Strong point explosion in vibrationally exciting gas

Group analysis of the two‐dimensional two‐temperature gas dynamics equations

“…2,3 Therefore, it is of interest to the systematic study of mathematical properties of the two-temperature model, in particular, the group properties and invariant solutions, and compare them with the analogous properties of the well-studied ideal gas model. The first results in this direction were obtained in previous studies 4,5 for a system of spatially one-dimensional equations. In particular, a modification of the relaxation time in the Landau-Teller equation was proposed.…”

“…It can be seen that the entropy production is zero only in equilibrium flow, when T = T v . It follows from Equation (10) that a meaningful comparison of two models, the classical gas dynamics equations and the equations with the Landau-Teller equation, on the basis of invariant solutions is only possible for unsteady nonisentropic flows, as was done in previous studies 4,5 for unsteady one-dimensional in space flows with shock waves.…”

“…In this regard, in Siriwat et al, 4 it was assumed that for flows with large space-time gradients of macroparameters, the time dependence at small time intervals can be approximated by a simple relation of the form…”

“…At the same time, it was shown in Siriwat et al 4 that the model with $$$ \tau = const $$$ does not contain invariant solutions used for constructing the solution of a strong point explosion, because in the Lie algebra (), there is absent the generator of simultaneous expansion of the independent variables $$$ {\tilde{X}}_6 $$$ defining the class of self‐similar solutions well‐known in the gas dynamics 14…”

“…It can be seen that the Lie algebra (), in contrast to (), contains the generator of the expansion of the independent variables $$$ {\tilde{X}}_6 $$$. In the one‐dimensional case in space, this made it possible to obtain self‐similar solutions with strong shock waves, 4,5 which adequately described the well‐known physical effects of the lagging growth of the vibrational temperature from the static temperature with its subsequent leveling.…”