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.

References in corpus (4)

• A full Eulerian finite difference approach for solving fluid-structure coupling problems
• Crossover from tumbling to tank-treading-like motion in dense simulated suspensions of red blood cells
• Diffuse interface models of locally inextensible vesicles in a viscous fluid
• Time integration for diffuse interface models for two-phase flow

Cited by in corpus (15)

• An immersed boundary method for the fluid-structure interaction of slender flexible structures in viscous fluid
• Improved phase-field models of melting and dissolution in multi-component flows
• The Poisson ratio of the cellular actin cortex is frequency-dependent
• Viscoelastic Cahn--Hilliard models for tumour growth
• An ALE method for simulations of axisymmetric elastic surfaces in flow
• An interface and geometry preserving phase-field method for fully Eulerian fluid-structure interaction
• Eulerian framework for contact between solids represented as phase fields
• Post-buckling Dynamics of Spherical Shells
• Numerical simulation of the coalescence-induced polymeric droplet jumping on superhydrophobic surfaces
• Sharp-interface limits of Cahn-Hilliard models and mechanics with moving contact lines
• A computational model of self-organized shape dynamics of active surfaces in fluids
• A coupled discontinuous Galerkin-Finite Volume framework for solving gas dynamics over embedded geometries
• A hybrid phase field method for fluid-structure interactions in viscous fluids
• On a diffuse interface model for incompressible viscoelastic two-phase flows
• Parametric finite element approximation of two-phase Navier--Stokes flow with viscoelasticity