Inviscid and viscous stationary waves of gas flow through contracting–expanding nozzles

In this work we study steady states of one-dimensional viscous isentropic compressible flows through a contracting–expanding nozzle. Treating the viscosity coefficient as a singular parameter, the steady-state problem can be viewed as a singularly perturbed system. For a contracting–expanding nozzle, a complete classification of steady states is given and the existence of viscous profiles is established via the geometric singular perturbation theory. Particularly interesting is the existence of a maximal sub-to-super transonic wave and its role in the formation of other complicated transonic waves consisting of a sub-to-super portion.