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Research of turbulence Rayleigh-Bénard convection with high Ra number is a hot topic in physics research in the world. DNS simulation is one of the important means to study the subject. The computing work is hard to achieve when the calculation size is increased and the grid number is bigger. Numerical simulation for high Ra turbulent convection faces some major challenges. So the direct (non iterative) solution method of efficient large-scale parallel computation for the 3D turbulent convection is created in this paper. Main difficulties are the parallel computing technology for the pressure Poisson equation. The mass efficient parallel approximate solution with the block tridiagonal equations of OpenMP and MPI used simultaneously after decoupling pressure Poisson equation using FFT is presented. Through the validation of the efficiency of this method in parallel computing, the new method for direct solution of parallel computing have good parallel efficiency and computational time. Results of thermal convection in 3D narrow cavity show that the convection characteristics calculated by using the new method is reasonable. The direct solution method for efficient large-scale parallel computation of 3D turbulent convection created in this paper also is likely to be a breakthrough in computing technology about efficient large-scale parallel computing incompressible NS equations in some special cases.
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Keywords:
- direct solution method of Poisson equation /
- parallel computation /
- Rayleigh-Bé /
- nard convection /
- direct numerical simulation
[1] Castaing G, Gunaratne F, Heslot L 1989 J. Fluid Mech. 24 1
[2] Puits R, Resagk C, Thess A 2010 Phys. Rev. E 81 016307
[3] He X, Funfschilling D, Nobach H, Bodenschatz E, Ahlers G 2012 American Physical Society 108 024502
[4] Ahlers G, Grossmann S, Lohse D 2009 Review of Modern Physics 81 503 537
[5] Stringano G, Verzicco R 2006 J. Fluid Mech. 548 1
[6] Shishkina O, Wagner C2006 J. Fluid Mech. 546 51
[7] Shishkina O, Wagner C 2007 Phys. Fluids 19 085107
[8] Stevens R J A M, Verzicco R, Lohse D 2010 J. Fluid Mech. 643 495
[9] Zhang H, Zhang W, Sun X H 2008 Ninth international conferenceon parallel and distributed computing, applications and technologies (PDCAT2008)
[10] Zhang W, Zhang H 2007 J. Shanghai University 13(5) 498 (in Chinese) [张武, 张衡 2007 上海大学学报 13(5) 498]
[11] Chorin A J 1967 J. Comput. Phys. 2 12
[12] Press W H, Teukolsky S A, Vetterling W T, Flannery B P 2007 Numerical Recipes: The Art. of Scientific Computing (3rd ed.)
[13] Harlow F H, Welch J E 1965 Phys. Fluids. 8 2182
[14] Frigo M, Johnson S G 2005 Proc. IEEE 93 216231
[15] Xu W, Bao Y 2013 Acta Mech. Sin. 45 666 (in Chinese) [徐炜, 包芸 2013 力学学报 45 666]
[16] Zou H Y 2012 Master Thesis (Sun Yat-sen University) (in Chinese) [邹鸿岳 2012 硕士论文 (中山大学)]
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[1] Castaing G, Gunaratne F, Heslot L 1989 J. Fluid Mech. 24 1
[2] Puits R, Resagk C, Thess A 2010 Phys. Rev. E 81 016307
[3] He X, Funfschilling D, Nobach H, Bodenschatz E, Ahlers G 2012 American Physical Society 108 024502
[4] Ahlers G, Grossmann S, Lohse D 2009 Review of Modern Physics 81 503 537
[5] Stringano G, Verzicco R 2006 J. Fluid Mech. 548 1
[6] Shishkina O, Wagner C2006 J. Fluid Mech. 546 51
[7] Shishkina O, Wagner C 2007 Phys. Fluids 19 085107
[8] Stevens R J A M, Verzicco R, Lohse D 2010 J. Fluid Mech. 643 495
[9] Zhang H, Zhang W, Sun X H 2008 Ninth international conferenceon parallel and distributed computing, applications and technologies (PDCAT2008)
[10] Zhang W, Zhang H 2007 J. Shanghai University 13(5) 498 (in Chinese) [张武, 张衡 2007 上海大学学报 13(5) 498]
[11] Chorin A J 1967 J. Comput. Phys. 2 12
[12] Press W H, Teukolsky S A, Vetterling W T, Flannery B P 2007 Numerical Recipes: The Art. of Scientific Computing (3rd ed.)
[13] Harlow F H, Welch J E 1965 Phys. Fluids. 8 2182
[14] Frigo M, Johnson S G 2005 Proc. IEEE 93 216231
[15] Xu W, Bao Y 2013 Acta Mech. Sin. 45 666 (in Chinese) [徐炜, 包芸 2013 力学学报 45 666]
[16] Zou H Y 2012 Master Thesis (Sun Yat-sen University) (in Chinese) [邹鸿岳 2012 硕士论文 (中山大学)]
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