Compressible Heterogeneous Two-Phase Flows

The modeling and the numerical simulation of two-phase flows are investigated for several decades. When dealing with very heterogeneous problems, for instance a water flow with many bubbles, one has to make use of averaged models since the description of each phase and interface is out of reach. Whatever the average is, the resulting models often suffer from severe mathematical pathologies: lack of hyperbolicity, non-conservative products, non-preservation of admissible states. In 1986, Baer and Nunziato proposed an original model which possesses interesting features from the mathematical point of view. Our goal is to provide a (partial) state of art on this model and its derivatives, but also to list some open questions.