## 26.13.1 Smoothing

Two smoothing methods available in FLUENT are:

• Laplace smoothing: It can be applied to all types of grids, but it is recommended to use it for quadrilateral and hexahedral grids.

• Skewness-based smoothings: It is recommended for triangular and tetrahedral grids. This method can be used alternatively with face swapping (see Section  26.13.3).

Laplacian Smoothing

When you use this method, a Laplacian smoothing operator is applied to the unstructured grid to reposition nodes. The new node position is the average of the positions of its node neighbors. The relaxation factor (with value between 0.0 and 1.0) multiplies the computed node position increment. A value of zero results in no movement of the node and a value of unity results in movement equivalent to the entire computed increment. Figure  26.13.2 illustrates the new node position for a typical configuration of quadrilateral cells. The dashed line is the original grid and the solid line is the final grid.

This repositioning strategy improves the skewness of the mesh, but relaxes the clustering of node points. In extreme circumstances, the present operator may create grid lines that cross over the boundary, creating negative cell volumes. This is most likely to occur near sharp or coarsely resolved convex corners, especially if you perform multiple smoothing operations with a large relaxation factor. Figure  26.13.3 illustrates an initial tetrahedral grid before one unrelaxed smoothing iteration creates grid lines that cross over each other (Figure  26.13.4).

The default smoothing parameters are designed to improve grid quality with minimal adverse effects, but save a case file before smoothing the mesh. If you apply a conservative relaxation factor and start with a good quality initial grid, the frequency of failure due to smoothing is extremely low in two dimensions. However, corruption of the grid topology occurs much more frequently in three dimensions, particularly with tetrahedral grids.

The smoothing operator can also be applied repeatedly, but as the number of smoothing sweeps increase, the node points have a tendency to pull away from boundaries and the grid tends to lose any clustering characteristics.

To perform Laplacian smoothing, do the following:

1.   In the Smooth/Swap Grid panel (Figure  26.13.1), select laplace in the Method drop-down list under Smooth.

2.   Set the factor by which to multiply the computed position increment for the node in the Relaxation Factor field. The lower the factor, the more reduction in node movement.

3.   Specify the number of successive smoothing sweeps to be performed on the grid in the Number of Iterations field. The default value is 4.

4.   Click the Smooth button.

Skewness-Based Smoothing

When you use skewness-based smoothing, FLUENT applies a smoothing operator to the grid, repositioning interior nodes to lower the maximum skewness of the grid. FLUENT will try to move interior nodes to improve the skewness of cells with skewness greater than the specified "minimum skewness.'' This process can be very time-consuming, so perform smoothing only on cells with high skewness.

Improved results can be obtained by smoothing the nodes several times. There are internal checks that will prevent a node from being moved if moving it causes the maximum skewness to increase, but it is common for the skewness of some cells to increase when a cell with a higher skewness is being improved. Thus, you may see the average skewness increase while the maximum skewness is decreasing.

 Carefully consider whether the improvements to the mesh due to a decrease in the maximum skewness are worth the potential increase in the average skewness. Performing smoothing only on cells with very high skewness (e.g., 0.8 or 0.9) may reduce the adverse effects on the average skewness.

To perform skewness-based smoothing, do the following:

1.   In the Smooth/Swap Grid panel (Figure  26.13.1), select skewness in the Method drop-down list under Smooth.

2.   Set the minimum cell skewness value for which node smoothing will be attempted in the Minimum Skewness field. FLUENT will try to move interior nodes to improve the skewness of cells with skewness greater than this value. By default, Minimum Skewness is set to 0.4 for 2D and 0.8 for 3D.

3.   Specify the number of successive smoothing sweeps to be performed on the grid in the Number of Iterations field. The default value is 4.

4.   Click the Smooth button.

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