Investigation of solving 3D Navier–Stokes equations with hybrid spectral scheme using GPU

Abstract

The approach of accelerating application 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 necessary. The spectral-finite-difference schemes usually used in the direction numerical simulation (DNS) for turbulent channel flows are studied here. 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 major computational kernels of the scheme are the fast Fourier transfer (FFT) and the linear equation solver, which are both implemented on GPU. The performance study of the scalar diffusion equation shows at least 20 × speedup. For 3D Navier-Stokes equation, the performance on a single Nvidia S2050 card shows 25 times speedup.