Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-24T04:42:46.392Z Has data issue: false hasContentIssue false
  • English
  • Français

A Robust Immersed Boundary-Lattice Boltzmann Method for Simulation of Fluid-Structure Interaction Problems

Published online by Cambridge University Press:  22 June 2016

Jie Wu ,
Jing Wu ,
Jiapu Zhan ,
Ning Zhao  and
Tongguang Wang
Jie Wu*
Affiliation:
Department of Aerodynamics, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing 210016, Jiangsu, China
Jing Wu*
Affiliation:
Department of Aerodynamics, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing 210016, Jiangsu, China
Jiapu Zhan*
Affiliation:
Department of Aerodynamics, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing 210016, Jiangsu, China
Ning Zhao*
Affiliation:
Department of Aerodynamics, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing 210016, Jiangsu, China
Tongguang Wang*
Affiliation:
Department of Aerodynamics, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing 210016, Jiangsu, China
*
*Corresponding author. Email addresses:[email protected] (Jie Wu), [email protected] (Jing Wu), [email protected] (J. Zhan), [email protected] (N. Zhao), [email protected] (T. Wang)
*Corresponding author. Email addresses:[email protected] (Jie Wu), [email protected] (Jing Wu), [email protected] (J. Zhan), [email protected] (N. Zhao), [email protected] (T. Wang)
*Corresponding author. Email addresses:[email protected] (Jie Wu), [email protected] (Jing Wu), [email protected] (J. Zhan), [email protected] (N. Zhao), [email protected] (T. Wang)
*Corresponding author. Email addresses:[email protected] (Jie Wu), [email protected] (Jing Wu), [email protected] (J. Zhan), [email protected] (N. Zhao), [email protected] (T. Wang)
*Corresponding author. Email addresses:[email protected] (Jie Wu), [email protected] (Jing Wu), [email protected] (J. Zhan), [email protected] (N. Zhao), [email protected] (T. Wang)
Get access

Abstract

A robust immersed boundary-lattice Boltzmann method (IB-LBM) is proposed to simulate fluid-structure interaction (FSI) problems in this work. Compared with the conventional IB-LBM, the current method employs the fractional step technique to solve the lattice Boltzmann equation (LBE) with a forcing term. Consequently, the non-physical oscillation of body force calculation, which is frequently encountered in the traditional IB-LBM, is suppressed greatly. It is of importance for the simulation of FSI problems. In the meanwhile, the no-slip boundary condition is strictly satisfied by using the velocity correction scheme. Moreover, based on the relationship between the velocity correction and forcing term, the boundary force can be calculated accurately and easily. A few test cases are first performed to validate the current method. Subsequently, a series of FSI problems, including the vortex-induced vibration of a circular cylinder, an elastic filament flapping in the wake of a fixed cylinder and sedimentation of particles, are simulated. Based on the good agreement between the current results and those in the literature, it is demonstrated that the proposed IB-LBM has the capability to handle various FSI problems effectively.

Keywords

Immersed boundary-lattice Boltzmann methodfractional stepsuppression of force non-physical oscillationfluid-structure interaction
Type
Research Article
Information
Communications in Computational Physics , Volume 20 , Issue 1 , July 2016 , pp. 156 - 178
Copyright
Copyright © Global-Science Press 2016 

