Compressible fluid dynamics is of great practical interest in many industrial applications, ranging from chemistry to aeronautical industry, and to nuclear field as well. At the same time, modelling and simulation of compressible flows is a very complex task, requiring the development of specific approaches, in order to describe the effect of pressure on the fluid velocity field. Compressibility effects become even more important in the study of two-phase flows, due to the presence of a gaseous phase. In addition, compressibility is also expected to have a significant impact on other physics, such as chemical or nuclear reactions occurring in the mixture. In this perspective, multiphysics represents a useful approach to address this complex problem, providing a way to catch all the different physics that come into play as well as the coupling between them.In this work, a multiphysics model is developed for the analysis of the generation IV Molten Salt Fast Reactor (MSFR), with a specific focus on the compressibility effects of the fluid that acts as fuel in the reactor. The fuel mixture compressibility is expected to have an important effect on the system dynamics, especially in very rapid super-prompt-critical transients. In addition, the presence of a helium bubbling system used for online fission product removal could modify the fuel mixture compressibility, further affecting the system transient behaviour. Therefore, the MSFR represents an application of concrete interest, inherent to the analysis of compressibility effects and to the development of suitable modelling approaches. An OpenFOAM solver is developed to handle the fuel compressibility, the presence of gas bubbles in the reactor as well as the coupling between the system neutronics and fluid dynamics. The outcomes of this analysis point out that the fuel compressibility plays a crucial role in the evolution of fast transients, introducing delays in the expansion feedbacks that strongly affect the system dynamics. Moreover, it is found that the gas bubbles significantly alter the fuel compressibility, yielding even larger differences compared to the incompressible approximation usually adopted in the current MSFR solvers.