Cuda implementation of gpu-accelerated spectrally accurate algorithm

Graphics processor units (GPU), with potential impact on computationally intensive algorithms such as the simulation of turbulent flow, are gradually become the mainstream of scientific computing. It’s worth making full use of GPU's powerful ability of floating point calculation to improve the computational efficiency. In this paper flow problems have been solved with spectral accuracy using a discretization based on Fourier expansions in the stream-wise direction, Chebyshev expansions in the wall-normal direction and Galerkin projection for construction of the relevant algebraic equations. The iterative solution method approximates the nonlinear terms using information from the most recent iteration, resulting in the first-order fixed-point method. The algorithm is transformed for adaption of GPU architecture and parallel platform, and the results of numerical simulations demonstrate the acceleration of CUDA implementation.