
Fully Eulerian Multiphase Fluid-Structure Interaction: A Monolithic Finite Element Framework
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This study introduces a monolithic finite element method for phase-field modeling of multiphase fluid-structure interaction within a fully Eulerian framework. The application of phase-field methods in Eulerian formulations for large-scale multiphase fluid-structure interaction, especially using finite element approaches, remains relatively underexplored. The proposed method addresses this gap by utilizing individual phase indicators to represent each fluid or solid phase, enabling efficient modeling of evolving interfaces on a fixed mesh. The fluid dynamics are governed by the Navier-Stokes equations, while the structural behavior is modeled using a hyperelastic neo-Hookean material. The continuum framework [1, 2, 3] integrates the Navier-Stokes equations with the Cahn-Hilliard phase-field model and the Oldroyd-B equation. The Cahn-Hilliard model determines interface position, and the Oldroyd-B equation computes the left Cauchy-Green stress tensor, essential for evaluating elastic stresses in solids. The computational approach employs a residual-based variational multiscale method for solving the Navier-Stokes equations. The Cahn-Hilliard equation is discretized using a mixed finite element method, while for the Oldroyd-B equation we employ a stabilized Galerkin finite element approach with stabilization achieved via the Streamline-Upwind/Petrov-Galerkin (SUPG) method. The framework is verified through two-dimensional simulation benchmarks and extended to tackle three-dimensional cases, including solid-solid contact problems. This work advances the application of phase-field models in Eulerian finite element simulations, contributing a robust framework for tackling complex multiphase interactions in fluid-structure systems. REFERENCES [1] Mokbel, D., Abels, H., & Aland, S. A phase-field model for fluidstructure interaction. J. Comput. Phys., 372, 823-840, (2018). [2] Aland, S., & Auerbach, P. A ternary phase-field model for wetting of soft elastic structures. Int. J. Num. Meth. Engng., 122, 4114-4128, (2021). [3] Valizadeh, N., Zhuang, X., & Rabczuk, T. A monolithic finite element method for phasefield modeling of fully Eulerian fluid-structure interaction. Comput. Methods Appl. Mech. Eng., Under Review, (2024).