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Numerical Study of Stability and Accuracy of the Immersed Boundary Method Coupled to the Lattice Boltzmann BGK Model

Published online by Cambridge University Press:  03 June 2015

Yongguang Cheng ,
Luoding Zhu  and
Chunze Zhang
Yongguang Cheng*
Affiliation:
State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, P.R. China
Luoding Zhu*
Affiliation:
Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, Indianapolis, IN 46202, USA
Chunze Zhang
Affiliation:
State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, P.R. China
*
Corresponding author.Email:ygcheng@whu.edu.cn
Email:lzhu@math.iupui.edu
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Abstract

This paper aims to study the numerical features of a coupling scheme between the immersed boundary (IB) method and the lattice Boltzmann BGK (LBGK) model by four typical test problems: the relaxation of a circular membrane, the shearing flow induced by a moving fiber in the middle of a channel, the shearing flow near a non-slip rigid wall, and the circular Couette flow between two inversely rotating cylinders. The accuracy and robustness of the IB-LBGK coupling scheme, the performances of different discrete Dirac delta functions, the effect of iteration on the coupling scheme, the importance of the external forcing term treatment, the sensitivity of the coupling scheme to flow and boundary parameters, the velocity slip near non-slip rigid wall, and the origination of numerical instabilities are investigated in detail via the four test cases. It is found that the iteration in the coupling cycle can effectively improve stability, the introduction of a second-order forcing term in LBGK model is crucial, the discrete fiber segment length and the orientation of the fiber boundary obviously affect accuracy and stability, and the emergence of both temporal and spatial fluctuations of boundary parameters seems to be the indication of numerical instability. These elaborate results shed light on the nature of the coupling scheme and may benefit those who wish to use or improve the method.

Keywords

76M2874F10Immersed boundary methodlattice Boltzmann methodfluid-structure interactionflexible boundarycomplex boundaryaccuracystabilityverification.
Type
Research Article
Information
Communications in Computational Physics , Volume 16 , Issue 1 , July 2014 , pp. 136 - 168
Copyright
Copyright © Global Science Press Limited 2014

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