Numerical methods are an integral part of the design process of modern turbomachinery and contribute to a significant increase in time and resource efficiency. Numerous methods used for this purpose are based on the assumption of a calorically perfect gas, which enables a suitable approximation of the real fluid properties in the context of conventional working media such as air. In utilising alternative energy sources, such processes are becoming increasingly relevant for which the choice of working medium can be tailored to the application. The fluids used due to their special thermophysical properties can only be described inadequately by the model of the calorically perfect gas and are therefore classified as non-ideal. Since it is often impossible to take this non-ideality or possible phase change phenomena into account using established numerical methods, a design of related turbomachinery first requires the development of suitable methods. The approach for calculating numerical flux terms presented in this work contributes to that and can be applied to single-phase and two-phase flows of non-ideal fluids. In addition to high numerical robustness against discontinuities, it is characterised in particular by its applicability to arbitrary equations of state. Various modelling approaches can be used to describe the dispersed phase formed during a phase change in different degrees of detail. Thus, the droplet size distribution can be modelled as either monodispersed or polydispersed, whereby, in the latter case, it is described through its statistical moments. Furthermore, the developed method enables the consideration of velocity differences between the phases, which lays the foundation for a detailed investigation of the movement of the dispersed phase in the flow field. By tabulating the thermophysical quantities, it is also possible to achieve an increase in calculation time efficiency that is relevant in the context of the design process. The associated loss in terms of accuracy of description is minimised by using a Taylor series approach for interpolation. A verification and validation based on a representative selection of test cases demonstrates the applicability of the developed method to single-phase and two-phase flows of compressible non-ideal fluids of different molecular complexity. In particular, the phase change based on homogeneous non-equilibrium condensation is described in high agreement with results of experimental investigations.