ABSTRACT

This paper deals with a parallel implementation of the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm to numerically solve the Navier–Stokes system of equations for viscous incompressible flows. A mechanism of interprocess communication using a mesh decomposition with virtual cells and an algebraic multigrid method is proposed. A method of distributed matrix storage and an algorithm for matrix-vector operations reducing the number of interprocess communications are presented. The results of a series of numerical experiments on structured and unstructured grids (including a problem of external aerodynamics) are presented. Based on the results obtained, an analysis of the influence of multigrid solver settings on the overall efficiency of the algorithm is made. It is shown that the parallel algorithm based on an algebraic multigrid technique proposed for the SIMPLE method makes it possible to efficiently calculate problems on hundreds of processors.

中文翻译：

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基于多重网格方法的SIMPLE算法的高效并行实现

摘要

本文讨论了SIMPLE（压力链接方程的半隐式方法）算法的并行实现，以数值求解粘性不可压缩流的Navier-Stokes方程组。提出了一种利用虚拟单元的网格分解和代数多重网格方法进行进程间通信的机制。提出了一种分布式矩阵存储的方法和一种矩阵向量运算的算法，可减少进程间通信的数量。给出了一系列关于结构化和非结构化网格的数值实验的结果（包括外部空气动力学问题）。基于获得的结果，分析了多网格求解器设置对算法整体效率的影响。