  We consider a model for flow of liquid and gas in a pipe. We assume that the
gas is ideal and that the liquid is incompressible. Under this assumption the
resulting equations, expressing conservation of mass and momentum, splits into
two subsystems such that the gas flow is independent of the liquid flow, and
the liquid flow is described by a conservation law parametrized by the mass
fraction of gas. When solving these equations numerically, we propose to
stagger the gas and liquid variables with respect to each other. The advantage
of this is that in finite volume methods one can use numerical flux functions
designed for 2x2 systems of hyperbolic conservation laws to solve both the gas
flow and the liquid flow, rather than a much more complicated numerical flux
for the whole 4x4 system. We test this using the Roe numerical flux for both
subsystems, and compare the results with results produced by using the
second-order Nessyahu--Tadmor scheme for the second subsystem.
