Scalability and Parallel Efficiency of Block-pipelinged Algorithm for Direct Simulation of Turbulent Compressible Mixing Layer Flows

摘要

Data dependency is one of main difficulties in paral-lel implementation of numerical algorithms on distributed memory parallel computers. A typical example is the so-lution of tridiagonal linear system of equations, which is frequently encountered in numerical solution of PDE_s. Al-though significant progess has been made in designing par-allel algorithms which are suitable for distributed memory systems, this difficulty still remains a problem for many al-gorithm designers, especially for those working in the field of CFD(1). We have presented in (2) an algorithm for ef-ficiently solving a set of tridiagonal linear systems of equa-tions on distributed memory parallel systems, the "block pipelined algorithm", It permits to obtain good parallel speedup while maintaining the same computational com-plexity as optimal sequential algorithms. The basic idea is , when dealing with parallelization based on domain decom-position, if data dependency occurs in one space direction, then parallelism can often by exploited in other space direc-tions. In this paper we will give some more detailed analy-sis on the parallel performance and scalability properties of the block pipelinged algorithm, Numerical results concern-ing its parallel efficiency in direct simulation of trubulent compressible mixing laryer flows will also be presented.