  We present a novel partitioned iterative formulation for modeling of
fluid-structure interaction in two-phase flows. The variational formulation
consists of a stable and robust integration of three blocks of differential
equations, viz., incompressible viscous fluid, a rigid or flexible structure
and two-phase indicator field. The fluid-fluid interface between the two
phases, which may have high density and viscosity ratios, is evolved by solving
the conservative phase-field Allen-Cahn equation in the arbitrary
Lagrangian-Eulerian coordinates. While the Navier-Stokes equations are solved
by a stabilized Petrov-Galerkin method, the conservative Allen-Chan phase-field
equation is discretized by the positivity preserving variational scheme. Fully
decoupled implicit solvers for the two-phase fluid and the structure are
integrated by the nonlinear iterative force correction in a staggered
partitioned manner. We assess the accuracy and stability of the new
phase-field/ALE variational formulation for two- and three-dimensional problems
involving the dynamical interaction of rigid bodies with free-surface. We
consider the decay test problems of increasing complexity, namely free
translational heave decay of a circular cylinder and free rotation of a
rectangular barge. Through numerical experiments, we show that the proposed
formulation is stable and robust for high density ratios across fluid-fluid
interface and for low structure-to-fluid mass ratio with strong added-mass
effects. Using three-dimensional unstructured meshes, we demonstrate the
second-order temporal accuracy of the coupled phase-field/ALE method. Finally,
we demonstrate the three-dimensional phase-field FSI formulation for a
practical problem of internal two-phase flow in a flexible circular pipe
subjected to vortex-induced vibrations due to external fluid flow.
