Acceleration waves and oscillating gas bubbles modelled by rational extended thermodynamics

The study of acceleration waves for a rarefied polyatomic gas is carried out in planar, cylindrical and spherical geometry referring to the rational extended thermodynamics theory with 14 moments. The case of a rarefied monatomic gas is determined as a limit case, and the role of geometry and molecular degrees of freedom is investigated. In addition, the behaviour of an acceleration wave travelling inside an oscillating gas bubble is modelled by the 14-moment PDE system under adiabatic condition. We show that dissipation combined with hyperbolicity tends to inhibit shock formation, and that the dynamic pressure cannot be zero inside the oscillating bubble. This fact can produce observable effects even in the Navier–Stokes approximation, if the gas exhibits high bulk viscosity.

Compact acoustic travelling waves in a class of fluids with nonlinear material dispersion

We apply a phenomenological theory of continua put forth by Rubin, Rosenau and Gottlieb in 1995 to an important class of compressible media. Regarding the material characteristic length coefficient, α , not as constant, but instead as a quadratic function of the velocity gradient, we carry out an in-depth analysis of one-dimensional acoustic travelling waves in inviscid, non-thermally conducting fluids. Analytical and numerical methods are employed to study the resulting waveforms, a special case of which exhibits compact support. In particular, a phase plane analysis is performed; simplified approximate/asymptotic expressions are presented; and a weakly nonlinear, KdV-like model that admits compact travelling wave solutions (TWSs), but which is not of the class K ( m , n ), is derived and analysed. Most significantly, our formulation allows for compact, pulse-type, acoustic waveforms in both gases and liquids.