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12.2.4 Computational Effort: CPU Time and Solution Behavior

In terms of computation, the Spalart-Allmaras model is the least expensive turbulence model of the options provided in FLUENT, since only one turbulence transport equation is solved.

The standard $k$- $\epsilon$ model clearly requires more computational effort than the Spalart-Allmaras model since an additional transport equation is solved. The realizable $k$- $\epsilon$ model requires only slightly more computational effort than the standard $k$- $\epsilon$ model. However, due to the extra terms and functions in the governing equations and a greater degree of non-linearity, computations with the RNG $k$- $\epsilon$ model tend to take 10-15% more CPU time than with the standard $k$- $\epsilon$ model. Like the $k$- $\epsilon$ models, the $k$- $\omega$ models are also two-equation models, and thus require about the same computational effort.

Compared with the $k$- $\epsilon$ and $k$- $\omega$ models, the RSM requires additional memory and CPU time due to the increased number of the transport equations for Reynolds stresses. However, efficient programming in FLUENT has reduced the CPU time per iteration significantly. On average, the RSM in FLUENT requires 50-60% more CPU time per iteration compared to the $k$- $\epsilon$ and $k$- $\omega$ models. Furthermore, 15-20% more memory is needed.

Aside from the time per iteration, the choice of turbulence model can affect the ability of FLUENT to obtain a converged solution. For example, the standard $k$- $\epsilon$ model is known to be slightly over-diffusive in certain situations, while the RNG $k$- $\epsilon$ model is designed such that the turbulent viscosity is reduced in response to high rates of strain. Since diffusion has a stabilizing effect on the numerics, the RNG model is more likely to be susceptible to instability in steady-state solutions. However, this should not necessarily be seen as a disadvantage of the RNG model, since these characteristics make it more responsive to important physical instabilities such as time-dependent turbulent vortex shedding.

Similarly, the RSM may take more iterations to converge than the $k$- $\epsilon$ and $k$- $\omega$ models due to the strong coupling between the Reynolds stresses and the mean flow.


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