发表机构
Polytechnique Montréal（蒙特利尔理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种并行有限元求解器，用于零质量比下二维和三维圆柱涡激振动模拟，通过单片方法同时求解流固耦合，验证二阶精度，并预测高雷诺数下的非周期振荡。
AI 中文摘要
我们提出了一种并行策略，用于研究在二维和三维中安装在平移弹簧上的刚性、无质量圆柱体的涡激振动（VIV）。在没有质量或阻尼的情况下，其运动仅由流体力和弹簧恢复力控制，并且是对流动的即时响应。我们关注低弹簧刚度，这会产生高折减速度和最大振荡幅度。提出了一种在任意拉格朗日-欧拉框架下采用隐式时间步进的单片有限元方法，同时求解流体流动、圆柱体动力学和网格运动。网格运动使用具有可变拉梅系数的线弹性伪固体建模，圆柱体上的无滑移条件通过耦合到位置自由度的拉格朗日乘子强制执行；我们探索了三种策略来在分布式框架中强制执行这种力-位置耦合。据我们所知，这项工作首次提出了用于零质量比下三维流固耦合的分布式求解器。该求解器通过制造解进行了验证，并在时间上具有二阶精度。对雷诺数从100到300的二维和三维VIV的数值研究再现了先前二维研究中获得的VIV响应，并预测了从$Re = 300$开始的非周期三维振荡。使用直接求解器MUMPS，所提出的方法可扩展到多达768个计算核心。
英文摘要
We present a parallel strategy for the study of the vortex-induced vibrations (VIV) of a rigid, massless cylinder mounted on translational springs, in two and three dimensions. Without mass or damping, its motion is governed solely by the fluid forces and the spring restoring force, and is an immediate response to the flow. We focus on low spring stiffness, yielding high reduced velocity and maximal oscillation amplitude. A monolithic finite element method in an arbitrary Lagrangian-Eulerian framework with implicit time stepping is proposed, solving the fluid flow, cylinder dynamics, and mesh motion simultaneously. Mesh movement is modelled with a linear elastic pseudo-solid with variable Lamé coefficients, and the no-slip condition on the cylinder is enforced with a Lagrange multiplier coupled to the position degrees of freedom; three strategies are explored to enforce this force-position coupling in a distributed framework. To the best of our knowledge, this work is the first to propose a distributed solver for three-dimensional fluid-structure interaction at zero mass ratio. The solver is verified with manufactured solutions, and exhibits second-order accuracy in time. A numerical study of two- and three-dimensional VIV for Reynolds numbers from 100 to 300 reproduces the VIV responses obtained in previous two-dimensional studies, and predicts nonperiodic 3D oscillations starting at $Re = 300$. Using the direct solver MUMPS, the proposed method scales to up to 768 compute cores.
Comments43 pages, 18 figures
