  Multiphase flows are characterized by sharp moving interfaces, separating
different fluids or phases. In many cases the dynamics of the interface
determines the behavior of the flow. In a coarse, or reduced order model, it
may therefore be important to retain a sharp interface for the resolved scales.
Here, a process to coarsen or filter fully resolved numerical solutions for
incompressible multiphase flows while retaining a sharp interface is examined.
The different phases are identified by an index function that takes different
values in each phase and is coarsened by solving a constant coefficient
diffusion equation, while tracking the interface contour. Small flows scales of
one phase, left behind when the interface is moved, are embedded in the other
phase by solving another diffusion equation with a modified diffusion
coefficient that is zero at the interface location to prevent diffusion across
the interface, plus a pressure like equation to enforce incompressibility of
the coarse velocity field. Examples of different levels of coarsening are
shown. A simulation of a coarse model, where small scales are treated as a
homogeneous mixture, results in a solution that is similar to the filtered
fully resolved field for the early time Rayleigh-Taylor instability.
