Spectral problems for the orientation-free discrete kinetic models

We present computations using orientation-free discrete velocity models for the dispersion relationship of ultrasound propagation in monatomic hard-sphere gases (or a type of gas composed of a system of vortices). Comparisons with previous verified fixed-orientation results for the propagation of the sound mode in rarefied gases show that, if collective excitations are considered, an orientation-free eight-velocity model can capture more physical insights. We also demonstrate the symmetry property of the spectra using the orientation-free eight-velocity model.