A more robust method for solving the governing equations of a one-dimensional stage-by-stage dynamic compression system model was developed and validated. The improved method was then applied to two-dimensional post-stall models. The improvement in robustness was achieved by modeling the governing equations with upwind differencing and use of implicit time integration. A special form of upwind flux, flux difference splitting with source term treatment, FDSS, was developed for the model. A two-dimensional axisymmetric model was developed to allow post-stall modeling of split flowpath systems such as turbofans. This model was an entirely new concept. Additionally, a two-dimensional axial-circumferential model of rotating stall cell development and propagation was developed based on previous work. All of the models developed applied upwind differencing techniques to improve upon central-difference methods. / Ph. D.