Spectral problems for the discrete velocity models

We use the discrete velocity models to study the spectral problems related to the 1D plane wave propagation in monatomic gases which are fundamental i n the rarefied gases dynamics and nonequilibrium statistical thermodynamics . The results show that 6- and 8-velocity models can only capture the propa gation of diffusion mode (entropy wave) in the intermediate Knudsen number regime. 4-velocity model instead captures the propagation of sound mode qui te well after the comparison with the continuum-mechanic results.