Full Eulerian finite element method of a phase field model for fluid–structure interaction problem

Sun, Pengtao; Xu, Jinchao; Zhang, Lixiang

doi:10.1016/j.compfluid.2013.11.010

Cited by 46 publications

(34 citation statements)

References 23 publications

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“…Finally, a more drastic approach is to represent the solid also as a third phase and eliminate totally the ALE formulation in favor of a phase-field representation for the fluid-fluid as well as the fluid-structure interactions. We have followed the work of [41] for the Allen-Cahn equation and the results look promising but the governing equations may not be consistent with the standard elasticity equations. This is a fundamental open issue that we plan to address in the future For the Cahn-Hilliard equation, i.e., Eq.…”

Section: Discussionmentioning

confidence: 92%

“…ALE, originally developed by [37,38,39], overcomes the shortcomings of purely Lagrangian and purely Eulerian descriptions and leads to accurate treatment of FSI [40]. Although ALE may be computationally more expensive [41] compared to other techniques, i.e., the coordinate transformation [1] or the use of non-conforming mesh with immersed boundary methods [41], it combines generality and accuracy that is required for FSI in two-phase systems.…”

Section: Introductionmentioning

confidence: 99%

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

Zheng

Karniadakis

2016

Computer Methods in Applied Mechanics and Engineering

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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-β 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 [1]. 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.

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Section: Discussionmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

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

Zheng

Karniadakis

2016

Computer Methods in Applied Mechanics and Engineering

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“…While phase-field methods are state-of-the-art for multi-phase flow problems, only one preliminary approach has been made to provide a phase-field model for FSI [23]. This might be due to the fact, that the interface in phase-field method is diffuse with a finite thickness, making it harder to combine the solid and the fluid material in a consistent way.…”

Section: Introductionmentioning

confidence: 99%

A phase-field model for fluid–structure interaction

Mokbel

Abels

Aland

2018

Journal of Computational Physics

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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.

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“…The integral into the summation over the elements is the SUPG stabilization. The non-dimensional stabilization parameter is computed similarly to (23), that is…”

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confidence: 99%

A residual‐based Allen–Cahn phase field model for the mixture of incompressible fluid flows

Vasconcelos

Rossa²,

Coutinho

2014

Numerical Methods in Fluids

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SUMMARYThe hydrodynamics of fluid mixtures is receiving more and more attention in many science and engineering applications. Within the techniques for dealing with front displacements and moving boundaries between different density and/or viscosity fluids, phase fields are a class of models in which a diffusive transition region is taken into account instead of a steep interface. Although these models have a physical motivation, they require the definition of extra parameters. In order to make it less parameter dependent, the classic Allen-Cahn phase field model is modified, exploring its similarities with residual-based discontinuitycapturing schemes, making the phase field equation dependent on its own residual. We solve the coupling between incompressible viscous fluid flow and the phase field advective-diffusive-reactive transport to simulate the main processes in interface tension and/or buoyancy driven problems. For the solution of the Navier-Stokes and transport equations, we use a stabilized finite element formulation. The implementation has been performed using the libMesh finite element library, written in C++ , which provides support for adaptive mesh refinement and coarsening. A chemical convection benchmark problem is used to validate the proposed model, and then we solve two bubble interaction problems.

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Full Eulerian finite element method of a phase field model for fluid–structure interaction problem

Cited by 46 publications

References 23 publications

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

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

A phase-field model for fluid–structure interaction

A residual‐based Allen–Cahn phase field model for the mixture of incompressible fluid flows

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