[Paper Review] An interface and geometry preserving phase-field method for fully Eulerian fluid-structure interaction

Xiaoyu Mao, Rajeev K. Jaiman|arXiv (Cornell University)|Jan 28, 2022

Lattice Boltzmann Simulation Studies4 citations

TL;DR

This paper presents an interface and geometry preserving (IGP) phase-field method for fully Eulerian fluid-structure interaction, using a gradient-minimizing velocity field (GMV) to suppress curvature-driven interface distortion and maintain sharp solid boundaries. The method achieves stable, accurate simulations of complex FSI problems with large deformations and topological changes, validated through benchmark flows and a vibrating plate case.

ABSTRACT

We present an interface and geometry preserving (IGP) method for the modeling of fully Eulerian fluid-structure interaction via phase-field formulation. While the hyperbolic tangent interface profile is preserved by the time-dependent mobility model, the proposed method maintains the geometry of the solid-fluid interface by reducing the volume-conserved mean curvature flow. To achieve the reduction in the curvature flow, we construct a gradient-minimizing velocity field (GMV) for the convection of the order parameter. The constructed velocity field enables the preservation of the solid velocity in the solid domain while extending the velocity in the normal direction throughout the diffuse interface region. With this treatment, the GMV reduces the normal velocity difference of the level sets of the order parameter which alleviates the undesired thickening or thinning of the diffuse interface region due to the convection. During this process, the time-dependent mobility coefficient is substantially reduced and there is a lesser curvature flow. The GMV ensures that the diffuse interface region moves with the solid bulk such that the fluid-solid interface conforms to the geometry of the solid. Using the unified momentum equation and the phase-dependent interpolation, we integrate the IGP method into a fully Eulerian variational FSI solver based on the incompressible viscous fluid and the neo-Hookean solid. We first demonstrate the ability of the phase-field-based IGP method for the convection of circular and square interfaces with a prescribed velocity field. The variational FSI framework with the IGP method is then examined for the flow passing a fixed deformable block in a channel domain. Finally, the vibration of a plate attached behind a stationary cylinder subjected to incoming flow is employed to assess the fully Eulerian framework for a large aspect ratio and sharp corners.

Motivation & Objective

• To address the challenge of interface distortion and geometric degradation in fully Eulerian fluid-structure interaction simulations.
• To preserve the sharpness and fidelity of solid-fluid interfaces during large deformations and topological changes.
• To develop a variational, fully Eulerian FSI framework that maintains geometric consistency without remeshing or complex interface tracking.
• To reduce volume-conserved mean curvature flow in the diffuse interface region through a novel velocity field design.

Proposed method

• The method employs a time-dependent mobility model to preserve the hyperbolic tangent profile of the phase-field interface.
• A gradient-minimizing velocity field (GMV) is constructed to minimize normal velocity differences across level sets of the order parameter.
• The GMV ensures that the diffuse interface region moves with the solid bulk, preserving the solid’s geometry during convection.
• The GMV extends solid velocity into the diffuse interface region, reducing convective distortion and curvature flow.
• A unified momentum equation with phase-dependent interpolation enables coupling between incompressible viscous fluid and neo-Hookean solid in a variational finite element framework.
• The method integrates with a fully Eulerian variational FSI solver, avoiding mesh distortion and remeshing.

Experimental results

Research questions

• RQ1 Can a fully Eulerian FSI method preserve the geometric shape of solid boundaries during large deformations and topological changes?
• RQ2 How can curvature-driven interface thickening or thinning be suppressed in phase-field-based FSI simulations?
• RQ3 To what extent does the GMV reduce volume-conserved mean curvature flow in the diffuse interface region?
• RQ4 How does the IGP method perform in benchmark FSI problems with complex interface motion and sharp corners?

Key findings

• The IGP method successfully maintains the circular and square interface shapes under prescribed convection, demonstrating suppression of geometric distortion.
• The method achieves second-order accuracy in space, as confirmed by mesh convergence studies with relative $L^2$ error decreasing with mesh refinement.
• The diffuse interface model converges to reference data as $ε$ and $η$ are reduced, showing agreement with benchmark solutions.
• The framework accurately simulates a deformable block in cavity flow, with interface positions matching reference data at $t=20$.
• The method captures the vibration of a plate behind a cylinder with large aspect ratio and sharp corners, confirming robustness in complex geometries.