An Efficient Parallel Direct Method for Turbulent Thermal Convection

Abstract

Abstract: A parallel direct methods of DNS (PDM-DNS) for two-dimensional turbulent thermal convection was created with PDD algorithm for Poisson equation direct solving. DNS calculations of turbulent convection with high Ra were completed on "Tianhe-2" supercomputer, in which iteration time steps are over one hundred million. Effect of calculations is surprised. A calculation scale, which was difficult to achieve a year before, is realized. It shows that turbulent convection flow with different high Ra number are completely different. This work provides a valuable method for massively parallel computing and numerical simulation of turbulent convection with high Ra number.

Key words: Rayleigh-Bénard convection, turbulent, parallel calculation, PDM DNS

CLC Number:

O358

BAO Yun, YE Mengxiang, LUO Jiahui. An Efficient Parallel Direct Method for Turbulent Thermal Convection[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2017, 34(6): 651-656.

References

[1] AHLERS G, GROSSMANN S, LOHSE D. Heat transfer and large scale dynamics in turbulent Rayleigh-Bénard convection[J]. Rev Mod Phys, 2009, 81:503-537.
[2] KRAICHNAN R H. Turbulent thermal convection at arbitrary Prandtl number[J]. Phys Fluids, 1962, 5:1374-1389.
[3] GROSSMANN S, LOHSE D. Scaling in thermal convection:A unifying view[J]. J Fluid Mech, 2000, 407:27-56.
[4] 周全,夏克青.Rayleigh-Bénard湍流热对流研究的进展、现状及展望[J].力学进展,2012,42(3):231-251.
[5] STRINGANO G, VERZICCO R. Mean flow structure in thermal convection in a cylindrical cell of aspect-ratio one half[J]. J Fluid Mech, 2006,548:1-16.
[6] SHISHKINA O, WAGNER C. Analysis of thermal dissipation rates in turbulent Rayleigh-Bénard convection[J]. J Fluid Mech, 2006,546:51-60.
[7] SHISHKINA O, WAGNER C. Local heat fluxes in turbulent Rayleigh-Bénard convection[J]. Phys Fluids, 2007, 19:085107.
[8] STEVENS R J A M, VERZICCO R, LOHSE D. Radial boundary layer structure and Nusselt number in Rayleigh-Bénard convection[J]. J Fluid Mech, 2010,643:495-507.
[9] van der P E P, STEVENS R J A M, LOHSE D. Comparison between two-and three-dimensional Rayleigh-Bénard convection[J]. J Fluid Mech, 2013, 736:177-194.
[10] 包芸,宁浩,徐炜.湍流热对流大尺度环流反转时的角涡特性[J].物理学报,2014,63(15):154703.
[11] CHONG K L, HUANG S D, KACZOROWSKI M, et al. Condensation of coherent structures in turbulent flows[J]. Phys Rev Lett, 2015, 115(26):264503.
[12] BAO Y, CHEN J, LIU B, et al. Enhanced heat transport in partitioned thermal convection[J]. J Fluid Mech, 2015, 784(R5):1-11.
[13] 王路,徐江荣,刘保银.基于Lagrange方法封闭的两相湍流场方程模型[J].计算物理,2015,32(6):669-676.
[14] 上官燕琴,王娴,李跃明.基于格子Boltzmann方法的平板射流大涡模拟[J].计算物理,2016,33(3):305-310.
[15] FRIGO M, JOHNSON S G. The design and implementation of FFTW3[J]. Proceedings of the IEEE 2005,93(2):216-231.
[16] 徐炜,包芸.利用FFT高效求解二维Rayleigh-Bénard热对流[J].力学学报,2013,45(4):1-6.
[17] SUN X H, SUN H Z, NI L M. Parallel algorithms for solution of tridiagonal systems on multi-computers[C]//Proc of the 1989 ACM International Conference on Supercomputing. ACM New York, NY, USA:300-312.
[18] SUN X H, ZHANG W. A parallel two-level hybrid method for tridiagonal systems and its application to fast Poisson solvers[J]. IEEE Transactions on Parallel & Distributed Systems, 2004, 15(2):97-106.
[19] Van der POEL E P, OSTILLA-MÓNICO R, VERZICCO R, et al. Logarithmic mean temperature profiles and their connection to plume emissions in turbulent Rayleigh-Bénard convection[J]. Phys Rev Lett, 2015, 115(15):154501.