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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 differential-spectral method is usually used in the direct numerical simulation of channel turbulence. This paper mainly studies the implementation of the differential-spectral method on a single GPU. Due to the rapid development of hardware in GPU and different support for double-precision computing by GPU hardware, this dissertation first verifies the accuracy of numerical computation on GPU, and uses the differential-spectral hybrid method to solve the scalar diffusion equation. The GPU and CPU The numerical results are compared with the analytical solution to determine the accuracy of the numerical algorithm implemented on the GPU. The scalar diffusion equation is solved on an Nvidia S2050 single GPU with an approximate 20-fold speedup and a three-dimensional incompressible Navier-Stokes equation with a 25-fold speedup.