A Novel Adaptive Variational Fully-Eulerian Scheme for Fluid-Structure Interaction

Explicit interface tracking and body-fitted approaches pose numerical challenges for fluid-structure

interaction with flexible multibody contact dynamics e.g., self-contact between octopus arms or

large topological changes of soft solids. We present a novel interface-driven adaptive model using

the fully-Eulerian method for FSI problems. The fully-Eulerian approach involves a fixed background

mesh on which the interface is represented implicitly. The two domains are modeled by the phase-

field finite element formulation using the convective Allen-Cahn equation coupled with the unified

continuum equations. The adaptive refinement/coarsening for the unstructured grid is determined

by appropriate indicators and carried out by the newest vertex bisection algorithm. 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 for the increasing complexity of

problems. Finally, we demonstrate our fully-Eulerian interface-driven adaptive FSI model to simulate

the contact problem between an elastic and rigid solid using a popular bouncing elastic ball problem.