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6.2.2 Mesh Quality

The quality of the mesh plays a significant role in the accuracy and stability of the numerical computation. The attributes associated with mesh quality are node point distribution, smoothness, and skewness.

Regardless of the type of mesh used in your domain, checking the quality of your grid is essential. Depending on the cell types in the mesh (tetrahedral, hexahedral, polyhedral, etc.), different quality criteria are evaluated:

The "aspect ratio" is a measure of the stretching of a cell, and is defined as the ratio of the maximum distance between the cell centroid and face centroids to the minimum distance between the nodes of the cell (see Figure  6.2.2). If the quality of your grid is questionable, then a warning will appear in the console noting the problems FLUENT has detected with your mesh. The warnings that you see use rules of thumb and although it is a warning, you may still be able to run the case successfully.

Figure 6.2.2: Measurements Involved in Calculating the "Aspect Ratio"
figure

To check the quality of your grid, you can use the text command:

grid $\rightarrow$ quality

A message will be printed to the console. The example below demonstrates the output the text command yields.

Grid Quality:
Applying quality criteria for triangular/mixed cells.
Maximum cell squish =  4.61001e-01
Maximum cell skewness =  4.48776e-01
Maximum `aspect_ratio' =  5.23830e+00



Node Density and Clustering


Since you are discretely defining a continuous domain, the degree to which the salient features of the flow (such as shear layers, separated regions, shock waves, boundary layers, and mixing zones) are resolved , depends on the density and distribution of nodes in the mesh. In many cases, poor resolution in critical regions can dramatically alter the flow characteristics. For example, the prediction of separation due to an adverse pressure gradient depends heavily on the resolution of the boundary layer upstream of the point of separation.

Resolution of the boundary layer (i.e., mesh spacing near walls) also plays a significant role in the accuracy of the computed wall shear stress and heat transfer coefficient . This is particularly true in laminar flows where the grid adjacent to the wall should obey


 y_p \sqrt{\frac{u_{\infty}}{\nu x}} \;\;\; \leq \;\;\; 1 (6.2-1)


where $y_p$ = distance to the wall from the adjacent cell centroid
  $u_{\infty}$ = free-stream velocity
  $\nu$ = kinematic viscosity of the fluid
  $x$ = distance along the wall from the starting point of the boundary layer

Equation  6.2-1 is based upon the Blasius solution for laminar flow over a flat plate at zero incidence [ 322].

Proper resolution of the mesh for turbulent flows is also very important. Due to the strong interaction of the mean flow and turbulence, the numerical results for turbulent flows tend to be more susceptible to grid dependency than those for laminar flows. In the near-wall region, different mesh resolutions are required depending on the near-wall model being used. See Section  12.11 for guidelines.

In general, no flow passage should be represented by fewer than 5 cells. Most cases will require many more cells to adequately resolve the passage. In regions of large gradients, as in shear layers or mixing zones, the grid should be fine enough to minimize the change in the flow variables from cell to cell. Unfortunately, it is very difficult to determine the locations of important flow features in advance. Moreover, the grid resolution in most complicated 3D flow fields will be constrained by CPU time and computer resource limitations (i.e., memory and disk space). Although accuracy increases with larger grids, the CPU and memory requirements to compute the solution and postprocess the results also increase. Solution-adaptive grid refinement can be used to increase and/or decrease grid density based on the evolving flow field, and thus provides the potential for more economical use of grid points (and hence reduced time and resource requirements). See Chapter  26 for information on solution adaption.



Smoothness


Truncation error is the difference between the partial derivatives in the governing equations and their discrete approximations. Rapid changes in cell volume between adjacent cells translate into larger truncation errors. FLUENT provides the capability to improve the smoothness by refining the mesh based on the change in cell volume or the gradient of cell volume. For information on refining the grid based on change in cell volume. (See Sections  26.4 and  26.8).



Cell Shape


The shape of the cell (including its skewness and aspect ratio) also has a significant impact on the accuracy of the numerical solution.



Flow-Field Dependency


The effect of resolution, smoothness, and cell shape on the accuracy and stability of the solution process is dependent on the flow field being simulated. For example, very skewed cells can be tolerated in benign flow regions, but can be very damaging in regions with strong flow gradients.

Since the locations of strong flow gradients generally cannot be determined a priori, you should strive to achieve a high-quality mesh over the entire flow domain.


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