Axial compressors are used in a wide variety of aerodynamic applications and areone of the most important components in aero-engines. The operability of compressors ishowever limited at low-mass flow rates by fluid dynamic instabilities such as stall andsurge. These instabilities can lead to engine failure and loss of engine power which cancompromise the aircraft safety and reliability. Therefore, a better understanding of howstall occurs and the causes behind its inception is extremely important.In the vicinity of the stall line, the flow field is inherently unsteady due to theinteractions between adjacent rows of blades, formation of separation cells, and theviscous effects including shock-boundary layer interaction. Accurate modeling of thesephenomena requires a proper set of stable and accurate boundary conditions at the rotorstatorinterface that conserve mass, momentum and energy, while eliminating falsereflections.As a part of this effort, an existing 3D Navier-Stokes analysis for modeling singlestage compressors has been modified to model multi-stage axial compressors andturbines. Several rotor-stator interface boundary conditions have been implemented.These have been evaluated for the first stage (a stator and a rotor) of the two stage fuelturbine on the space shuttle main engine (SSME). Their effectiveness in conservingglobal properties such as mass, momentum, and energy across the interface, whileyielding good performance predictions has been evaluated. While all the methods gavesatisfactory results, a characteristic based approach and an unsteady sliding meshapproach are found to work best.Accurate modeling of the formation of stall cells requires the use of advancedturbulence models. As a part of this effort, a new advanced turbulence model calledHybrid RANS/KES (HRKES) has been developed and implemented. This model solvesMenter's k--SST model near walls and switches to a Kinetic Eddy Simulation (KES)model away from walls. The KES model solves directly for local turbulent kinetic energyand local turbulent length scales, alleviating the grid spacing dependency of the lengthscales found in other Detached Eddy Simulation (DES) and Hybrid RANS/LES (HRLES)models. Within the HRKES model, combinations of two different blending functionshave been evaluated for blending the near wall model to the KES model. The use ofrealizability constraints to bound the KES model parameters has also been studied forseveral internal and external flows.The current methodology is used in the prediction of the performance map for theNASA Stage 35 compressor configuration as a representative of a modern compressorstage. The present approach is found to satisfactory predict the onset of stall. It is foundthat the rotor blade tip leakage vortex and its interaction with the shock wave is mainlythe reason behind the stall inception in this compressor stage.