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Computing Fluid-Structure Interaction by the Partitioned Approach with Direct Forcing

Part of: Coupling of solid mechanics with other effects

Published online by Cambridge University Press:  05 December 2016

Asim Timalsina ,
Gene Hou  and
Jin Wang
Asim Timalsina*
Affiliation:
Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA 23529, USA
Gene Hou*
Affiliation:
Department of Mechanical and Aerospace Engineering, Old Dominion University, Norfolk, VA 23529, USA
Jin Wang*
Affiliation:
Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA
*
*Corresponding author. Email addresses:atimalsi@odu.edu (A. Timalsina), ghou@odu.edu (G. Hou), Jin-Wang02@utc.edu (J.Wang)
*Corresponding author. Email addresses:atimalsi@odu.edu (A. Timalsina), ghou@odu.edu (G. Hou), Jin-Wang02@utc.edu (J.Wang)
*Corresponding author. Email addresses:atimalsi@odu.edu (A. Timalsina), ghou@odu.edu (G. Hou), Jin-Wang02@utc.edu (J.Wang)
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Abstract

In this paper, we propose a new partitioned approach to compute fluid-structure interaction (FSI) by extending the original direct-forcing technique and integrating it with the immersed boundary method. The fluid and structural equations are calculated separately via their respective disciplinary algorithms, with the fluid motion solved by the immersed boundary method on a uniform Cartesian mesh and the structural motion solved by a finite element method, and their solution data only communicate at the fluid-structure interface. This computational framework is capable of handling FSI problems with sophisticated structures described by detailed constitutive laws. The proposed methods are thoroughly tested through numerical simulations involving viscous fluid flow interacting with rigid, elastic solid, and elastic thin-walled structures.

Keywords

Fluid-structure interactionimmersed boundary methodpartitioned approach

MSC classification

Secondary: 65Z05: Applications to physics 74F10: Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
Type
Research Article
Information
Communications in Computational Physics , Volume 21 , Issue 1 , January 2017 , pp. 182 - 210
Copyright
Copyright © Global-Science Press 2016 

