Detonation cycles are identified as an efficient alternative to the Brayton cycles used in power and propulsion applications. Rotating Detonation Engine (RDE) operating on a detonation cycle works by compressing the working fluid across a detonation wave, thereby reducing the number of compressor stages required in the thermodynamic cycle. Numerical analyses of RDEs are flexible in understanding the flow field within the RDE, however, three-dimensional analyses are expensive due to the differences in time-scale required to resolve the combustion process and flow-field. The alternate two-dimensional analyses are generally modeled with perfectly premixed fuel injection and do not capture the effects of improper mixing arising due to discrete injection of fuel and oxidizer into the chamber. To model realistic injection in a 2-D analysis, the current work uses an approach in which, a Probability Density Function (PDF) of the fuel mass fraction at the chamber inlet is extracted from a 3-D, cold-flow simulation and is used as an inlet boundary condition for fuel mass fraction in the 2-D analysis. The 2-D simulation requires only 0.4% of the CPU hours for one revolution of the detonation compared to an equivalent 3-D simulation. Using this method, a perfectly premixed RDE is comparing with a non-premixed case. The performance is found to vary between the two cases. The mean detonation velocities, time-averaged static pressure profiles are found to be similar between the two cases, while the local detonation velocities and peak pressure values vary in the non-premixed case due to local pockets fuel rich/lean mixtures. The mean detonation cell sizes are similar, but the distribution in the non-premixed case is closer due to stronger shock structures. An analytical method is used to check the effects of fuel-product stratification and heat loss from the RDE and these effects adversely affect the local detonation velocity. Overall, this method of modeling captures the complex physics in an RDE with the advantage of reduced computational cost and therefore can be used for design and diagnostic purposes.