應用多鬆弛時間晶格波茲曼法模擬大範圍雷諾數下周期性山坡紊流流場

MRT-LBM simulations of turbulent flows over periodic hills at different Reynolds numbers

蘇紀維(Chi-Wei Su)

指導教授 ： 林昭安

國立清華大學/工學院/動力機械工程學系/碩士(2018年)

摘要

本研究為在雷諾數 Re = 700, 1400, 2800, 5600, 10595 下，用 D3Q19 多鬆弛時間晶格波茲曼法模擬週期性山坡紊流流場。其中，山坡表面的部分採用了 BFL 曲面邊界修正法，外力部分則是採用了郭照立等人提出的作用力模型來驅動流場。模擬結果在不同雷諾數和不同位置橫截面下與 Breuer 等人的結果進行了比較，並得到了一致的觀察結果和發現。簡言之，週期性山坡紊流流場以晶格波茲曼法進行了完整的重現。此外，本研究應用了 CUDA 及 MPI 平行運算的架構在高速圖形顯示卡叢集上進行運算，並且進行了優化來獲得更高的運算效率。

關鍵字

晶格波茲曼法 ； 多鬆弛時間 ； 曲面邊界 ； 圖形顯示卡計算叢集 ； 平行處理 ； BFL邊界修正法

並列摘要

In this work, turbulent channel flows over 3D periodic hills were simulated using the D3Q19 multiple-relaxation-time lattice Boltzmann method (MRT-LBM) at Reynolds numbers Re = 700, 1400, 2800, 5600, 10595. The BFL bounce-back rule for curved boundaries was implemented on hill surfaces, and Guo et al.’s body force model was added to drive the flow. Several observations and investigations were made that showed good agreement with Breuer et al.’s findings of with different Re numbers and streamwise locations. In brief, the LBM scheme for flows over periodic hills was well constructed. Additionally, the simulations were conducted on a multi-GPU cluster with both CUDA and MPI implemented, and some optimizations were applied for higher efficiency.

並列關鍵字

Lattice Boltzmann method ； MRT ； curved boundary ； GPU cluster ； MPI ； BFL method

參考文獻

[1] U. Frisch, B. Hasslacher, and Y. Pomeau, “Lattice-gas automata for the navier-stokes equation,” Physical review letters, vol. 56, no. 14, p. 1505, 1986.

[2] S. Wolfram, “Cellular automaton fluids 1: Basic theory.”

[3] P. B. E. G. M. Krook, P. Bhatnagar, and E. Gross, “A model for collision processes in gases,” Phy. Rev, vol. 94, pp. 511–524, 1954.

[4] S. Chen, H. Chen, D. Martnez, and W. Matthaeus, “Lattice boltzmann model for simulation of magnetohydrodynamics,” vol. 67, pp. 3776–3779.

[5] Y. H. Qian, D. D’Humières, and P. Lallemand, “Lattice bgk models for navier-stokes equation,” EPL (Europhysics Letters), vol. 17, no. 6, p. 479, 1992.