三维Navier-Stokes方程的差分-谱方法混合法在GPU上的实现与优化

摘要

差分-谱方法通常在槽道湍流的直接数值模拟中使用,本文主要研究差分-谱方法在单GPU卡上的实现.由于GPU的硬件发展十分迅速,不同的GPU硬件对双精度计算的支持有所不同,本文首先验证GPU上数值计算的精度,用差分-谱混合法求解标量扩散方程,并将GPU和CPU上获取的数值结果与解析解进行对比,以确定GPU上数值算法实现的精确度.标量扩散方程在Nvidia S2050单GPU卡上求解,获得接近20倍的加速比,三维不可压缩Navier-Stokes方程达到了25倍的加速比.%The approach of accelerating the applications with GPUs already delivers impressive computational performance compared to the traditional CPU. The hardware architecture of GPU is a significant departure from CPUs,hence the redesign and validation of the numerical algorithm are required. The spectral-finite-difference scheme is usually used in the direction, and the numerical simulation (DNS) of turbulent channel flows is studied. In order to validate the numerical accuracy,the scalar diffusion equation is first solved with this scheme,and the results from GPU and CPU are validated with the analytical solution. The performance study of the scalar diffusion equation shows at least 20X speedup. For the 3D full Navier-Stokes equation,the performance on GPU shows a 24X speedup.