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A hierarchy of models for two-phase flows. (English) Zbl 0998.76088

Summary: 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 conservation laws with relaxation. At first order in the density ratio, we get a simplified system with viscosity, while in the limit we obtain a system of two conservation laws, the system which describes pressureless gases with constraint and undetermined pressure. We examine formal properties of this constraint model, and introduce sticky blocks’ solutions. We also propose numerical methods for this last model, and the results are compared with two previous models.

MSC:

76T10 Liquid-gas two-phase flows, bubbly flows
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