A phase-field/ALE method for simulating fluid-structure interactions in two-phase flow

We present a phase-field/ALE method for simulating fluid-structure interactions (FSI) in two-phase flow. We solve the Navier-Stokes equation coupled with the Cahn-Hilliard equation and the structure equation in an arbitrary Lagrangian Eulerian (ALE) framework. For the fluid solver, a spectral/hp element method is employed for spatial discretization and backward differentiation for time discretization. For the structure solver, a Galerkin method is used in Lagrangian coordinates for spatial discretization and the Newmark-beta scheme for time discretization. The mesh is updated from the initial configuration by a harmonic mapping constructed from the velocity of the interface between the fluid and the structure subdomains. To test the accuracy of the phase-field approach of this multi-physics method, we first simulate two-phase co-annular laminar flow in a stationary pipe and compare the results with the analytical solution. To test the accuracy of the FSI solver, we simulate a pipe conveying single-phase flow and compare the results with an existing validated code (Newman and Karniadakis, 1997). Finally, we present two numerical simulations of FSI in two-phase flow, specifically, in a flexible pipe conveying two fluids that induce self-sustained oscillations, and in external cross flow past a circular cylinder that modifies the classical vortex street due to a Kelvin-Helmholtz instability. These three-dimensional simulations demonstrate the capability of the method in dealing with FSI problems in two-phase flow with moving grids as well as its robustness and efficiency in handling different fluids with large contrast in physical properties. (C) 2016 Published by Elsevier B.V.