An Efficient Parallel Implementation for Three-Dimensional Incompressible Pipe Flow Based on SIMPLE

SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm is important in the simulation of steady flows. As the traditional 3-D SIMPLE algorithm is time-consuming, we propose a parallel SIMPLE algorithm based on a novel tiling strategy -- alternate tiling, through replacing the original linear system and reordering the iteration space tiles. The novelty of our parallel algorithm lies in the introduction of the sequence of iteration space tiles as the sequence of execution, the time skewing technique to partition the iteration space, update operations of the grids from two directions alternately, and the improvement of the data locality. The effectiveness of the parallel algorithm and serial model of finite difference stencil algorithm are validated. Numerical experiments on distributed clusters show that the cache misses and the cost of communication and synchronization are reduced by reordering the tiles of iteration space, and the parallel SIMPLE algorithm based on alternate tiling has a good data locality and parallel efficiency in the three-dimensional incompressible pipe flow project.