三维Navier-Stokes方程分步法的并行算法在异构平台上实现初探

本文选取了三维不可压缩流动方程的分步法(fractional-step method),其中动量方程使用BiCGSTAB算法进行迭代求解,而压力泊松方程使用Fourier变换法进行直接求解。本文研究该算法在集群平台上的并行算法,从区域分解入手,分析一维、两维、三维区域划分三种情况下,各并行处理器上的计算量与通讯量,根据分析结果使用两维区域分解。分析BiCGSTAB算法和泊松Fourier变换法在GPGPU异构平台上的移植方法。最后,本文分析了BiCGSTAB和泊松方程Fourier变换法两种算法在CPU集群和GPGPU异构平台上的并行性能结果。

Investigation of the Parallelization of the Fractional-Step Method to 3D Incompressible NavierStokes Equations on Heterogeneous Platforms

This paper implements the classical fractional-step method for 3Dincompressible Navier-Stokes equations in parallel using message passing interface ( MPI ), and investigatesthe mapping of parallel algorithm on the GPGPU heterogeneous platform usingCUDA.The momentum equation is solved with Bi-CGSTAB algorithm and the pressure Poisson equation is directly solved with the Fourier method.With the analysis of the computation and communication ratio on each MPI processorsfrom 1D , 2D and 3D domain decompositions , the 2D domain decomposition is found to have the smallestcomputation and communication ratio and is chosen in this study.The performance results for the CPU clusters and GPGPU platform are discussed.