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Special Section Articles

An Improved Direct-Forcing Immersed Boundary Method for Fluid-Structure Interaction Simulations1

[+] Author and Article Information
Xiaojue Zhu

Graduate Research Assistant
LNM, Institute of Mechanics,
Chinese Academy of Sciences,
Beijing 100190, China
e-mail: zhuxiaojue@lnm.imech.ac.cn

Guowei He

Professor and Director
LNM, Institute of Mechanics,
Chinese Academy of Sciences,
Beijing 100190, China
e-mail: hgw@lnm.imech.ac.cn

Xing Zhang

Associate Professor
LNM, Institute of Mechanics,
Chinese Academy of Sciences,
Beijing 100190, China
e-mail: zhangx@lnm.imech.ac.cn

This manuscript is submitted to the special issue on immersed boundary method. Preliminary version of this paper appeared as FEDSM2013-16472 in ASME 2013 Fluids Engineering Division Summer Meeting, Incline Village, NV, July 7–11, 2013.

2Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received May 13, 2013; final manuscript received December 4, 2013; published online February 28, 2014. Assoc. Editor: Zhongquan Charlie Zheng.

J. Fluids Eng 136(4), 040903 (Feb 28, 2014) (9 pages) Paper No: FE-13-1310; doi: 10.1115/1.4026197 History: Received May 13, 2013; Revised December 04, 2013

In the present work, we present an improved version of the direct-forcing immersed boundary (IB) method proposed in Wang and Zhang (2011, “An Immersed Boundary Method Based on Discrete Stream Function Formulation for Two- and Three-Dimensional Incompressible Flows,” J. Comput. Phys., 230(9), pp. 3479–3499). In order to obtain an accurate prediction of local surface force, measures have been taken to suppress the unphysical spatial oscillations in the Lagrangian forcing. A fluid-structure interaction (FSI) solver has been developed by using the improved IB method for the fluid and the finite difference method for the structure. Several flow problems are simulated to validate our method. The testing cases include flows over a stationary cylinder and a stationary flat plate, two-dimensional flow past an inextensible flexible filament, and three-dimensional flow past a flapping flag. The results obtained in the present work agree well with those from the literature.

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Figures

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Fig. 1

Schematic representation of the Lagrangian coordinate system s on the filament. The length of the filament is L.

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Fig. 2

Schematic representation of the Lagrangian coordinate system s1 and s2 on the flag. The longitudinal coordinate s1 ranges from 0 to L, and the spanwise coordinate s2 ranges from 0 to H, where L and H denote the length and width of the flag, respectively.

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Fig. 3

The distribution of Lagrangian force correction F'x along the cylinder's surface by using Eq. (23) and setting the right hand side of Eq. (23) to −100 at each Lagrangian point. The Lagrangian grid width and Eulerian grid width are both 0.02. θ denotes the angle between the radical direction and the horizontal direction.

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Fig. 4

Two ways of computing forcing component on a staggered mesh: (a) original way used in Ref. [6] and (b) more consistent way of computing forcing component. In (a), the Eulerian forcing (vector) is defined at cell centers, and each forcing component is interpolated (individually) to cell edges via simple average. In (b), each Eulerian forcing component is defined at cell edges, and no extra interpolation is needed.

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Fig. 5

The distribution of Lagrangian intermediate velocity U→* along the cylinder's surface. The Eulerian grid width is 0.02 while in case (a) Δs/h = 1 and in case (b) Δs/h = 2.

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Fig. 6

Distribution of (a) pressure coefficient Cp and (b) skin-friction coefficient Cf on the surface of the cylinder for Re = 40

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Fig. 7

Distributions of pressure coefficient difference ΔCp and skin-friction coefficient (Cf) along the flat-plate surface at Re = 200 and two angles of attack: (a) Cf for α = 0deg, (b) ΔCp for α = 10deg, and (c) Cf for α = 10deg

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Fig. 8

Comparison of the predicted free-end position with the analytical result

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Fig. 9

Vorticity contours in wake of a flapping flexible filament

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Fig. 10

Time history of y-position of the trailing edge: (a) γ=0.0015 and (b) γ = 0.0

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Fig. 11

The instantaneous shape of a flapping flag in the three-dimensional simulation

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Fig. 12

Time history of the transverse displacement of point A in Fig. 2 for Fr = 0.0

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