Commun. Comput. Phys., 9 (2011), pp. 1375-1396.


Immersed Boundary-Lattice Boltzmann Coupling Scheme for Fluid-Structure Interaction with Flexible Boundary

Yongguang Cheng 1, Hui Zhang 2*, Chang Liu 1

1 State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China.
2 School of Electrical Engineering, Wuhan University, Wuhan 430072, China.

Received 30 October 2009; Accepted (in revised version) 21 December 2010
Available online 18 February 2011
doi:10.4208/cicp.301009.211210s

Abstract

Coupling the immersed boundary (IB) method and the lattice Boltzmann (LB) method might be a promising approach to simulate fluid-structure interaction (FSI) problems with flexible structures and complex boundaries, because the former is a general simulation method for FSIs in biological systems, the latter is an efficient scheme for fluid flow simulations, and both of them work on regular Cartesian grids. In this paper an IB-LB coupling scheme is proposed and its feasibility is verified. The scheme is suitable for FSI problems concerning rapid flexible boundary motion and a large pressure gradient across the boundary. We first analyze the respective concepts, formulae and advantages of the IB and LB methods, and then explain the coupling strategy and detailed implementation procedures. To verify the effectiveness and accuracy, FSI problems arising from the relaxation of a distorted balloon immersed in a viscous fluid, an unsteady wake flow caused by an impulsively started circular cylinder at Reynolds number 9500, and an unsteady vortex shedding flow past a suddenly started rotating circular cylinder at Reynolds number 1000 are simulated. The first example is a benchmark case for flexible boundary FSI with a large pressure gradient across the boundary, the second is a fixed complex boundary problem, and the third is a typical moving boundary example. The results are in good agreement with the analytical and existing numerical data. It is shown that the proposed scheme is capable of modeling flexible boundary and complex boundary problems at a second-order spatial convergence; the volume leakage defect of the conventional IB method has been remedied by using a new method of introducing the unsteady and non-uniform external force; and the LB method makes the IB method simulation simpler and more efficient.

AMS subject classifications: 76M28, 74F10

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Key words: Lattice Boltzmann method, immersed boundary method, fluid-structure interaction, flexible boundary, complex boundary.

*Corresponding author.
Email: chengyg2004@yahoo.com.cn (Y. Cheng), hzhang@whu.edu.cn (H. Zhang), beryl1988@163.com (C. Liu)
 

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