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12.11.1 Near-Wall Mesh Guidelines

Wall Functions

The log-law, which is valid for equilibrium boundary layers and fully developed flows, provides upper and lower bounds on the acceptable distance between the cell centroid and the wall for wall-adjacent cells. The distance is usually measured in the wall unit, $y^+$ ( $\equiv \rho u_{\tau} y/\mu$), or $y^*$. Note that $y^+$ and $y^*$ have comparable values when the first cell is placed in the log-layer.

Enhanced Wall Treatment

Although the enhanced wall treatment is designed to extend the validity of near-wall modeling beyond the viscous sublayer, it is still recommended that you construct a mesh that will fully resolve the viscosity-affected near-wall region. In such a case, the two-layer component of the enhanced wall treatment will be dominant and the following mesh requirements are recommended (note that, here, the mesh requirements are in terms of $y^+$, not $y^*$):

Spalart-Allmaras Model

The Spalart-Allmaras model in its complete implementation is a low-Reynolds-number model. This means that it is designed to be used with meshes that properly resolve the viscous-affected region, and damping functions have been built into the model in order to properly attenuate the turbulent viscosity in the viscous sublayer. Therefore, to obtain the full benefit of the Spalart-Allmaras model, the near-wall mesh spacing should be as described in Section  12.11.1 for the enhanced wall treatment.

However, as discussed in Section  12.3.7, the boundary conditions for the Spalart-Allmaras model have been implemented so that the model will work on coarser meshes, such as would be appropriate for the wall function approach. If you are using a coarse mesh, you should follow the guidelines described in Section  12.11.1.

In summary, for best results with the Spalart-Allmaras model, you should use either a very fine near-wall mesh spacing (on the order of $y^+ = 1$) or a mesh spacing such that $y^+ \geq 30$.

$k$- $\omega$ Models

Both $k$- $\omega$ models available in FLUENT are available as low-Reynolds-number models as well as high-Reynolds-number models. If the Transitional Flows option is enabled in the Viscous Model panel, low-Reynolds-number variants will be used, and, in that case, mesh guidelines should be the same as for the enhanced wall treatment. However, if this option is not active, then the mesh guidelines should be the same as for the wall functions.

Large Eddy Simulation

For the LES implementation in FLUENT, the wall boundary conditions have been implemented using a law-of-the-wall approach as described in Section  12.9.4. This means that there are no computational restrictions on the near-wall mesh spacing. However, for best results, it might be necessary to use a very fine near-wall mesh spacing (on the order of $y^+ = 1$).

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