A phase-field model for fluid–structure interaction

Abstract

In this paper, we develop a novel phase-field model for fluid–structure interaction (FSI), that is capable to handle very large deformations as well as topology changes like contact of the solid to a wall. The model is based on a fully Eulerian description of the velocity field in both, the fluid and the elastic domain. Viscous and elastic stresses in the Navier–Stokes equations are restricted to the corresponding domains by multiplication with their characteristic functions. The solid is described as a hyperelastic neo-Hookean material and the elastic stress is obtained by solving an additional Oldroyd-B – like equation. Thermodynamically consistent forces are derived by energy variation. The convergence of the derived equations to the traditional sharp interface formulation of fluid–structure interaction is shown by matched asymptotic analysis. The model is evaluated in a challenging benchmark scenario of an elastic body traversing a fluid channel. A comparison to reference values from Arbitrary Lagrangian Eulerian (ALE) simulations shows very good agreement. We highlight some distinct advantages of the new model, like the avoidance of re-triangulations and the stable inclusion of surface tension. Further, we demonstrate how simple it is to include contact dynamics into the model, by simulating a ball bouncing off a wall. We extend this scenario to include adhesion of the ball, which to our knowledge, cannot be simulated with any other FSI model. While we have restricted simulations to fluid–structure interaction, the model is capable to simulate any combination of viscous fluids, visco-elastic fluids and elastic solids.