The discrete Boltzmann models are used to study the spectral problems related to the one-dimensional plane wave propaogation in monatomic gases which are fundamental in the nonequilibrium tatistical thermodynamics. The results show that the 8-velocity model can only describe the propagation of the diffusion mode (entropy wave) in the intermediate Knudsen number regime. The 4- and 6-velocity models, instead, can describe the propagation rnof sound modes quite well, after comparison with the continuum-mechanical results.
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