  The linearized, compressible Navier-Stokes equations can be used to model
acoustic wave propagation in the presence of viscous and thermal boundary
layers. However, acoustic boundary layers are notorious for invoking
prohibitively high resolution requirements on numerical solutions of the
equations. We derive and present a strategy for how viscous and thermal
boundary-layer effects can be represented as a boundary condition on the
standard Helmholtz equation for the acoustic pressure. This boundary condition
constitutes an $O(\delta)$ perturbation, where $\delta$ is the boundary-layer
thickness, of the vanishing Neumann condition for the acoustic pressure
associated with a lossless sound-hard wall. The approximate model is valid when
the wavelength and the minimum radius of curvature of the wall is much larger
than the boundary layer thickness. In the special case of sound propagation in
a cylindrical duct, the model collapses to the classical Kirchhoff solution. We
assess the model in the case of sound propagation through a compression driver,
a kind of transducer that is commonly used to feed horn loudspeakers. Due to
the presence of shallow chambers and thin slits in the device, it is crucial to
include modeling of visco-thermal losses in the acoustic analysis. The
transmitted power spectrum through the device calculated numerically using our
model agrees well with computations using a hybrid model, where the full
linearized, compressible Navier-Stokes equations are solved in the narrow
regions of the device and the inviscid Helmholtz equations elsewhere. However,
our model needs almost two orders of magnitude less memory and computational
time than the more complete model.
