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

Published online by Cambridge University Press:  03 June 2015

X. Wang ,
C. Shu ,
J. Wu  and
L. M. Yang
X. Wang
Affiliation:
Department of Aerodynamics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Yudao Street, Nanjing 210016, China
C. Shu*
Affiliation:
Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore
J. Wu
Affiliation:
Department of Aerodynamics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Yudao Street, Nanjing 210016, China
L. M. Yang
Affiliation:
Department of Aerodynamics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Yudao Street, Nanjing 210016, China
*
*Corresponding author. styled-contentURL:http://serve.me.nus.edu.sg/shuchang/, Email: [email protected]
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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.

Keywords

76M2876M25Immersed boundary methodlattice Boltzmann methodvelocity correctionLagrange interpolationno-slip boundary condition
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 6 , Issue 6 , December 2014 , pp. 811 - 829
Copyright
Copyright © Global-Science Press 2014

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References

[1]Peskin, C. S., Numerical analysis of blood flow in the heart, J. Comput. Phys., 25 (1977), pp. 220–252.CrossRefGoogle Scholar
[2]Goldstein, D., Hadler, R. and Sirovich, L., Modeling a no-slip flow boundary with an external force field, J. Comput. Phys., 105 (1993), 354.CrossRefGoogle Scholar
[3]Lai, M. C. and Peskin, C. S., An immersed boundary method with formal second-order accuracy and reduced numerical viscosity, J. Comput. Phys., 160 (2000), pp. 705–719.Google Scholar
[4]Tseng, Y. H. and Ferziger, J. H., A ghost-cell immersed boundary method for flow in complex geometry, J. Comput. Phys., 192 (2003), pp. 593–623.Google Scholar
[5]Lima, L. F.Silva, E, Silveira-Neto, A. and Damasceno, J. J. R., Numerical simulation of two-dimensional flows over a circular cylinder using the immersed boundary method, J. Comput. Phys., 189 (2003), pp. 351–370.Google Scholar
[6]Feng, Z. G. and Michaelides, E. E., The immersed boundary-lattice Boltzmann method for solvingfluid-particles interaction problems, J. Comput. Phys., 195 (2004), pp. 602–628.CrossRefGoogle Scholar
[7]Feng, Z. G. and Michaelides, E. E., Proteus: a direct forcing method in the simulations of particulate flows, J. Comput. Phys., 202 (2005), pp. 20–51.Google Scholar
[8]Fadlum, E., Verzicco, R., Orlandi, P. and Mohd-Yusof, J., Combined immersed-boundary finite-difference methods for three dimensional complex flow simulations, J. Comput. Phys., 161 (2000), pp. 35–60.Google Scholar
[9]Niu, X. D., Shu, C., Chew, Y. T. and Peng, Y., A momentum exchange-based immersed boundary-lattice Boltzmann method for viscous fluid flows, Phys. Lett. A, 354 (2006), pp. 173–182.Google Scholar
[10]Ladd, A. J. C., Numerical simulations of particulate suspensions via a discretized Boltzmann equation part I: Theoretical foundation, J. Fluid Mech., 271 (1994), pp. 285–310.Google Scholar
[11]Kim, J., Kim, D. and Choi, H., An immersed-boundary finite-volume method for simulations of flow in complex geometries, J. Comput. Phys., 171 (2001), pp. 132–150.Google Scholar
[12]Shu, C., Liu, N. Y. and Chew, Y. T., A novel immersed boundary velocity correction-lattice Boltzmann method and its application to simulate flow past a circular cylinder, J. Comput. Phys., 226 (2007), pp. 1607–1622.Google Scholar
[13]Wu, J. and Shu, C., Implicit velocity correction-based immersed boundary-lattice Boltzmann method and its applications, J. Comput. Phys., 228 (2009), pp. 1963–1979.Google Scholar
[14]Guo, Z., Zheng, C. and Shi, B., Discrete lattice effects on the forcing term in the lattice Boltzmann method, Phys. Rev. E, 65 (2002), 046308.Google Scholar
[15]Qian, Y. H., D’Humieres, D. and Lallemand, P., Lattice BGK model for Navier-stokes equation, Europhys. Lett., 17 (1992), pp. 479–484.CrossRefGoogle Scholar
[16]He, X., Chen, S. and Zhang, R., A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh-Taylor instability, J. Comput. Phys., 152 (1999), pp. 642–663.CrossRefGoogle Scholar
[17]Chen, D. J., Lin, K. H. and Lin, C. A., Immersed boundary method based lattice Boltzmann to simulate 2D and 3D complex geometry flows, Int. J. Mod. Phys. C, 18 (2007), pp. 585–594.CrossRefGoogle Scholar
[18]Shu, C., Niu, X. D. and Chew, Y. T., Taylor series expansion-and least square-based lattice Boltzmann method: two-dimensional formulation and its applications, Phys. Rev. E, 65 (2002), 036708.Google Scholar
[19]Dennis, S. C. R. and Chang, G. Z., Numerical solutions for steady flow past a circular cylinder at Reynolds number up to 100, J. Fluid Mech., 42 (1970), pp. 471–489.Google Scholar
[20]Fornberg, B., A numerical study of steady viscous flow past a circular cylinder, J. Fluid Mech., 98 (1980), pp. 819–855.Google Scholar
[21]He, X. and Doolen, G., Lattice Boltzmann method on curvilinear coordinates system: flow around a circular cylinder, J. Comput. Phys., 134 (1997), pp. 306–315.Google Scholar
[22]Braza, M., Chassaing, P. and Ha-Minh, H., Numerical study and physical analysis of the pressure and velocity fields in the near wake of a circular cylinder, J. Fluid Mech., 165 (1986), 79.CrossRefGoogle Scholar
[23]Liu, C., Zheng, X. and Sung, C. H., Preconditioned multigrid methods for unsteady incompressible flows, J. Comput. Phys., 139 (1998), 35.Google Scholar
[24]Ding, H., Shu, C., Yeo, K. S. and Xu, D., Simulation of incompressible viscous flows past a circular cylinder by hybrid FD scheme and meshless least square-based finite difference method, Comput. Methods Appl. Mech. Eng., 193 (2004), pp. 727–744.Google Scholar
[25]Williamson, C. H. K., Oblique and parallel models of vortex shedding in the wake of a circular cylinder at low Reynolds number, J. Fluid Mech, 206 (1989), 579.Google Scholar