*3.3. Assessment of Deformed Mesh Quality*

This section discusses the influence of shape deformation on the mesh quality using the metric defined in Section 2.1.2. Figure 12a displays the mesh orthogonality angle distribution plotted on a symmetry plane of selected exceptionally deformed duct geometry. Although a fall in the quality criterion is evident in the strongly warped regions, the bulk values are well above the warning limit of 20◦.

Figure 12b shows a histogram of the minimum value of the orthogonality angle for all solutions produced in the course of optimization. The dashed line denotes the metric's reference value for the baseline geometry. The bulk of generated solutions maintain the quality criterion value close to the reference level. Some cases, however, report a reduction in the orthogonality angle, yet still without violating the warning limit. Finally, a few solutions show criterion values below 20◦. Such distortion in the mesh elements might trigger a warning for the flow solver. After inspection, the cases were identified as

excessively deformed and, as such, located far from the objective target. These instances did not harm the solver's stability and convergence; hence, they were accepted.
