Conservation laws and invariant solutions of the non-linear governing equations associated with a thermodynamic model of a rotating detonation engines with Korobeinikov׳s chemical source term

• The nonlinear RDE model detonation engine is investigated from the group theoretical standpoint.
• Equations incorporate approximation of Korobeinikov׳s chemical reaction model.
• The transformations that leave the equations invariant are found.
• The conservation equations were constructed and the invariant solutions were obtained.

The non-linear governing gas dynamics equations that are used as a descriptor of a rotating detonation engine are investigated from the group theoretical standpoint. The equations incorporate approximation of Korobeinikov׳s chemical reaction model that are used to describe the two-dimensional detonation field on a surface of a two-dimensional cylindrical chamber without thickness. The transformations that leave the equations invariant are found. On the basis of these transformations, the conservation equations were constructed and the invariant solutions were obtained for specific form of the equation of state, for which the equations are non-linearly self-adjoint. The invariant solutions are given in terms of the functions that satisfy non-linear ordinary differential equations. The above reduction simplifies the analysis of the original non-linear system of partial differential equations on a surface of rotating cylinder.