We develop a numerical method to simulate a two-phase compressible flow
with sharp phase interface on Eulerian grids. The scheme makes use of a levelset to
depict the phase interface numerically. The overall scheme is basically a finite volume
scheme. By approximately solving a two-phase Riemann problem on the phase interface,
the normal phase interface velocity and the pressure are obtained, which is used
to update the phase interface and calculate the numerical flux between the flows of
two different phases. We adopt an aggregation algorithm to build cell patches around
the phase interface to remove the numerical instability due to the breakdown of the
CFL constraint by the cell fragments given by the phase interface depicted using the
levelset function. The proposed scheme can handle problems with tangential sliping
on the phase interface, topological change of the phase interface and extreme contrast
in material parameters in a natural way. Though the perfect conservation of the mass,
momentum and energy in global is not achieved, it can be quantitatively identified in
what extent the global conservation is spoiled. Some numerical examples are presented
to validate the numerical method developed.
