Hostname: page-component-76fb5796d-vvkck Total loading time: 0 Render date: 2024-04-25T11:13:55.025Z Has data issue: false hasContentIssue false
  • English
  • Français

Immersed Boundary-Lattice Boltzmann Coupling Scheme for Fluid-Structure Interaction with Flexible Boundary

Published online by Cambridge University Press:  20 August 2015

Yongguang Cheng ,
Hui Zhang  and
Chang Liu
Yongguang Cheng*
Affiliation:
State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China
Hui Zhang*
Affiliation:
School of Electrical Engineering, Wuhan University, Wuhan 430072, China
Chang Liu*
Affiliation:
State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China
*
Email:chengyg2004@yahoo.com.cn
Corresponding author.Email:hzhang@whu.edu.cn
Email:beryll988@163.com
Get access

Abstract

Coupling the immersed boundary (IB) method and the lattice Boltzmann (LB) method might be a promising approach to simulate fluid-structure interaction (FSI) problems with flexible structures and complex boundaries, because the former is a general simulation method for FSIs in biological systems, the latter is an efficient scheme for fluid flow simulations, and both of them work on regular Cartesian grids. In this paper an IB-LB coupling scheme is proposed and its feasibility is verified. The scheme is suitable for FSI problems concerning rapid flexible boundary motion and a large pressure gradient across the boundary. We first analyze the respective concepts, formulae and advantages of the IB and LB methods, and then explain the coupling strategy and detailed implementation procedures. To verify the effectiveness and accuracy, FSI problems arising from the relaxation of a distorted balloon immersed in a viscous fluid, an unsteady wake flow caused by an impulsively started circular cylinder at Reynolds number 9500, and an unsteady vortex shedding flow past a suddenly started rotating circular cylinder at Reynolds number 1000 are simulated. The first example is a benchmark case for flexible boundary FSI with a large pressure gradient across the boundary, the second is a fixed complex boundary problem, and the third is a typical moving boundary example. The results are in good agreement with the analytical and existing numerical data. It is shown that the proposed scheme is capable of modeling flexible boundary and complex boundary problems at a second-order spatial convergence; the volume leakage defect of the conventional IB method has been remedied by using a new method of introducing the unsteady and non-uniform external force; and the LB method makes the IB method simulation simpler and more efficient.

