基于多GPU并行格子Boltzmann方法的方管湍流模拟

Multi-GPUs simulation of turbulent square duct flow in lattice Boltzmann method

采用CUDA(Compute Unified Device Architecture)和MPI(Message-Passing-Interface)在超级计算机Mole-8.5E上实现了格子Boltzmann方法(LBM)多GPU并行算法,通过三维顶盖驱动方腔流算例验证了多GPU并行LBM算法的准确性和有效性,利用该并行算法分别对雷诺数Re_(τ)为300,600,1200下的充分发展的方管湍流进行了大规模模拟。研究发现,当计算网格尺寸小于黏性底层厚度(即Δ^(+)<5)时,在壁面附近的相关传递特性统计误差较小,预测精度满足工程应用范围;Re_(τ)为300,600时,不同网格尺寸Δ^(+)下的模拟结果表明LBM在方管流中心湍流特性统计具有网格弱相关性,Re_(τ)为600时,与DNS(Direct Numerical Simulation)相比,Δ^(+)=1.667,3.750,6.250时平均流向速度的平均误差分别是1.357%,2.994%和4.766%;Re_(τ)分别为300,600和1200时,对应网格尺寸Δ^(+)分别为0.833,1.667和3.333时的方管湍流模拟中,成功捕捉到了二次流特性,预测得到的中心面流向速度、脉动均方根速度等的规律与文献基本吻合,进一步验证了单松弛LBM的可靠性,相关计算结果也为理解高Re_(τ)下的方管湍流特性提供了参考。方管湍流的模拟验证了单松弛LBM多GPU并行算法在超大规模网格计算中的潜力,为进一步实现实际工程流动所需更大规模的数值模拟奠定了基础。

Compute unified device architecture(CUDA)and message-passing-interface(MPI)were used to implement the lattice Boltzmann method(LBM)multi-GPUs parallel algorithm on supercomputing system Mole-8.5E.The accuracy and effectiveness of the multi-GPUs parallel LBM algorithm was verified by the three-dimensional lid-driven cavity flow.Using this parallel algorithm,large-scale simulations of fully developed turbulent square duct flows with Reynolds numbers Re_(τ)of 300,600,and 1200 were carried out.Numerical results showed that when the grid size was less than the viscous sublayer,Δ^(+)<5,the statistical error of the transfer characteristics near the wall was low,and the simulation accuracy met the need of engineering application.Meanwhile,when Re_(τ)was 300 and 600,the simulation results at different grid sizesΔ^(+)showed that the LBM had a weak grid-dependent in the statistics of turbulence characteristics in the square duct central area,and when Re_(τ)was 600,the averaged errors of the mean streamwise velocity predicted by LBM atΔ^(+)=1.667,3.750,and 6.250 compared with direct numerical simulation(DNS)were 1.357%,2.994%,and4.766%,respectively.The characteristics of turbulent square duct flow were studied when Re_(τ)was 300,600,and1200,and the corresponding grid sizeΔ^(+)was 0.833,1.667,and 3.333,respectively.The secondary flows were successfully captured,and the predicted mean streamwise velocity,pulsating root-mean-square(rms)velocity and other trends and results were consistent with the literature,which further verified the reliability of the single relaxation time(SRT)LBM,and the numerical results also provided a reference for understanding the turbulence characteristics of turbulent square duct flow at high Re_(τ).The simulation of turbulent square duct flow verified the potential of the SRT LBM multi-GPUs parallel algorithm in ultra-large-scale grid computing,and laid the foundation for further realization of the larger-scale numerical simulation required in practical engineering.