The diffuse interface approximation to fluid-structure interaction

TL;DR

This paper introduces a diffuse interface phase-field model for fluid-structure interaction, proves its convergence to sharp interface models, and proposes a novel second-order numerical method with computational examples.

Contribution

It develops a unified Eulerian phase-field formulation for fluid-structure interaction, proves convergence to sharp interface models, and introduces a new strongly coupled numerical scheme.

Findings

Proved convergence of diffuse interface model to sharp interface problem.

Developed a second-order partitioned numerical method for the coupled system.

Validated the method with two computational examples.

Abstract

We consider a fluid-structure interaction problem in the Eulerian, phase-field formulation. The problem is described using the Navier--Stokes equations for a viscous, incompressible fluid, coupled with the incompressible hyperelasticity system, both written in the Eulerian coordinates. This allows the problem to be written in a unified formulation, using a single field for the fluid and structure velocities. To track the position of the domain, we use a phase-field approach, resulting in a coupled Cahn--Hilliard--Navier--Stokes-type of problem for the diffuse interface fluid-structure interaction. Under certain assumptions, we prove the convergence of the diffuse interface model to the sharp interface fluid-structure interaction problem. To solve the problem numerically, we propose a novel, strongly coupled, second-order partitioned computational method where the system is decoupled into the Cahn--Hilliard problem, the transport problem for the left Cauchy--Green deformation tensor, and the Navier--Stokes problem. The problems are solved iteratively until convergence at each time step. The performance of the method is illustrated on two computational examples.