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] Hu, H.H., Direct simulation of flows of solid-liquid mixtures, Int. J. Multiphase Flow, 22:335–352, 1996.CrossRefGoogle Scholar
[2] Perot, B. and Nallapati, R., Amoving unstructured staggeredmeshmethod for the simulation of incompressible free-surface flows, J. Comput. Phys. 184:192–214, 2003.CrossRefGoogle Scholar
[3] Rendall, T. C. S. and Allen, C. B., Efficient mesh motion using radial basis functions with data reduction algorithms, J. Comput. Phys. 228:6231–6249, 2009.CrossRefGoogle Scholar
[4] Peskin, C. S., Numerical analysis of blood flow in the heart, J. Comput. Phys. 25:220–252, 1977.CrossRefGoogle Scholar
[5] Udaykumar, H. S., Mittal, R., Rampunggoon, P. and Khanna, A., A sharp interface Cartesian grid method for simulating flows with complex moving boundaries, J. Comput. Phys. 174:345–380, 2001.CrossRefGoogle Scholar
[6] Kim, D. and Choi, H., Immersed boundary method for flow around an arbitrarily moving body, J. Comput. Phys. 212:662–680, 2006.CrossRefGoogle Scholar
[7] Mittal, R., Dong, H., Bozkurttas, M., Najjar, F. M., Vargas, A. and von Loebbecke, A., A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries, J. Comput. Phys. 227:4825–4852, 2008.CrossRefGoogle ScholarPubMed
[8] Goldstein, D., Handler, R. and Sirovich, L., Modeling a no-slip flowboundary with an external force field, J. Comput. Phys. 105:354–366, 1993.CrossRefGoogle Scholar
[9] Lai, M.-C. and Peskin, C. S., An immersed boundary method with formal second-order accuracy and reduced numerical viscosity, J. Comput. Phys. 160:705–719, 2000.CrossRefGoogle Scholar
[10] Griffith, B. E., Hornung, R. D., McQueen, D.M. and Peskin, C. S., An adaptive, formally second order accurate version of the immersed boundary method, J. Comput. Phys. 223:10–49, 2007.CrossRefGoogle Scholar
[11] Aidun, C. K. and Clausen, J. R., Lattice-Boltzmann method for complex flows. Annu. Rev. Fluid Mech. 42:439–472, 2010.CrossRefGoogle Scholar
[12] Feng, Z.-G. and Michaelides, E. E., The immersed boundary-lattice Boltzmann method for solving fluid-particles interaction problems, J. Comput. Phys. 195:602–628, 2004.CrossRefGoogle Scholar
[13] Feng, Z.-G. and Michaelides, E. E., Proteus: A direct forcing method in the simulations of particulate flows, J. Comput. Phys. 202:20–51, 2005.CrossRefGoogle Scholar
[14] Niu, X. D., Shu, C., Chew, Y. T. and Peng, Y., A momentum exchanged-based immersed boundary-lattice Boltzmann method for simulating incompressible viscous flows, Phys. Lett. A, 354:173–182, 2006.CrossRefGoogle Scholar
[15] Zhang, J., Johnson, P. C. and Popel, A. S., An immersed boundary lattice Boltzmann approach to simulate deformable liquid capsules and its application tomicroscopic blood flows, Phys. Biol. 4:285–295, 2007.CrossRefGoogle ScholarPubMed
[16] Sui, Y., Chew, Y. T., Roy, P. and Low, H., A hybrid method to study flow-induced deformation of three-dimensional capsules, J. Comput. Phys. 227:6351–6371, 2008.CrossRefGoogle Scholar
[17] Wu, J. and Shu, C., Implicit velocity correction-based immersed boundary-lattice Boltzmann method and its applications, J. Comput. Phys. 228:1963–1979, 2009.CrossRefGoogle Scholar
[18] Hao, J. and Zhu, L., A lattice Boltzmann based implicit immersed boundarymethod for fluid-structure interaction, Comput. Math. Appl. 59:185–193, 2010.CrossRefGoogle Scholar
[19] Tian, F.-B., Luo, H., Zhu, L., Liao, J. C. and Lu, X.-Y., An efficient immersed boundary-lattice Boltzmann method for the hydrodynamic interaction of elastic filaments, J. Comput. Phys. 230:7266–7283, 2011.CrossRefGoogle ScholarPubMed
[20] Suzuki, K. and Inamuro, T., A higher-order immersed boundary-lattice Boltzmann method using a smooth velocity field near boundaries, Comput. Fluids, 76:105–115, 2013.CrossRefGoogle Scholar
