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Interface-Reproducing Capturing (IRC) Technique for Fluid-Structure Interaction: Methods and Applications

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Frontiers in Computational Fluid-Structure Interaction and Flow Simulation

Abstract

How to enhance the interface-capturing (IC) computation of fluid–structure interaction (FSI) is a long-standing issue for IC approaches. This chapter introduces approaches based on an extended finite element method (XFEM) and a Lagrange multiplier (LM) method, as well as our contribution to the problem. The XFEM-based approach develops a framework for an interface-reproducing capturing (IRC) method whose spatial functions are locally equivalent to those of interface-tracking (IT) methods. The XFEM enriches the velocity and pressure function spaces of the local flow around the interface. This enrichment reproduces requisite discontinuities at the interface. Simultaneously, the LM method imposes continuity on the fluid and structure to couple them, and thus the fluid captures the interface. This chapter gives an overview, describes the methods and solution techniques, and shows verifications and applications, focusing mainly on computing the fluid–thin-structure interaction (FTSI). The verifications reveal how continuity and discontinuity at the interface affect the FSI computation and why the IRC method is effective. Applications to flow-induced flutter of flexible thin objects show the ability of the proposed method to take on the challenge of computing complex FSI problems. Applications to flows past fixed objects show its ability to compute simple problems with ease. The IRC method therefore has two aspects and potentials. Open issues mentioned in this chapter indicate that there is still much room for advancing the IC method.

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Notes

  1. 1.

    An elegant technique and concept proposed by Tezduyar and named FSILT-ED (fluid–solid interface locator technique-extended domain) can be found in [28, 33, 34, 37]. FSILT-ED applies a stabilized LM method or a penalty method at the interface, with an elaborate treatment of the interpolation of pressure across the interface, introducing fluid domains extended virtually from one side of the interface to the other. We consider the ED technique as a way to extrapolate from one side to the interface in a finite element. See [28, 33, 34, 37].

  2. 2.

    XFEM can accept various types of enrichment function ϕ(x, t). For example, as well as the edge function e(x, t), the ramp function r(x, t) given by

    $$\displaystyle \begin{aligned} r\left(\mathbf{x},t\right) =\sum_{I\in Q_{f}}N_{I}\left|F_{I}\right|-e\left(\mathbf{x},t\right) {} \end{aligned} $$
    (53)

    can reproduce a weak discontinuity and is generally considered superior to the edge function in doing so because it can reproduce the discontinuity within crossed elements without the need for partially enriched surrounding elements called blending elements in XFEM. However, if we adopt the ramp function, the interfacial velocity has time-dependent enrichment terms as follows:

    $$\displaystyle \begin{aligned} \mathbf{v}\left({\mathbf{x}}_{i},t\right)=\sum_{I\in Q_{fi}}N_{I}{\mathbf{V}}_{I}+r\left({\mathbf{x}}_{i},t\right)\sum_{I\in Q_{fi}}N_{I}\tilde{\mathbf{V}}_{I}, \quad \mathrm{with}\quad r\left({\mathbf{x}}_{i},t\right)=\sum_{I\in Q_{fi}}N_{I}\left|F_{I}\right|. {} \end{aligned} $$
    (54)

    For FSI and flow with moving boundaries, enrichment functions that meet neither ∂ϕ(xi, t)∕∂t = 0 nor ϕ(xi, t) = 0 seem to cause temporal instability even if the time dependence is accounted for in the computation. We therefore select the edge function for the enrichment.

  3. 3.

    The multiplier mesh for 𝜖 = 2 is twice as coarse as that for 𝜖 = 1 if nf is fixed. Therefore, the multipliers shown in Figs. 11 and 12 are twice as coarse as those of Figs. 9 and 10, respectively.

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Acknowledgements

I would like to thank Professor Tayfun E. Tezduyar at Rice University, USA, for useful comments on advanced FSI and stabilization techniques. I would also like to thank Dr. Jun-ichi Matsumoto at AIST, Japan, for daily discussions about computational flow techniques.

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  1. Integrated Macroscopic Simulation Team, Research Center for Computational Design of Advanced Functional Materials, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki, Japan

    Tomohiro Sawada

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  1. Mechanical Engineering, Rice University, Houston, TX, USA

    Tayfun E. Tezduyar

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Sawada, T. (2018). Interface-Reproducing Capturing (IRC) Technique for Fluid-Structure Interaction: Methods and Applications. In: Tezduyar, T. (eds) Frontiers in Computational Fluid-Structure Interaction and Flow Simulation. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-96469-0_11

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