多松弛时间格子Boltzmann方法在GPU上的实现

Multi-relaxation-time lattice Boltzmann method implemented on GPU

近年来，随着统一计算设备构架（CUDA）的出现，高端图形处理器（GPU）在图像处理、计算流体力学等科学计算领域的应用得到了快速发展。属于介观数值方法的格子Boltzmann方法（LBM）是1种新的计算流体力学（CFD）方法，具有算法简单、能处理复杂边界条件、压力能够直接求解等优势，在多相流、湍流、渗流等领域得到了广泛应用。LBM由于具有内在的并行性，特别适合在GPU上计算。采用多松弛时问模型（MRT）的LBM，受松弛因子的影响较小并且数值稳定性较好。本文实现了MRT-LBM在基于CUDA的GPU上的计算，并通过计算流体力学经典算例——二维方腔流来验证计算的正确性。在雷诺数Re＝[10，10^4]之间，计算了多达26种雷诺数的算例，并将Re=10^2，4×10^2，10^3，2×10^3，5×10^3，7．5x10^3算例对应的主涡中心坐标与文献中结果进行了对比。计算结果与文献数值实验符合较好，从而验证了算法实现的正确忡，并显示出MRT-LBM具有更优的数值稳定性。奉文还分析了在GPU上MRT-LBM的计算性能并与CPU的计算进行了比较，结果表明，GPU可以极大椭栅mMR下TRM的计簋。NvTDIA Tesla C2050相对于单核Intel Xeon 5430 CPU的加速比约为60倍。

In recent years, with the release of compute unified device architecture （CUDA）, high-performance graphical processing units （GPU） have been widely applied to computational science areas, such as computational fluid dynamics, besides the traditional image processing. Lattice Boltzmann method （LBM）, as a mesoscopic numerical method, is an alternative technique for computational fluid dynamics （CFD）. It has many advantages including simplicity, handling complicated boundary conditions easily and solving pressure directly, which makes it widely applied to many fields, such as multiphase flows, turbulence and flows in porous media. LBM is also very suitable to be implemented on GPUs due to its natural parallelism. LBM with the relaxation-time models of multi-relaxation-time （MRT） is less affected by relaxation factor and posses better numerical stability. In this paper, LBM-MRT is implemented on GPU based on CUDA and the implementation was validated by the classical two-dimensional cavity flow. Altogether 26 cases were calculated with the Reynolds numbers ranging from 10 to 10^4. The center coordinates of main vortex in the cases with the Reynolds numbers Re=10^2, 4×10^2, 10^3, 2×10^3, 5×10^3, 7.5×10^3 have been compared with the results reported in literatures. The simulation results not only agree well with previous conclusions but also show good numerical stability. The performance of MRT-LBM on GPU was analyzed and compared with that of CPU. The results indicate that with an NVIDIA Tesla C2050, a nearly 60 fold speedup over that of one core of the Intel Xeon 5430 CPU was achieved.