Unsteady one-dimensional flows of a vibrationally excited gas

Complete group analysis of the system of one-dimensional unsteady equations of the dynamics of a vibrationally excited gas is performed in the case of cylindrical and spherical symmetry. It is shown that the admitted Lie algebra does not contain the scaling generator of independent variables that defines the well-known self-similar solutions of strong shock wave problems for the similar system of the gas dynamics equations of an ideal gas. A modification of the characteristic relaxation time is proposed, which makes it possible to extend the admitted Lie algebra of the system by the generator of simultaneous scaling of independent variables and introduce a class of self-similar solutions. Using the problem of a strong linear explosion as an example, it is shown that the solution of the modified system of equations is physically consistent and fairly accurately describes the well-known effect of the divergence of static and vibrational temperatures behind the wave front.