Keywords

76M2874F10Lattice Boltzmann methodimmersed boundary methodfluid-structure interactionflexible boundarycomplex boundary
Type
Research Article
Information
Communications in Computational Physics , Volume 9 , Issue 5 , May 2011 , pp. 1375 - 1396
Copyright
Copyright © Global Science Press Limited 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Peskin, C. S., Flow Patterns Around Heart Valves: A Digital Computer Method for Solving the Equations of Motion, PhD thesis, Physiol., Albert Einstein Coll. Med., Univ. Microfilms., 378 (1972), 72–102.Google Scholar
[2]Peskin, C. S., and McQueen, D. M., A General Method for the Computer Simulation of Biological Systems Interacting with Fluids-Biological Fluid Dynamics, ed. by Ellington, C. P. et al., the Company of Biologists Limited, Cambridge, 1995.Google Scholar
[3]McQueen, D. M., and Peskin, C. S., A three-dimensional computer model of the human heart for studying cardiac fluid dynamics, Comput. Graphics., 34 (2000), 56–60.Google Scholar
[4]Lemmon, J. D., and Yoganathan, A. P., Three-dimensional computational model of left heart diastolic function with fluid-structure interaction, J. Biomech. Eng., 122 (2000), 109–117.Google ScholarPubMed
[5]Lemmon, J. D., and Yoganathan, A. P., Computational modeling of left heart diastolic function: examination of ventricular dysfunction, J. Biomech. Eng., 122 (2000), 297–303.Google Scholar
[6]Miller, L. A., and Peskin, C. S., When vortices stick: an aerodynamic transition in tiny insect flight, J. Exp. Biology., 207 (2004), 3073–3088.Google Scholar
[7]Mitta, R., Dong, H., Bozkurttas, M., and Loebbecke, A., Analysis of flying and swimming in nature using an immersed boundary method, 36th AIAA Fluid Dynamics Conference and Exhibit, San Francisco, California, 2006.Google Scholar
[8]Fauci, L. J., and Peskin, C. S., A computational model of aquatic animal locomotion, J. Comput. Phys., 77 (1988), 85–108.CrossRefGoogle Scholar
[9]Zhu, L., and Peskin, C. S., Simulation of a flapping flexible filament in a flowing soap film by the immersed boundary method, J. Comput. Phys., 179 (2002), 452–468Google Scholar
[10]Zhu, L., He, G., Wang, S., Miller, L., Zhang, X., You, Q., and Fang, S., An immersed boundary method based on the lattice Boltzmann approach in three dimensions, with application, Comput. Math. Appl., 2010, article in press, doi: 10.1016/j.camwa.2010.03.022.Google Scholar
[11]Zhang, J., Johnson, P. C., and Popel, A. S., An immersed boundary lattice Boltzmann approach to simulate deformable liquid capsules and its application to microscopic blood flows, Phys. Biol., 4 (2007), 285–295.CrossRefGoogle ScholarPubMed
[12]Zhang, J., Johnson, P. C., and Popel, A. S., Red blood cell aggregation and dissociation in shear flows simulated by lattice Boltzmann method, J. Biomech., 41 (2008), 47–55.Google Scholar
[13]Dillon, R., Fauei, L. J., Fogelson, A. L., and Gaver, D., Modeling biofilm processes using the immersed boundary method, J. Comput. Phys., 129 (1996), 57–73.Google Scholar
[14]Kim, Y., and Peskin, C. S., 2-D Parachute simulation by the immersed boundary method, SIAM J. Sci. Comput., 28 (2006), 2294–2312.Google Scholar
[15]Kim, Y., and Peskin, C. S., 3-D Parachute simulation by the immersed boundary method, Comput. Fluids., 38 (2009), 1080–1090.CrossRefGoogle Scholar
[16]Peskin, C. S., The immersed boundary method, Acta. Numer., 11 (2002), 479–517.Google Scholar
[17]Chen, S., and Doolen, G. D., Lattice Boltzmann method for fluid flows, Annu. Rev. Fluid. Mech., 30 (1998), 329–364.Google Scholar
[18]Zheng, H. W., Shu, C., and Chew, Y. T., A lattice Boltzmann model for multiphase flows with large density ratio, J. Comput. Phys., 218 (2006), 353–371.Google Scholar
[19]Pan, C. X., Luo, L. S., and Miller, C. T., An evaluation of lattice Boltzmann schemes for porous medium flow simulation, Comput. Fluids., 35 (2006), 898–909.Google Scholar
[20]Chen, S., Chen, H. D., Martinez, D., and Matthaeus, W., Lattice Boltzmann model for simulation of magnetohydrodynamics, Phys. Rev. Lett., 67 (1991), 3776–3779.CrossRefGoogle ScholarPubMed
[21]Aidun, C. K., and Lu, Y. N., Lattice Boltzmann simulation of solid particles suspended in fluid, J. Stat. Phys., 81 (1995), 49–61.CrossRefGoogle Scholar
[22]Zhang, R., Shan, X., and Chen, H., Efficient kinetic method for fluid simulation beyond the Navier-Stokes equation, Phys. Rev. E., 74 (2006), 046703.Google Scholar
[23]Gan, Y. B., Xu, A. G., Zhang, G. C., Yu, X. J., and Li, Y., Two-dimensional lattice Boltzmann model for compressible flows with high Mach number, Phys. A., 387 (2008), 1721–1732.Google Scholar
[24]Feng, Z. G., and Michaelides, E. E., The immersed boundary-lattice Boltzmann method for solving fluid-particles interaction problems, J. Comput. Phys., 195 (2004), 602–628.Google Scholar
[25]Peng, Y., and Shu, C. et al., Application of multi-block approach in the immersed boundary-lattice Boltzmann method for viscous fluid flows, J. Comput. Phys., 218 (2006), 460–478.Google Scholar
[26]Shu, C., Liu, N., 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), 1607–1622.Google Scholar
[27]Dupuis, A., Chatelain, P., and Koumoutsakos, P., An immersed boundary-lattice Boltzmann method for the simulation of the flow past an impulsively started cylinder, J. Comput. Phys., 227 (2008), 4486–4498.Google Scholar
[28]Niu, X. D., Shu, C., Chew, Y. T., and Peng, Y., A momentum exchange-based immersed boundary-lattice Boltzmann method for simulating incompressible viscous flows, Phys. Lett. A., 354 (2006), 173–182.CrossRefGoogle Scholar
[29]Cheng, Y. G., and Li, J. P., Introducing unsteady non-uniform source terms into the lattice Boltzmann model, Int. J. Numer. Meth. Fluids., 56 (2008), 629–641.Google Scholar
[30]Peskin, C. S., and Printz, B. F., Improved volume conservation in the computation of flows with immersed elastic boundaries, J. Comput. Phys., 105 (1993), 33–46.CrossRefGoogle Scholar
[31]Li, Z. L., and Lai, M. C., The immersed interface method for the Navier-Stokes equations with singular forces, J. Comput. Phys., 171 (2001), 822–842.Google Scholar
[32]Xu, S., and Wang, Z. J., An immersed interface method for simulating the interaction of a fluid with moving boundaries, J. Comput. Phy., 216 (2006), 454–493.Google Scholar
[33]Lee, L., and LeVeque, R. J., An immersed interface method for incompressible Navier-Stokes equations, SIAM J. Sci. Comput., 25 (2003), 832–856.Google Scholar
[34]d’Humires, D., Ginzburg, I., Krafczyk, M., Lallemand, P., and Luo, L. S., Multiple-relaxation-time lattice Boltzmann models in three dimensions, Philos. Trans. Royal. Soc. A., 360 (2002), 437–451.Google Scholar
[35]Newren, E. P., Enhancing the Immersed Boundary Method: Stability, Volume Conservation and Implicit Solvers, PhD dissertation of The University of Utah, USA, 2007.Google Scholar
[36]Mittal, R., and Iaccarino, G., Immersed boundary methods, Annu. Rev. Fluid. Mech., 37 (2003), 239–261.Google Scholar
[37]Loc, Ta Phuoc, and Rouard, R., Numerical solution of the early statge of the unsteady viscous flow around a circular cylinder: a comparison with experimental visualization and measurements, J. Fluid. Mech., 160 (1985), 93–117.Google Scholar
[38]Badr, H. M., Coutanceau, M., and Dennis, S. C. R. et al., Unsteady flow past a rotating circular cylinder at Reynolds numbers 103 and 104, J. Fluid. Mech., 220 (1990), 459–484.Google Scholar
[39]Griffith, B. E., and Peskin, C. S., On the order of accuracy of the immersed boundary method: higher order convergence rates for sufficiently smooth problems, J. Comput. Phys., 208 (2005), 75–105.Google Scholar
[40]Le, G., and Zhang, J., Boundary slip from the immersed boundary lattice Boltzmann models, Phys. Rev. E., 79(2) (2009), 026701.Google Scholar
[41]Lallemand, P., and Luo, L. S., Theory of the lattice Boltzmann method: dispersion, dissipation, isotropy, Galilean invariance, and stability, Phys. Rev. E., 61(6) (2000), 6546–6562.Google Scholar