## 2 Materials and Methods
### Numerical Model and Methods
#### 2.2.4 Mesh Generation and Mesh Motion  
The starting mesh was the fine mesh proposed by [PERSON] et al. [50], which was subjected to a mesh independence study. Since the subglottal pressure in [PERSON] et al. [50] was lower than the current study, the mesh independence study was reprocessed and extended. The maximum axial velocity at the glottis and 10 mm downstream of the glottal duct exit, the mean static pressure along the center axis and the flow rate were deviated by only 0.4%, 0.01%, 1.2% and 0.07%, respectively, from the finest mesh in the mesh independence study containing approximately 40 million cells. Therefore, the proposed mesh is valid for the higher subglottal pressure applied in this study. The mesh consisted of hexahedral elements that were refined in the glottal area (glottis refinement) and near supraglottal region (Figure 4). The overset mesh approach provided by STAR-CCM+ was employed to manage the mesh motion for moving boundaries. In this method, a fixed Eulerian background mesh is assigned to the whole numerical domain and an overset mesh wrapped around each vocal fold. The cells in the overset regions are always active and deform according to the movement of the boundaries in an Arbitrary Lagrangian-Eulerian (ALE) manner. The cells in the background region are fixed and  
\begin{table}
\begin{tabular}{l l l l} \hline \hline  & \(\mathbf{P_{s}}\) & \(\mathbf{P_{out}}\) & **Supraglottal Channel Length** \\ \hline C1 & \(\mathrm{P^{\prime}_{s}(t)}\) & \(\mathrm{P_{0}}\) & 60 mm \\ C2 & \(\mathrm{P^{\prime}_{s}}\) & \(\mathrm{P_{0}}\) & 60 mm \\ C3 & \(\mathrm{P^{\prime}_{s}(t)}\) & \(\mathrm{P^{\prime}_{60}(t)}\) & 60 mm \\ C4 & \(\mathrm{P^{\prime}_{s}}\) & \(\mathrm{P^{\prime}_{60}(t)}\) & 60 mm \\ C5 & \(\mathrm{P^{\prime}_{s}}\) & \(\mathrm{P_{0}}\) & 190 mm \\ \hline \hline \end{tabular}
\end{table}
Table 1: Simulation cases with boundary conditions for comparison with the experimental results. \(\mathrm{P^{\prime}(t)}\), \(\mathrm{P_{s}}\), \(\mathrm{P_{out}}\) and \(\mathrm{P_{60}}\) are the time-varying experimental pressure, subglottal pressure, outlet pressure and pressure at 60 mm downstream of the glottis exit, respectively.  
Figure 3: Experimental (**a**) subglottal pressure waveform (\(\mathrm{P^{\prime}_{s}(t)}\)) and (**b**) pressure waveform at 60 mm downstream of the glottis exit (\(\mathrm{P^{\prime}_{60}(t)}\)). The red lines are the corresponding mean pressure values.  
become inactive wherever they overlap with the overset cells. As a result, the total number of cells changes during an oscillation cycle depending on the distance between the vocal folds. Furthermore, some cells are required between the overset and background regions as interpolation layers. Therefore, complete closure of the glottis was not possible in this model and a minimum glottal gap of 0.2 mm was forced in the glottis during the glottal closure, which caused negligible leakage.  
For this starting mesh, the total number of cells ranged between 2.1 and 2.9 million cells. The corresponding time step size was \(1\times 10^{-6}\) s. This led to a mean CFL number of 5 which is appropriate for implicit solvers [63; 64]. More details of the mesh motion strategies and the mesh independence study can be found in [PERSON] et al. [50].