A supersonic inlet turbine can extract substantial energy from the highly fluctuating and transonic flow delivered by a rotating detonation combustor (RDC). However, a transition duct is necessary to achieve the supersonic inlet conditions required by the turbine. In this work, the supersonic transition duct is designed with the method of characteristics (MOC). A generalized implementation of the MOC is proposed for the generation of annular ducts with asymmetric and rotated hub and shroud walls. The model is extended to deal with ideal and non-ideal flows, namely flows characterized by non-ideal thermodynamic effects, and its accuracy has been verified through comparison with results obtained with computational fluid dynamics (CFD) simulations. In addition, boundary layer flow equations are combined with the MOC to predict viscous losses on the endwalls and to adjust duct geometry by accounting for the boundary layer thickness. Furthermore, it is essential to predict the effects of the large unsteadiness generated by the detonation combustor for an efficient operation of the turbine. The maximum incidence angle at the turbine inlet is predicted with a one-dimensional annular duct model. Supersonic duct flow behavior to unsteady inlet conditions is characterized through two-dimensional inviscid axisymmetric unsteady CFD simulations. The accuracy of the reduced order models is finally verified with a three-dimensional unsteady viscous simulation assuming inlet flow conditions representative of RDC operation.