Using the lattice-Boltzmann method

a numerical simulation was performed for the attenuation of plane sound waves both in one and two-dimensional channels. Sine-type velocity and density were given as the sound source at the inlet. In the vertical direction

periodic boundary condition was adopted for one-dimensional channel

and non-slip boundary condition for two-dimensional channel. Profiles of the density

velocity and pressure gradient were obtained. The results show that the waves will attenuate along the propagating direction due to the internal viscous dissipation of the propagation medium

and the friction of the walls which is only for the two-dimensional case. The attenuation of the sound waves leads to a negative exponent pressure gradient. With the increase of the wavelength or the decrease of the medium viscosity

the attenuation of sound waves becomes slower

and the pressure gradient becomes smaller. For both cases

the results agree well with the analytical solutions. In addition

the sound level of the source was presented.