Efficiency analysis of parallel implementation of simple algorithm on multi-processor computers

This paper describes the details of parallel implementation of a SIMPLE algorithm for numerical solution of the Navier-Stokes system of equations on arbitrary unstructured grids. Implemented iteration schemes of serial and parallel options of the SIMPLE algorithm are shown. When describing parallel implementation, special attention is paid to the description of computational data exchange between the processors under the condition of the grid model decomposition using fictitious cells. We discuss specific features for the distributed matrices storage and implementation of the vector-matrix operations in the parallel mode. We show that the suggested way of matrix storage will allow reducing the number of inter-processor exchange. A series of numerical experiments illustrates multi-grid SLAE solver tuning as it affects the general efficiency of the algorithm (it includes the types of the cycles used - V, W and F, the number of smoothing operator iterations, and the number of cells for coarsening). Two ways (direct and indirect) of the efficiency evaluation for the numerical algorithm parallelization are shown. The paper provides the results of the internal and external flow problem solution with parallelization efficiency evaluation by two algorithms. It is shown that the suggested parallel implementation makes it possible to do efficient computation on the problems on a thousand of processors. Based on the results produced, general recommendations are given on the choice of optimal tuning of the multi-grid solver and optimal number of cells per processor.