Ultrasound propagation studied using the discrete kinetic theory

We use discrete kinetic models to study the dispersion relations of the one -dimensional plane-ultrasound-wave propagation in monatomic gases, which ar e fundamental in non-equilibrium statistical thermodynamics. The results sh ow that six- and eight-velocity models can capture the propagation of the d iffusion mode, which has not been reported on since 1965. A four-velocity m odel is seen to capture the propagation of the sound mode in the higher-Knu dsen-number regime quite well when we compare our calculated results on the dispersion (phase speed and absorption) relations with Greenspan's measure ments.