Thermo-acceleration waves and shock formation in Extended Thermodynamics of gravitational gases

Acceleration waves and oscillating gas bubbles modelled by rational extended thermodynamics

“…The behaviour of planar AWs in monatomic rarefied gases described by RET was already studied in many cases [8][9][10][11] and there is also a preliminary analysis for a polytropic gas described by a RET system with only six fields [15]. All the results confirm that shock formation is physically unlikely.…”

“…AWs can be generated in different materials and a large literature is devoted to this topic and to its application. For the sake of brevity, we quote here only some works related to gases [4][5][6][7][8][9][10][11] (and the references therein). In gases, AWs are produced by a perturbation, which could be caused for instance by a piston during its accelerated motion.…”

“…In fact, it has been shown that conservation laws provide for the transformation of an AW into a shock wave for any value of the initial amplitude [3,7,12], in contrast to the experimental evidence [13]. In a better model of balance laws, on the contrary, it is usually possible to identify a critical value of the initial amplitude below which the acceleration wave does not turn into a shock [2–4,7–9]. This modelling is consistent with experimental evidence if the threshold values for jump formation are sufficiently high.…”

Acceleration Waves in Rational Extended Thermodynamics of Rarefied Monatomic Gases

“…All the non-exceptional acceleration waves also exhibit a critical time, due to the hyperbolicity property of the equation set that is a time in which, for certain large values of the initial amplitude, the weak discontinuity wave becomes a strong discontinuity wave. However, this is more a mathematical question than a physical one, since in all the previous cases the initial critical amplitude is inversely proportional to τ, i.e., |G cr | 10 11 m/s 2 for helium at room temperature and usual pressure [8,9]. It is practically impossible to figure out an experiment where such a big discontinuity in the field derivative is generated, without a discontinuity in the field variables themselves.…”

“…However, this is not a sufficient condition: many authors stressed that a suitable dissipation is also required [3,4,7]. Under such conditions, the theory usually predicts the existence of a critical amplitude A cr and a critical time t cr [2,3,5,[7][8][9]. If the initial wave amplitude is greater than A cr , the evolution of the weak discontinuity, after the time t cr , brings to the shock formation.…”