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.
