Recently, we have developed a numerical method for the simulation of supercritical-fluid flows, in which a state-of-the-art computational fluid dynamics (CFD) method was coupled with a program package for thermophysical properties of fluids (PROPATH). This method was further coupled with mathematical models for the nucleation, condensation and coagulation governing the crystallisation and condensation. We applied this method to the rapid expansion of supercritical solutions (RESS). In RESS, supercritical carbon dioxide (scCO2) containing a solute material streams into a capillary nozzle, expanding in an expansion chamber. The RESS process includes multi-physics problems, such as the phase change from scCO2 to a CO2 gas flow, crystallisation of the solute material, a supersonic flow with an expansion jet with shocks, and CO2 condensation. In this chapter, we primarily explain the fundamental equations and numerical methods employed in the multi-physics CFD method for the simulation of scCO2 flows and derive the mathematical models of nucleation, condensation and coagulation based on the classical nucleation theory (CNT) for simulating non-equilibrium condensation of CO2 gas and crystallisation of solute materials. Lastly, we introduce some typical results for a RESS problem simulated by our method.