  Accurate simulations of sound propagation in narrow geometries need to
account for viscous and thermal losses. In this respect, effective boundary
conditions that model viscothermal losses in frequency-domain acoustics have
recently gained in popularity. Here, we investigate the time-domain analogue of
one such boundary condition. We demonstrate that the thermal part of the
boundary condition is dissipative in time domain as expected, while the viscous
part, unexpectedly, may lead to an infinite instability. A
finite-difference-time-domain scheme is developed for simulations of sound
propagation in a duct with only thermal losses, and the obtained transmission
characteristics are found to be in excellent agreement with frequency-domain
simulations.
