Robin-Neumann transmission conditions for fluid-structure coupling: Embedded boundary implementation and parameter analysis: Robin-Neumann transmission conditions for fluid-structure coupling
Robin-Neumann transmission conditions for fluid-structure coupling: Embedded boundary implementation and parameter analysis: Robin-Neumann transmission conditions for fluid-structure coupling
复制标题
流固耦合的 Robin-Neumann 传输条件：嵌入式边界实现和参数分析：流固耦合的 Robin-Neumann 传输条件
DOI：
10.1002/nme.5817
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发表时间：
2018
影响因子：
2.9
通讯作者：
Wang, Kevin G.
中科院分区：
文献类型：
--
作者：
Cao, Shunxiang;Main, Alex;Wang, Kevin G.
分区过程对于解决复杂的流体-结构相互作用（FSI）问题很有吸引力，因为它们允许现有的计算流体动力学（CFD）和计算结构动力学算法和求解器被组合和重用。然而，对于涉及不可压缩流动和强附加质量效应的问题（例如，重流体和细长结构），分区程序遭受数值不稳定性，这通常需要在流体和结构求解器之间进行额外的子迭代，因此显着增加了计算成本。本文研究了使用罗宾-诺依曼传输条件来缓解上述不稳定性问题。首先，在基于投影的不可压缩CFD和基于有限元的计算结构动力学的背景下，提出了嵌入式Robin边界方法。该方法利用算子分裂和改进的虚拟流体方法，在结构化非体协调CFD网格中嵌入的流体-结构界面上执行Robin传输条件。使用Turek和Hron基准问题演示和验证了该方法，该基准问题涉及在非定常涡主导的通道流中经历大瞬态变形的细长梁。其次，本文研究了Robin传输条件中的组合参数αf对数值稳定性和解的精度的影响。本文提出了一个使用Turek和Hron基准问题的数值研究和一个使用简化的FSI模型的分析研究，该模型具有欧拉-伯努利梁与二维不可压缩无粘流的相互作用。这两项研究都揭示了稳定性和精度之间的权衡：较小的α值往往会提高数值稳定性，但会降低分区解的精度。利用简化的FSI模型，推导并讨论了优化这一权衡的α f临界值。
Partitioned procedures are appealing for solving complex fluid‐structure interaction (FSI) problems, as they allow existing computational fluid dynamics (CFD) and computational structural dynamics algorithms and solvers to be combined and reused. However, for problems involving incompressible flow and strong added‐mass effect (eg, heavy fluid and slender structure), partitioned procedures suffer from numerical instability, which typically requires additional subiterations between the fluid and structural solvers, hence significantly increasing the computational cost. This paper investigates the use of Robin‐Neumann transmission conditions to mitigate the above instability issue. Firstly, an embedded Robin boundary method is presented in the context of projection‐based incompressible CFD and finite element–based computational structural dynamics. The method utilizes operator splitting and a modified ghost fluid method to enforce the Robin transmission condition on fluid‐structure interfaces embedded in structured non–body‐conforming CFD grids. The method is demonstrated and verified using the Turek and Hron benchmark problem, which involves a slender beam undergoing large transient deformation in an unsteady vortex‐dominated channel flow. Secondly, this paper investigates the effect of the combination parameter in the Robin transmission condition, ie,αf, on numerical stability and solution accuracy. This paper presents a numerical study using the Turek and Hron benchmark problem and an analytical study using a simplified FSI model featuring an Euler‐Bernoulli beam interacting with a two‐dimensional incompressible inviscid flow. Both studies reveal a trade‐off between stability and accuracy: smaller values ofαftend to improve numerical stability, yet deteriorate the accuracy of the partitioned solution. Using the simplified FSI model, the critical value ofαfthat optimizes this trade‐off is derived and discussed.