Performance Issues

In order to judge the industrial applicability of the turbulence models under consideration, their respective computational surplus over standard approaches has to be quantified, a few exemplary figures will be given here.

Table 1: WBC: Comparison of performance rates for the structured FLOWer code on a CRAY T3E-900

Looking at the linear models in the structured FLOWer code, it turns out that in terms of additional CPU costs, the LLR $k$-$\omega$ model requires approximately 25% more time per iteration than Wilcox $k$-$\omega$ and LEA $k$-$\omega$ about 17%. Additionally, it should be mentioned that SALSA only requires approximately 3% more CPU time than the original SA model [15]. For the two- as well as the one-equation models, the increase in memory requirements is not significant. The subsonic wing-body configuration was also investigated concerning the performance figures on a massively parallel architecture, viz. a CRAY T3E-900. Table 1 summarizes the achieved performance rates obtained with three different $k$-$\omega$ models. The figures also demonstrate that the more elaborate algorithms of the advanced models are in part counterbalanced by the higher performance rates achievable.

Turning the attention to the non-linear models in the unstructured TAU solver, performance measurements, as yet performed on the RAE aerofoil only, show that RQEVM costs about 6% and EARSM about 10% more than Wilcox $k$-$\omega$. Expectedly, this is less than the values determined for comparable models in a structured solver, owing to the fact that the computational effort for turbulence modelling constitutes a smaller fraction of the total cost in an unstructured code.

Finally, it should be mentioned that the use of models independent of topographical information, i.e. local models turned out to be advantageous, since the computation of the wall distance can be very tedious in complex three-dimensional configurations.