  The acoustic wave-propagation without mean flow and heat flux can be
described in terms of velocity and pressure by the compressible nonlinear
Navier-Stokes equations, where boundary layers appear at walls due to the
viscosity and a frequency interaction appears, $\textit{i.e.}$ sound at higher
harmonics of the excited frequency $\omega$ is generated due to nonlinear
advection. We use the multiharmonic analysis to derive asymptotic expansions
for small sound amplitudes and small viscosities both of order $\varepsilon^2$
in which velocity and pressure fields are separated into far field and
correcting near field close to walls and into contributions to the multiples of
$\omega$. Based on the asymptotic expansion we present approximate models for
either the pressure or the velocity for order $0$, $1$ and $2$, in which
impedance boundary conditions include the effect of viscous boundary layers and
contributions at frequencies $0$ and $2\cdot\omega$ depend nonlinearly on the
approximation at frequency $\omega$. In difference to the Navier-Stokes
equations in time domain, which has to be resolved numerically with meshes
adaptively refined towards the wall boundaries and explicit schemes require the
use of very small time steps, the approximative models can be solved in
frequency domain on macroscopic meshes. We studied the accuracy of the
approximated models of different orders in numerical experiments comparing with
reference solutions in time-domain.
