A hierarchy of models for two-phase flows

We derive a hierarchy of models for gas-liquid two-phase flows in the Limit of infinite density ratio, when the liquid is assumed to be incompressible. The starting model. is a system of nonconservative conservation laws with relaxation. At first order in the density ratio, we get a simplified system with viscosity, while at the Limit we obtain a system of two conservation laws, the system of pressureless gases with constraint and undetermined pressure. Formal properties of this constraint model are provided, and sticky blocks solutions are introduced. We propose numerical methods for this last model, and the results are compared with the two previous models.