A CUDA Pseudo-spectral Solver for Two-Dimensional Navier-Stokes Equation

In this paper, the two dimension incompressible Navier-Stokes equations with pseudo-spectral method are solved using the related subroutines in FFTW and CUFFT. Compared with the codes on CPU, the performance of the codes on GPU is much better, especially when the resolution increases. For the resolution of 2048 × 2048, the acceleration reaches 14.45 times. We also try to combine MPI (Message Passing Interface) and CUDA (Compute Unified Device Architecture) in our solver. Due to the inevitable frequent data transfers between Host and Device, the speedup is not so ideal compared with that of the single node, and 1.82 times acceleration is obtained in double precision for the resolution of 4096 × 4096.