Multidimensional wave fronts propagation along the beams associated with thermodynamic model of a rotating detonation engine

The main purpose here is to develop an analytic approach for investigating the wave front propagation on a surface of a cylinder that can be used as a descriptor of a detonation engine. The analysis is based on a weakly nonlinear approximated gas dynamic equations with incorporated approximation of the 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. We found that the wave fronts can be expressed analytically in explicit form for special classes of flow (e.g. isentropic gas flow). In more general cases, the dynamics of wave fronts can still be determined explicitly provided that the wave front is known at initial time and the exact solution is either known a priori, e.g. from experimental or numerical analysis.