[21] Favier, J., Revell, A. and Pinelli, A., A lattice Boltzmann-immersed boundarymethod to simulate the fluid interaction with moving and slender flexible objects, J. Comput. Phys. 261:145–161, 2014.CrossRefGoogle Scholar
[22] Yuan, H.-Z., Niu, X.-D., Shu, S., Li, M. and Yamaguchi, H., A momentum exchanged-based immersed boundary-lattice Boltzmann method for simulating a flexible filament in an incompressible flow, Comput. Math. Appl. 67:1039–1056, 2014.CrossRefGoogle Scholar
[23] Hu, Y., Yuan, H., Shu, S., Niu, X. and Li, M., An improved momentum exchanged-based immersed boundary-lattice Boltzmannmethod by using an iterative technique, Comput. Math. Appl. 68:140–155, 2014.CrossRefGoogle Scholar
[24] Yang, X., Zhang, X., Li, Z. and He, G. W.. A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations. J. Comput. Phys. 228:7821–7836, 2009.CrossRefGoogle Scholar
[25] 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. 226:1607–1622, 2007.CrossRefGoogle Scholar
[26] Wu, J. and Shu, C., Simulation of three-dimensional flows over moving objects by an improved immersed boundary-lattice Boltzmann method, Int. J. Numer. Meth. Fl. 68:977–1004, 2012.CrossRefGoogle Scholar
[27] Wu, J., Shu, C. and Zhao, N., Investigation of flow characteristics around a stationary circular cylinder with an undulatory plate. Eur. J. Mech. B-Fluid. 48:27–39, 2014.CrossRefGoogle Scholar
[28] Wu, J., Shu, C. and Zhao, N., Numerical investigation of vortex-induced vibration of a circular cylinder with a hinged flat plate, Phys. Fluids, 26:063601, 2014.CrossRefGoogle Scholar
[29] Xu, S. and Wang, Z. J., An immersed interfacemethod for simulating the interaction of a fluid with moving boundaries, J. Comput. Phys. 216:454–493, 2006.CrossRefGoogle Scholar
[30] Gao, T., Tseng, Y. and Lu, X., An improved hybrid Cartesian/immersed boundary method for fluid-solid flows, Int. J. Numer. Meth. Fl. 55:1189–1211, 2007.CrossRefGoogle Scholar
[31] Yang, J. and Stern, F., A simple and efficient direct forcing immersed boundary framework for fluid-structure interactions, J. Comput. Phys. 231:5029–5061, 2012.CrossRefGoogle Scholar
[32] Schneiders, L., Hartmann, D., Meinke, M. and Schröder, W., An accurate moving boundary formulation in cut-cell methods, J. Comput. Phys. 235:786–809, 2013.CrossRefGoogle Scholar
[33] Ahn, H. T. and Kallinderis, Y., Strongly coupled flow/structure interactions with a geometrically conservative ALE scheme on general hybrid meshes, J. Comput. Phys. 219:671–696, 2006.CrossRefGoogle Scholar
[34] Borazjani, I. and Sotiropoulos, F., Vortex-induced vibrations of two cylinders in tandem arrangement in the proximity-wake interference region, J. Fluid Mech. 621:321–364, 2009.CrossRefGoogle ScholarPubMed
[35] Bao, Y., Zhou, D. and Tu, J., Flow interference between a stationary cylinder and an elastically mounted cylinder arranged in proximity, J. Fluids Struct. 27:1425–1446, 2011.CrossRefGoogle Scholar
[36] Liao, J. C., Beal, D. N., Lauder, G. V. and Triantafyllou, M. S., Fish exploiting vortices decrease muscle activity, Science, 302:1566–1569, 2003.CrossRefGoogle ScholarPubMed
[37] Huang, W.-X., Shin, S. J. and Sung, H. J., Simulation of flexible filaments in a uniform flow by the immersed boundary method, J. Comput. Phys. 226:2206–2228, 2007.CrossRefGoogle Scholar
[38] Kang, S. K. and Hassan, Y. A., A direct-forcing immersed boundary method for the thermal lattice Boltzmann method, Comput. Fluids, 49:36–45, 2011.CrossRefGoogle Scholar
[39] Fortes, A., Joseph, D. D. and Lundgren, T. S., Nonlinear mechanics of fluidization of beds of spherical particles, J. Fluid Mech. 177:467–483, 1987.CrossRefGoogle Scholar