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高Ra数Rayleigh-Bénard热对流的湍流特性研究是当前国际上的一个热门研究课题, DNS模拟计算是研究该课题的重要手段之一. 当计算规模增大而网格数巨大时计算工作难以实现, 高Ra湍流热对流的数值模拟研究面临重大挑战. 本文创建了大规模高效并行计算的三维湍流热对流直接求解方法. 采用FFT变换解耦压力泊松方程, 将其变换成沿z方向上的块三对角方程组, 并利用块三对角方程的MPI与OpenMP联立的大规模高效并行近似解求解方案, 创建了可以高效并行计算的热对流直接求解方法. 通过对该方法并行效率的验证计算, 证明新的直接求解并行计算方法具有很好的并行效率和计算时效. 三维窄方腔热对流的计算结果表明, 本文方法计算的三维热对流特性是合理的. 本文创建的可大规模高效并行计算的三维湍流热对流直接求解方法, 也很可能是关于计算流体力学不可压NS方程大规模高效并行计算在特殊情况中计算技术上的一个突破.
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关键词:
- 泊松方程直接求解 /
- 并行计算 /
- Rayleigh-Bé /
- nard热对流 /
- DNS
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.-
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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