12.2.1 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 ANSYS 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 the ones with the standard $k$- $\epsilon$ model. Similar to the $k$- $\epsilon$ models, the $k$- $\omega$ models are also two-equation models, and require the same amount of 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 ANSYS FLUENT has reduced the CPU time per iteration significantly. On average, the RSM in ANSYS 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 a turbulence model can affect ANSYS FLUENT's ability 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.

For more information about the theory behind the Spalart-Allmaras model, see this section in the separate Theory Guide.

For more information about the theory behind the Standard and SST $k$- $\omega$models, see this section in the separate Theory Guide.

For more information about the theory behind the Standard, RNG, and Realizable $k$- $\epsilon$ models, see this section in the separate Theory Guide.

For more information about the theory behind the $k$- $kl$- $\omega$ Transition model, see this section in the separate Theory Guide.

For more information about the theory behind the SST model, see this section in the separate Theory Guide.

For more information about the theory behind the $v^2$- $f$ model, see this section in the separate Theory Guide.

For more information about the theory behind the Reynolds Stress model, see this section in the separate Theory Guide.

For more information about the theory behind the Detached Eddy Simulation model, see this section in the separate Theory Guide.

For more information about the theory behind the Large Eddy Simulation model, see this section in the separate Theory Guide.

For more information about the theory behind near-Wall treatments for wall-bounded turbulent flows, see this section in the separate Theory Guide.