[论文解读] 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 Studies被引用 4

一句话总结

本文提出了一种界面与几何保持（IGP）的相场方法，用于完全欧拉型流固耦合（FSI）模拟，采用梯度最小化速度场（GMV）抑制曲率驱动的界面畸变，并保持清晰的固相边界。该方法在大变形和拓扑变化条件下实现了复杂FSI问题的稳定、精确模拟，通过基准流动问题和振动板案例得到验证。

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.

研究动机与目标

• 为解决完全欧拉型流固耦合模拟中界面畸变与几何退化的问题。
• 在大变形和拓扑变化过程中保持固相-流相界面的清晰度与保真度。
• 开发一种变分、完全欧拉型FSI框架，无需重划分网格或复杂界面追踪即可保持几何一致性。
• 通过新型速度场设计，减少扩散界面区域内的体积守恒平均曲率流动。

提出的方法

• 该方法采用时间依赖的迁移率模型，以保持相场界面的双曲正切分布形态。
• 构建梯度最小化速度场（GMV），以最小化序参量等值面之间的法向速度差异。
• GMV确保扩散界面区域随固相本体移动，从而在对流过程中保持固体的几何形状。
• GMV将固体速度扩展至扩散界面区域，减少对流畸变与曲率流动。
• 通过相位相关插值的统一动量方程，实现在变分有限元框架下不可压缩粘性流体与新胡克型固体的耦合。
• 该方法与完全欧拉型变分FSI求解器集成，避免了网格畸变与重划分网格。

实验结果

研究问题

• RQ1 完全欧拉型FSI方法是否能在大变形和拓扑变化过程中保持固体边界的几何形状？
• RQ2 在基于相场的FSI模拟中，如何抑制曲率驱动的界面增厚或变薄？
• RQ3 GMV在多大程度上减少了扩散界面区域内的体积守恒平均曲率流动？
• RQ4 IGP方法在具有复杂界面运动和尖锐拐角的基准FSI问题中表现如何？

主要发现

• IGP方法在受控对流下成功保持了圆形和方形界面形状，证明了几何畸变的有效抑制。
• 空间二阶精度通过网格收敛性研究得到验证，相对$L^2$误差随网格细化而减小。
• 当$ε$和$η$减小时，扩散界面模型收敛至参考数据，与基准解保持一致。
• 该框架准确模拟了腔体内可变形块体的运动，$t=20$时界面位置与参考数据吻合。
• 该方法成功捕捉了高长宽比与尖锐拐角的圆柱后方平板的振动，证实了在复杂几何中的鲁棒性。