GPUによるマルチグリッド法を用いた2次元非圧縮性流体解析の高速計算

抄録

In order to accelerate incompressible flow analysis, 2-dimensional Navior-Stokes equation is solved on GPU (Graphics Processing Unit). The code has been developed in CUDA and all the dependent variables are allocated on the global memory without communications between CPU and GPU memories. The SMAC algorithm is applied and the spatial derivatives are represented by the finite difference on Cartesian grid. The Red&Black Multigrid (MG) method improves the convergence of the SOR method for the pressure Poisson equation. The 3-stage Runge-Kutta method is applied to integrate in time for the advection term with 3rd-order upwind scheme. For the neighbor-grid accesses, we use the small-size shared memory as a software-managed cache. The overall performance of the incompressible flow calculation achieves 17 GFLOPS and about 14-times speed-up to compare with the 1-core CPU calculation. We carry out the computing for the flows around a circle and the Strouhal numbers of the GPU results are in good agreement with those obtained experimentally. It is found that the GPU computing has great contribution for incompressible flow analysis from the engineering view point.