The use of supercritical carbon dioxide (SC-CO2) as a working fluid in energy conversion systems has many benefits, including high efficiency, compact turbomachinery, and the abundance of CO2. A very important issue for design optimization and performance analysis of future SC Brayton cycles is concerned with the SC-CO2 flow inside high-speed compressors and turbines. The objective of this paper is to present a novel modeling approach to, and its use in numerical simulations of, SC-CO2 flow inside a high-speed compact compressor. The proposed approach capitalizes on using three different physical and mathematical formulations of one-dimensional (1D) models, i.e., compressible and incompressible flow models using actual properties of SC-CO2 and a compressible ideal gas model, as a reference to verify the predictive capabilities of a three-dimensional (3D) incompressible flow model. The incompressible model has been used to perform simulations for a complete detailed multidimensional model of an SC-CO2 high-speed compact compressor. The advantages of the new model include numerical stability, computational efficiency, and physical accuracy. In particular, it has been shown that the model's predictions are consistent with selected published technical data.