel Computing, 17, pp. 265272 (1991).Google Scholar
25. Sun, X.-H., “Application and Accuracy of the Parallel Diagonal Dominant Algorithm,” Parallel Computing, 21, pp. 12411267 (1995).Google Scholar
26. Shishkina, O., Stevens, R., Grossmann, S. and Lohse, D., “Boundary Layer Structure in Turbulent Thermal Convection and its Consequences for the Required Numerical Resolution,” New Journal of Physics, 12, 75022 (2010).Google Scholar
27. He, X., Gils, D., Bodenschatz, E. and Ahlers, G., “Reynolds Numbers and the Elliptic Approximation Near the Ultimate State of Turbulent Rayleigh–Bénard Convection,” New Journal of Physics, 17, 63028 (2015).Google Scholar
28. van der Poel, E., Stevens, R. and Lohse, D., “Comparison Between Two- and Three-Dimensional Rayleigh–Bénard Convection,” Journal of Fluid Mechanics, 736, pp. 177194 (2013).Google Scholar
29. van der Poel, E., Stevens, R., Sugiyama, K. and Lohse, D., “Flow States in Two-Dimensional Rayleigh-Bénard Convection as a Function of Aspect-Ratio and Rayleigh Number,” Physics of Fluids, 24, 85104 (2012).Google Scholar