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

作　　者：Yongguang Cheng Luoding Zhu Chunze Zhang 

机构地区：[1]State Key Laboratory of Water Resources and Hydropower Engineering Science,Wuhan University,Wuhan 430072,P.R.China. [2]Department of Mathematical Sciences,Indiana University-Purdue University Indianapolis,Indianapolis,IN 46202,USA.

出　　处：《Communications in Computational Physics》2014年第6期136-168,共33页计算物理通讯（英文）

基　　金：the National Natural Science Foundation of China(NSFC,Grant numbers 10572106,10872153 and 11172219);the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20130141110013)。

摘　　要：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.

关 键 词：Immersed boundary method lattice Boltzmann method fluid-structure interaction flexible boundary complex boundary ACCURACY stability verification 

分 类 号：O17[理学—数学]