Volume 6, Issue 6
A Boundary Condition-Implemented Immersed Boundary-Lattice Boltzmann Method and Its Application for Simulation of Flows Around a Circular Cylinder

Adv. Appl. Math. Mech., 6 (2014), pp. 811-829.

Published online: 2014-06

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• Abstract

A boundary condition-implemented immersed boundary-lattice Boltzmann method (IB-LBM) is presented in this work. The present approach is an improvement to the conventional IB-LBM. In the conventional IB-LBM, the no-slip boundary condition is only approximately satisfied. As a result, there is flow penetration to the solid boundary. Another drawback of conventional IB-LBM is the use of Dirac delta function interpolation, which only has the first order of accuracy. In this work, the no-slip boundary condition is directly implemented, and used to correct the velocity at two adjacent mesh points from both sides of the boundary point. The velocity correction is made through the second-order polynomial interpolation rather than the first-order delta function interpolation. Obviously, the two drawbacks of conventional IB-LBM are removed in the present study. Another important contribution of this paper is to present a simple way to compute the hydrodynamic forces on the boundary from Newton's second law. To validate the proposed method, the two-dimensional vortex decaying problem and incompressible flow over a circular cylinder are simulated. As shown in the present results, the flow penetration problem is eliminated, and the obtained results compare very well with available data in the literature.

76M28, 76M25

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@Article{AAMM-6-811, author = {Wang , X.Shu , C.Wu , J. and Yang , L. M.}, title = {A Boundary Condition-Implemented Immersed Boundary-Lattice Boltzmann Method and Its Application for Simulation of Flows Around a Circular Cylinder}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2014}, volume = {6}, number = {6}, pages = {811--829}, abstract = {

A boundary condition-implemented immersed boundary-lattice Boltzmann method (IB-LBM) is presented in this work. The present approach is an improvement to the conventional IB-LBM. In the conventional IB-LBM, the no-slip boundary condition is only approximately satisfied. As a result, there is flow penetration to the solid boundary. Another drawback of conventional IB-LBM is the use of Dirac delta function interpolation, which only has the first order of accuracy. In this work, the no-slip boundary condition is directly implemented, and used to correct the velocity at two adjacent mesh points from both sides of the boundary point. The velocity correction is made through the second-order polynomial interpolation rather than the first-order delta function interpolation. Obviously, the two drawbacks of conventional IB-LBM are removed in the present study. Another important contribution of this paper is to present a simple way to compute the hydrodynamic forces on the boundary from Newton's second law. To validate the proposed method, the two-dimensional vortex decaying problem and incompressible flow over a circular cylinder are simulated. As shown in the present results, the flow penetration problem is eliminated, and the obtained results compare very well with available data in the literature.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2013.m-s2}, url = {http://global-sci.org/intro/article_detail/aamm/50.html} }
TY - JOUR T1 - A Boundary Condition-Implemented Immersed Boundary-Lattice Boltzmann Method and Its Application for Simulation of Flows Around a Circular Cylinder AU - Wang , X. AU - Shu , C. AU - Wu , J. AU - Yang , L. M. JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 811 EP - 829 PY - 2014 DA - 2014/06 SN - 6 DO - http://doi.org/10.4208/aamm.2013.m-s2 UR - https://global-sci.org/intro/article_detail/aamm/50.html KW - Immersed boundary method, lattice Boltzmann method, velocity correction, Lagrange interpolation, no-slip boundary condition. AB -

A boundary condition-implemented immersed boundary-lattice Boltzmann method (IB-LBM) is presented in this work. The present approach is an improvement to the conventional IB-LBM. In the conventional IB-LBM, the no-slip boundary condition is only approximately satisfied. As a result, there is flow penetration to the solid boundary. Another drawback of conventional IB-LBM is the use of Dirac delta function interpolation, which only has the first order of accuracy. In this work, the no-slip boundary condition is directly implemented, and used to correct the velocity at two adjacent mesh points from both sides of the boundary point. The velocity correction is made through the second-order polynomial interpolation rather than the first-order delta function interpolation. Obviously, the two drawbacks of conventional IB-LBM are removed in the present study. Another important contribution of this paper is to present a simple way to compute the hydrodynamic forces on the boundary from Newton's second law. To validate the proposed method, the two-dimensional vortex decaying problem and incompressible flow over a circular cylinder are simulated. As shown in the present results, the flow penetration problem is eliminated, and the obtained results compare very well with available data in the literature.

X. Wang, C. Shu, J. Wu & L. M. Yang. (1970). A Boundary Condition-Implemented Immersed Boundary-Lattice Boltzmann Method and Its Application for Simulation of Flows Around a Circular Cylinder. Advances in Applied Mathematics and Mechanics. 6 (6). 811-829. doi:10.4208/aamm.2013.m-s2
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