دانلود رایگان مقاله الگوریتم موازی برای شبیه سازی جریان بی نظم با توپولوژی مجازی MPI

abstract

A hybrid parallelisation technique for distributed memory systems is investigated for a coupled Fourierspectral/hp element discretisation of domains characterised by geometric homogeneity in one or more directions. The performance of the approach is mathematically modelled in terms of operation count and communication costs for identifying the most efficient parameter choices. The model is calibrated to target a specific hardware platform after which it is shown to accurately predict the performance in the hybrid regime. The method is applied to modelling turbulent flow using the incompressible Navier–Stokes equations in an axisymmetric pipe and square channel. The hybrid method extends the practical limitations of the discretisation, allowing greater parallelism and reduced wall times. Performance is shown to continue to scale when both parallelisation strategies are used.

5. Discussion

In this paper we presented a technique to parallelise a 3D incompressible Navier–Stokes algorithm discretised using a 2D spectral/hp element mesh coupled with a Fourier expansion in a third geometrically homogeneous direction. The implementation enables a flexible mixture of both elemental parallelism and modal parallelism. We have illustrated the hybrid parallelism technique on two prototype problems: turbulent flow in an axisymmetric pipe and turbulent flow in a channel. Both problems enjoy increased parallelism through the approach and consequently improved runtimes and greater energy efficiency. The optimal weighting of these strategies can be systematically chosen through the construction of a performance model, calibrated to a specific system through measurements of the two parallelism approaches independently. This enables rapid selection of the highestperforming combination of the strategies without costly trial-anderror testing. In the modern HPC environment, where energy is of increasing concern, selecting the optimal implementation to maximise performance is becoming increasingly important. Although experience and intuition can generally suggest the most suitable parallelisation approach for a specific problem, the decision is in general highly challenging, particularly when moving between HPC systems or when tackling problems on a range of different domains with the same algorithm. Even from a purely theoretical perspective, it can be appreciated that a single parallel approach cannot be optimal in all situations and this has been confirmed through numerical experimentation.