@Article{CiCP-16-136,
author = {Yongguang Cheng, Luoding Zhu and Chunze Zhang},
title = {Numerical Study of Stability and Accuracy of the Immersed Boundary Method Coupled to the Lattice Boltzmann BGK Model},
journal = {Communications in Computational Physics},
year = {2014},
volume = {16},
number = {1},
pages = {136--168},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.260313.291113a},
url = {http://global-sci.org/intro/article_detail/cicp/7037.html}
}