## 4 Results and Discussion  
### Reduction of Computational Costs  
The results obtained with different mesh resolutions M1-M3 (Table 2) were compared qualitatively and quantitatively with the results of the base mesh to evaluate their validity. The supraglottal flow fields at a representative instance in the last quarter of the oscillation cycle are displayed in Figure 8. It can be seen that the deflection of the glottal jet, which is a characteristic feature of the laryngeal flow, was reproduced with all the mesh resolutions. In general, the jet skews either upwards or downwards depending on the flow conditions in the supraglottal channel [50; 53]. In the instantaneous oscillation cycle shown in Figure 8, upward jet deflection was found for M1 and M3 and downward deflection for MB and M2. Regarding the flow field within the glottal duct (Figure 9), symmetry of the glottal jet was preserved by all the meshes. However, flow separation occurred more upstream for meshes MB and M3 whereas the jet remained attached to the glottal walls for M1 and M2. Thus, only M3 reproduced the typical intraglottal vortices in the region of separated flow. Thereby, the separation points were similarly estimated in M3 comparable to MB. These intraglottal vortices have been identified in the literature [68; 69] to increase the closing forces on the vocal folds and the intensity of tonal sound. According to [PERSON] and [PERSON] [70], elliptical jets show switching of the main axes in the cross-sectional plane along their streamwise evolution. This three-dimensional flow phenomenon has also been reported in experimental and numerical larynx models with elliptical glottis shapes [47; 48; 50; 51; 71]. In Figure 10, the iso-surfaces of the velocity magnitude (50 m/s) are provided at a representative time instance (0.58 T). In the coronal perspective (Figure 10, left column), the diameter of the jet increased during its streamwise evolution, whereas its diameter in the sagittal perspective (Figure 10, right column) decreased at the same time. This effect, called lengthwise _vena contracta_[47], was reproduced by all of the meshes. Additionally, the length of the jet was similar in all of them. Figure 8: Velocity magnitude contour plots with streamlines in the mid-coronal plane for all mesh resolutions MB-M3 (parts (**a–d**)) at the same time instance 0.8T in the oscillation cycle. The arrow shows the flow direction. The flow rates during an oscillation cycle are shown in Figure 11 for all four mesh resolutions. Meshes M1-M3 with decreased resolutions produced a very similar trend in comparison with the base mesh MB. During the closing phase of the cycle, M1-M3 exhibited higher flow rates, with the largest deviations for M1 and M2. The reason is the full attachment of the flow to the glottal walls in these meshes for the presented cycle whereas the flow separated from the walls in M3, similar to the base mesh. Subsequently, the increase in flow rate is the result of the divergent expansion of glottal  
Figure 10: Velocity magnitude iso-surface of 50 m/s at the time instance 0.58 T in the oscillation cycle in coronal (left column) and sagittal (right column) perspectives for meshes MB–M3 (parts (**a–d**)). Figure 9: Velocity magnitude contours with slashed streamlines in the mid-coronal plane of the glottal duct of different meshes MB–M3 (parts (**a–d**)) at the time instance of maximum glottal divergent angle (0.58 T). flow [72] in M1 and M2 (Figure 9b,c). The deviation of the flow rate in M3 was lowest owing to the very similar flow pattern to that of MB during the closing period. At the very beginning and end of the cycle with the closed glottis, MB, M1 and M2 produced flow leakage, which degenerated almost to zero in M3 owing to the blockage of the glottal duct as described in Section 2.2.5. Figure 12 shows the time evolution of the instantaneous static pressure and velocity at point P1 in the near supraglottal region (Figure 1).