  In this paper, we present a novel interface-driven adaptive variational
procedure using a fully Eulerian description of fluid-structure interaction.
The proposed fully-Eulerian procedure involves a fixed background unstructured
mesh on which the fluid-structure interface is treated implicitly. We model the
fluid-structure interaction by the phase-field finite element formulation
relying on a partitioned staggered integration of the convective Allen-Cahn
equation with the unified momentum equation for both solid and fluid dynamics.
We employ the positivity preserving variational scheme for a bounded and stable
solution of the Allen-Cahn phase-field equation. To evaluate the solid
stresses, the left Cauchy-Green deformation tensor is convected at each time
step to trace the evolution of the solid strain in the Eulerian reference
frame. We utilize the residual based error indicators and the newest vertex
bisection algorithm for the adaptive refinement/coarsening of the unstructured
mesh. The proposed nonlinear adaptive partitioned procedure restricts the
coarsening step to the last non-linear iteration while simultaneously ensuring
convergence properties of the coupled governing equations. We perform a
detailed convergence and accuracy analysis via two benchmark problems namely,
the pure solid system and a coupled fluid-solid system with an interface in a
rectangle domain. We next systematically assess the performance of the adaptive
procedure in terms of conservation properties for the increasing complexity of
problems. Finally, we demonstrate our fully-Eulerian interface-driven adaptive
FSI model to simulate the contact and bouncing phenomenon between an elastic
solid and a rigid wall.
