Resonance in rarefied gases

Dispersion and damping of ultrasound waves are a standard test for mathematical models of rarefied gas flows. Normally, one considers waves in semi-infinite systems in relatively large distance of the source. For a more complete picture, ultrasound propagation in finite closed systems of length L is studied by means of several models for rarefied gas flows: the Navier-Stokes-Fourier equations, Grad’s 13 moment equations, the regularized 13 moment equations, and the Burnett equations. All systems of equations are considered in simple 1-D geometry with their appropriate jump and slip boundary conditions. Damping and resonance are studied in dependence of frequency and length. For small L, all wave modes contribute to the solution.