多尺度流固耦合问题的准单块局部高阶ALE有限元方法
A quasi-monolithic localized high-order ALE finite element method for multi-scale fluid-structure interaction problems
AI总结：
提出一种准单块局部高阶任意拉格朗日-欧拉有限元方法，通过隐式耦合流体动量、不可压缩Neo-Hookean本构和左柯西-格林张量，并采用显式交错网格更新，实现微流控系统中多尺度流固耦合的高精度稳定模拟。
摘要：
本文针对微流控系统中的多尺度流固耦合问题，提出了一种准单块局部高阶任意拉格朗日-欧拉有限元方法。流体动量、不可压缩Neo-Hookean本构律以及左柯西-格林张量$\mathcal{B}$被组装成一个单一的隐式系统，而调和网格扩展则以交错方式显式更新。等参$\mathcal{P}_2$单元提供了弯曲流固界面的三阶几何逼近，二阶隐式-显式分区龙格-库塔方案在不引入后向欧拉耗散的情况下实现了二阶时间精度。局部更新策略将移动网格和变形历史限制在贴体子域内，并与预计算的稳态背景流耦合，从而弥合局部流固耦合动力学与宏观微通道几何之间的尺度差异。在单位流固密度比下进行的Turek-Hron FSI3基准测试，在$3\%$误差内再现了参考梁端振幅和频率，证实了在破坏传统分区方案稳定性的强附加质量耦合下的稳定性。螺旋微通道中的三维粒子聚焦模拟进一步展示了该框架在长程多尺度问题上的应用。
英文摘要：
This paper presents a quasi-monolithic localized high-order arbitrary Lagrangian-Eulerian (qMLH-ALE) finite element method for multi-scale fluid-structure interaction (FSI) in microfluidic systems. The fluid momentum, the incompressible Neo-Hookean constitutive law, and the left Cauchy-Green tensor $\mathcal{B}$ are assembled into a single implicit system, while the harmonic mesh extension is updated explicitly in a staggered manner. Isoparametric $\mathcal{P}_2$ elements provide third-order geometric approximation of curved fluid-solid interfaces, and a second-order implicit-explicit partitioned Runge-Kutta scheme delivers second-order temporal accuracy without the dissipation of backward Euler. A localized updating strategy confines the moving mesh and the deformation history to a body-fitted sub-domain coupled with a precomputed steady background flow, bridging the scale disparity between local FSI dynamics and the macroscopic microchannel geometry. The Turek-Hron FSI3 benchmark, performed at unit fluid-solid density ratio, reproduces the reference beam-tip amplitude and frequency within $3\%$, confirming stability under the strong added-mass coupling that destabilizes conventional partitioned schemes. Three-dimensional particle-focusing simulations in spiral microchannels further illustrate the framework on long-range multi-scale problems.
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