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References

[1] Bathe, K.J.. Finite Element Procedures, pp. 780–782. Prentice-Hall, Englewood CliVs, New Jersey, 1996.Google Scholar
[2] Calhoun, D.. A cartesian grid method for solving the two-dimensional streamfunction-vorticity equations in irregular regions. Journal of Computational Physics, 176(2):231–275, 2002.Google Scholar
[3] Dennis, S.C.R. and Chang, G.Z.. Numerical solutions for steady flow past a circular cylinder at reynolds numbers up to 100. Journal of Fluid Mechanics, 42(03):471–489, 1970.Google Scholar
[4] Dowell, E.H. and Hall, K.C.. Modeling of fluid-structure interaction. Annual Review of Fluid Mechanics, 33:445–490, 2001.Google Scholar
[5] Fadlun, E.A., Verzicco, R., Orlandi, P., and Mohd-Yusof, J.. Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. Journal of Computational Physics, 161(1):35–60, 2000.Google Scholar
[6] Farhat, C., Lesoinne, M., and LeTallec, P.. Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces. Computer Methods in Applied Mechanics and Engineering, 157:95–114, 1998.Google Scholar
[7] Fornberg, B.. A numerical study of steady viscous flow past a circular cylinder. Journal of Fluid Mechanics, 98(04):819–855, 1980.Google Scholar
[8] Goldstein, D., Handler, R., and Sirovich, L.. Modeling a no-slip flow boundary with an external force field. Journal of Computational Physics, 105:354–366, 1993.Google Scholar
[9] Guy, R.D. and Hartenstine, D.A.. On the accuracy of direct forcing immersed boundary methods with projection methods. Journal of Computational Physics, 229:2479–2496, 2010.Google Scholar
[10] Hou, G., Wang, J., and Layton, A.. Numerical methods for fluid-structure interaction - A review. Communication in Computational Physics, 12(2):337–377, 2012.Google Scholar
[11] Huang, W.X., Shin, S.J., and Sung, H.J.. Simulation of flexible filaments in a uniform flow by the immersed boundary method. Journal of Computational Physics, 226(2):2206–2228, 2007.Google Scholar
[12] Huang, W.X. and Sung, H.J.. An immersed boundary method for fluid–flexible structure interaction. Computer Methods in Applied Mechanics and Engineering, 198(33):2650–2661, 2009.Google Scholar
[13] Hubner, B., Walhorn, E., and Dinkler, D.. A monolithic approach to fluid-structure interaction using space-time finite elements. Computer Methods in Applied Mechanics and Engineering, 193:2087–2104, 2004.Google Scholar
[14] Jirásek, M.. Basic concepts and equations of solid mechanics. Revue Européenne de Génie Civil, 11(7-8):879–892, 2007.Google Scholar
[15] Li, Z.. An overview of the immersed interface method and its applications. Taiwanese Journal of Mathematics, 7:1–49, 2003.Google Scholar
[16] Luo, H., Dai, H., Ferreira de Sousa, P., and Yin, B.. On the numerical oscillation of the direct-forcing immersed-boundary method for moving boundaries. Computers & Fluids, 56:61–76, 2012.Google Scholar
[17] Mittal, R. and Iaccarino, G.. Immersed boundary methods. Annual Review of Fluid Mechanics, 37:239–261, 2005.Google Scholar
[18] Mohd-Yusof, J.. Combined immersed-boundary/b-spline methods for simulations of flow in complex geometries. Annual Research Briefs. NASA Ames Research Center, Stanford University Center of Turbulence Research: Stanford, pp. 317–327, 1997.Google Scholar
[19] Noor, D.Z., Chern, M.J., and Horng, T.L.. An immersed boundary method to solve fluid–solid interaction problems. Computational Mechanics, 44(4):447–453, 2009.Google Scholar
[20] Peskin, C.S.. The immersed boundary method. Acta Numerica, 11:479–517, 2002.Google Scholar
[21] Peskin, C.S.. The immersed boundary method in a simple special case, September 2007. Lecture notes. Retrieved on April, 14, 2013.Google Scholar
[22] Pletcher, R.H., Tannehill, J.C., and Anderson, D.A.. Computational Fluid Mechanics and Heat Transfer, Third Edition. CRC Press, 2011.Google Scholar
[23] Ryzhakov, P.B., Rossi, R., Idelsohn, S.R., and Onate, E.. A monolithic Lagrangian approach for fluid-structure interaction problems. Computational Mechanics, 46:883–899, 2010.Google Scholar
[24] Sotiropoulos, F. and Yang, X.. Immersed boundary methods for simulating fluid–structure interaction. Progress in Aerospace Sciences, 2013.Google Scholar
[25] Souli, M. and Benson, D.J. (Eds.). Arbitrary Lagrangian Eulerian and Fluid-Structure Interaction: Numerical Simulation. Wiley-ISTE, 2010.Google Scholar
[26] Steindorf, J. and Matthies, H.G.. Numerical efficiency of different partitioned methods for fluid-structure interaction. ZAMM - Journal of Applied Mathematics and Mechanics, 80(S2):557–558, 2000.Google Scholar
[27] Su, S.W., Lai, M.C., and Lin, C.A.. An immersed boundary technique for simulating complex flows with rigid boundary. Computers & Fluids, 36(2):313–324, 2007.Google Scholar
[28] Taira, K. and Colonius, T.. The immersed boundary method: A projection approach. Journal of Computational Physics, 225(2):2118–2137, 2007.Google Scholar
[29] Uhlmann, M.. An immersed boundary method with direct forcing for the simulation of particulate flows. Journal of Computational Physics, 209(2):448–476, 2005.Google Scholar
[30] Vierendeelsa, J., Dumontb, K., and Verdonckb, P.R.. A partitioned strongly coupled fluid-structure interaction method to model heart valve dynamics. Journal of Computational and Applied Mathematics, 215:602–609, 2008.Google Scholar
[31] Wang, J. and Layton, A.. Numerical simulations of fiber sedimentation in Navier-Stokes flows. Communications in Computational Physics, 5(1):61–83, 2009.Google Scholar
[32] Zhang, L.T. and Gay, M.. Immersed finite element method for fluid-structure interactions. Journal of Fluids and Structures, 23:839–857, 2007.Google Scholar
[33] Zhang, N. and Zheng, Z.C.. An improved direct-forcing immersed-boundary method for finite difference applications. Journal of Computational Physics, 221(1):250–268, 2007.Google Scholar
[34] Zhang, X., Zhu, X., and He, G.. An improved direct-forcing immersed boundary method for fluid-structure interaction simulations. In ASME 2013 Fluids Engineering Division Summer Meeting, V01AT08A005. American Society of Mechanical Engineers, 2013.Google Scholar