mask was represented by a simplified polygonal shape. The mask surface is the same as in Sect. \[SECtheory\], $S_{\mathrm{m}}=0.015833\, \mathrm{m^{2}}$, and it is modeled as a porous interface with pressure drop $\Delta p $ according to Eq. (\[EQpm\]), with viscous porous resistance $C_{\mathrm{m}}=2000\, \mathrm{m/s}$ unless stated otherwise. The top boundary ($y=0.2\, \mathrm{m}$) is set up as pressure outlet, with atmospheric pressure $p_{\infty}$ prescribed. Symmetry boundary conditions are prescribed at boundaries $x=0.4\, \mathrm{m}$, $y=-0.2\, \mathrm{m}$, $z=0\, \mathrm{m}$ and $z=0.1\, \mathrm{m}$. At the outward end surface $S_{\mathrm{t}}$ of the nose-channel, the velocity $u_{\mathrm{t}}$ is prescribed so that $u_{\mathrm{t}}S_{\mathrm{t}}=F_{\mathrm{t}}$. All other boundaries are impermeable, no-slip wall boundaries.

![Computational domain for 2D-flow simulations through a generic mask showing the pressure distribution, with close-up of nose, mask and gap; note that throughout this work, the pressure $p$ is given relative to atmospheric pressure $p_{\infty}$; after the simulation is finished, the pressure for inhaling with flow rate $F_{\mathrm{t}}=30\, \mathrm{L/min}$ is nearly uniform inside the mask[]{data-label="FIG2Ddom"}](images/Auswahl_073b.png){width="\linewidth"}

The simulations were performed quasi-two-dimensional (2D), i.e. the grid is only 1 cell thick in $z$-direction with symmetry conditions applied at front and back planes. With correctly prescribed total flow rate $F_{\mathrm{t}}$, nose cross-section area $S_{\mathrm{t}}$, mask filter surface $S_{\mathrm{m}}$ and 