factors were $0.8$ for velocities and $0.2$ for pressure. The initial conditions were pressure $p=p_{\infty}$, velocity $\mathbf{u}=0$ and density $\rho_{\mathrm{air}}=1.2\, \mathrm{kg/m^{3}}$. The time step was $\Delta t = 0.004\, \mathrm{s}$ and $6$ outer iterations were performed per time step. The total simulated time was selected $t_{\mathrm{end}}=0.5\, \mathrm{s}$, at which point a converged, quasi-steady solution was obtained in all simulations. Detailed information on finite-volume-based flow simulations can be found e.g. in Ferziger et al. (2020).

Simulations were performed for inhaling of air and compared to theoretical predictions from Sect. \[SECtheory\] for different gap height $H_{\mathrm{g}} \in [0.1\, \mathrm{mm}, 1\, \mathrm{mm}]$, gap width $B_{\mathrm{g}} \in [2.5\, \mathrm{cm}, 10\, \mathrm{cm}]$ and total flow rate $F_{\mathrm{t}} \in [30\, \mathrm{L/min}, 95\, \mathrm{L/min}]$.

To verify that the conclusions drawn from the 2D-flow simulations are applicable to realistic 3D-flow through face masks, also 3D-flow simulations were performed for a few representative configurations.

The simulation setup was the same as in the 2D-flow simulations, with the following exceptions: Head and mask had realistic geometries as shown in Fig. \[FIG3Dgeom\], and the air flows through the nostrils. The human head[^1] had a vertical distance between top of head and chin of $\approx 23\, \mathrm{cm}$. The face mask had a 