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.
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