Figure 6. Topological edge states with mass exchange considered.

(a)Velocity field in the supercell of the lattice found by solving the stationary Navier–Stokes equation with air motion produced by a pressure difference of 10 Pa across the fan, indicated by the grey region inside resonators. Arrows show the air velocity direction and magnitude, and the colour shows the local magnitude of the velocity, as indicated by the colour bar. (b) Acoustic band structure of the supercell for the velocity field shown in (a). Edge modes are plotted by red and black colours, and bulk modes are shown in blue. (c) Acoustic field profile corresponding to the topological edge mode shown by red in b.