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

Abstract

SummaryWe present a partitioned iterative formulation for the modeling of fluid‐structure interaction (FSI) in two‐phase flows. The variational formulation consists of a stable and robust integration of three blocks of differential equations, viz, an incompressible viscous fluid, a rigid or flexible structure, and a 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‐Cahn 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 and the generalized‐α method is employed for the time marching. We assess the accuracy and stability of the 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. Overall, the proposed variational formulation produces results with high accuracy and compares well with available measurements and reference numerical data. Using unstructured meshes, we demonstrate the second‐order temporal accuracy of the coupled phase‐field/ALE method via decay test of a circular cylinder interacting with the free surface. 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.