Shock structure and multiple sub-shocks in Grad 10-moment binary mixtures of monoatomic gases

Sub-shock formation in shock structure of a binary mixture of polyatomic gases

“…A sub-shock emerges only after the maximum characteristic velocity in the context of RET theory for a single fluid of rarefied gases according to the numerical calculations [23,24]. On the other hand, sub-shock may appear before the maximum characteristic velocity, and multiple sub-shock may also arise in the context of mixture theories [25][26][27] and toy models [24,28].…”

A Note on the Steady Navier–Stokes Equations Derived from an ES–BGK Model for a Polyatomic Gas

“…Profiles of different types appear, which become increasingly steep for increasing Mach number. It is well known that multi-temperature descriptions could give rise to other interesting phenomena in case of gas mixtures, such as the occurrence of (multiple) discontinuities in shock profiles [36][37][38]. Such shock waves may be generated in explosions [39,40], and could give rise to combustion phenomena [41,42].…”

Shock wave structure of multi-temperature Grad 10-moment equations for a binary gas mixture

“…mean velocity of the whole mixture) while the species temperatures are still well separate. This model is formally obtained starting from a kinetic description, by replacing the distribution functions with suitable Grad approximations [6,7] and assuming that species velocities share the same value.…”

“…We aim at testing such model on the classical problem of shock wave structure. The subject is topical and several interesting results on the occurrence of a smooth solution or on the presence of discontinuities (subshocks) have been proposed [13][14][15][16][17], especially for multi-velocity and multi-temperature Euler-like systems [3,18,19] and Grad 10-moment equations [6,7]. Since the 1950s [20] it has been well known that, even for a single gas, shock wave formation is not accurately described by Navier-Stokes equations, and higher-order closures, as Burnett [21] or Grad equations [22], are desirable.…”

“…The mathematical structure of Grad equations implies the occurrence of non-physical subshocks, namely of discontinuous shock wave solutions, for high Mach numbers, and suitable regularizations have been proposed to prevent these effects [23]. For a gas mixture the situation is much more involved, due to the possible presence of more critical values of the system parameters, corresponding to discontinuities in the shock wave profiles [6,7]. Here, we want to discuss the effects of a single velocity formulation on the shock profiles, by investigating strong and weak solutions and the presence of singular barriers [24] separating the limiting equilibrium states, and compare them with results obtained for multivelocity models [6,7,18].…”