# A hybrid variational Allen-Cahn/ALE scheme for the coupled analysis of two-phase fluid-structure interaction

## TL;DR

This paper introduces a stable, robust hybrid variational scheme combining Allen-Cahn phase-field and ALE methods for accurate, stable simulation of complex two-phase fluid-structure interactions with high density ratios.

## Contribution

It develops a novel partitioned iterative formulation integrating phase-field, ALE, and fluid-structure interaction models with second-order temporal accuracy.

## Key findings

- The formulation is stable for high density ratios.
- It demonstrates second-order accuracy in time.
- The method effectively simulates complex 3D two-phase FSI problems.

## Abstract

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.