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 the domain boundary. 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. To obtain the elastic stress, an additional Oldroyd-B -like equation is solved. 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.

Reversible elastic phase field approach and application to cell monolayers

“…In the framework proposed here, the simplest approach would be to let the distribution of engaged adhesive bonds modulate the substrate's spring stiffness density. Furtheron, in view of the viscoelastic flow behavior of monolayers migrating around an obstacle [22], a generalization of the approach to different viscoelastic models [49] would be highly interesting. We also envision extending our approach to multicellular situations in which single cell resolution is required, by using different phase fields for different cells [30,[74][75][76][77].…”

“…As expected, for the case with global suppression (γ = 0) the agreement worsens. Nevertheless, alternative approaches are either not reversible at all (as discussed above) or only work for the incompressible case [49].…”

A review on computational modelling of phase-transition problems

“…We favour the phase-field approach because, in addition to the purely geometric interpretation that we have just described, it may also be understood as a generalized approach to thermomechanics that allows us to derive mathematical models for interface problems by using the Coleman-Noll approach and classical balance laws for mass, linear momentum, angular momentum and energy [6]. This has led to an enormous number of applications of the phase-field method to material science [10,11], solid mechanics [12][13][14][15], fluid mechanics [7,[16][17][18][19], biomechanics [20][21][22][23][24] and interface problems in general [25][26][27][28].…”

An ALE method for simulations of axisymmetric elastic surfaces in flow

“…However, the inclusion of shear and dilational surface elasticity is traditionally not considered in these approaches, as it is not clear how to carry the reference coordinates along the elastic structure. Notably, some first steps have been done in this direction recently for level set [37] and phase-field methods [38].…”