Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-27T14:11:53.087Z Has data issue: false hasContentIssue false

A One-Continuum Approach for Mutual Interaction of Fluids and Structures

Published online by Cambridge University Press:  18 May 2015

I. Farahbakhsh
Affiliation:
Department of Ocean Engineering, Amirkabir University of Technology, Tehran, Iran
H. Ghassemi*
Affiliation:
Department of Ocean Engineering, Amirkabir University of Technology, Tehran, Iran
F. Sabetghadam
Affiliation:
Mechanical and Aerospace Engineering Department, Science and Research Branch, Islamic Azad University, Tehran, Iran
*
*Corresponding author (gasemi@aut.ac.ir)
Get access

Abstract

A new simulation method for solving fluid-structure two-way coupling problems has been developed. All the basic equations are numerically solved on a fixed Cartesian grid using a finite difference scheme. A new definition of velocity-vorticity formulation aids us to introduce an immersed boundary method that does not require a force term to impose the no-slip condition on the solid boundaries. The proposed method is easy to implement and apply for two-way fluid-structure interaction problems. The dynamics of a falling and rising circular cylinder in a quiescent fluid as well as the motion of a circular cylinder in a lid-driven cavity are considered to evaluate the capabilities of the presented method.

Type
Research Article
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2015 

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

REFERENCES

1.Karagiozis, K., Kamakoti, R., Cirak, F. and Pantano, C., “A Computational Study of Supersonic Disk-Gap-Band Parachutes Using Large-Eddy Simulation Coupled to a Structural Membrane,” Journal of Fluids and Structures, 27, pp. 175192 (2011).CrossRefGoogle Scholar
2.Hrona, J. and Mádlík, M., “Fluid-Structure Interaction with Applications in Biomechanics,” Nonlinear Analysis: Real World Applications, 8, pp. 14311458 (2007).Google Scholar
3.Zhao, H., Freund, J. B. and Moser, R. D., “A Fixed-Mesh Method for Incompressible Flow-Structure Systems with Finite Solid Deformations,” Journal of Computational Physics, 227, pp. 31143140 (2008).CrossRefGoogle Scholar
4.Huang, W. X. and Sung, H. J., “An Immersed Boundary Method for Fluid-Flexible Structure Interaction,” Computer Methods in Applied Mechanics and Engineering, 198, pp. 26502661 (2009).CrossRefGoogle Scholar
5.Curet, O. M., AlAli, I. K., MacIver, M. A. and Patankar, N. A., “A Versatile Implicit Iterative Approach for Fully Resolved Simulation of Self- Propulsion,” Computer Methods in Applied Mechanics and Engineering, 199, pp. 24172424 (2010).CrossRefGoogle Scholar
6.Yeo, K. S., Ang, S. J. and Shu, C., “Simulation of Fish Swimming and Manoeuvring by an SVD-GFD Method on a Hybrid Meshfree-Cartesian Grid,” Computers & Fluids, 39, pp. 403430 (2010).CrossRefGoogle Scholar
7.Herschlag, G. and Miller, L., “Reynolds Number Limits for Jet Propulsion: A. Numerical Study of Simplified Jellyfish,” Journal of Theoretical Biology, 285, pp. 8495 (2011).Google Scholar
8.Hou, G., Wang, J. and Layton, A., “Numerical Methods for Fluid-Structure Interaction-A Review,” Communications in Computational Physics, 12, pp. 337377 (2012).Google Scholar
9.Loon, R. V., Anderson, P. D., Vosse, F. N. V. D. and Sherwin, S. J., “Comparison of Various Fluid- Structure Interaction Methods for Deformable Bodies,” Computers & Structures, 85, pp. 833843 (2007).CrossRefGoogle Scholar
10.Le, D. V., White, J., Peraire, J., Lim, K. M. and Khoo, B. C., “An Implicit Immersed Boundary Method for Three-Dimensional Fluid-Membrane Interactions,” Journal of Computational Physics, 228, pp. 84278445 (2009).CrossRefGoogle Scholar
11.Vanella, M., Rabenold, P. and Balaras, E., “A Direct-Forcing Embedded-Boundary Method with Adaptive Mesh Refinement for Fluid-Structure Interaction Problems,” Journal of Computational Physics, 229, pp. 64276449 (2010).Google Scholar
12.Ii, S., Sugiyama, K., Takeuchi, S., Takagi, S. and Matsumoto, Y., “An Implicit Full Eulerian Method for the Fluid-Structure Interaction Problem,” International Journal for Numerical Methods in Fluids, 65, pp. 150165 (2011).CrossRefGoogle Scholar
13.Sugiyama, K., Ii, S., Takeuchi, S., Takagi, S. and Matsumoto, Y., “Full Eulerian Simulations of Bio-concave Neo-Hookean Particles in a Poiseuille Flow,” Computational Mechanics, 46, pp. 147157 (2010).Google Scholar
14.Takagi, S., Sugiyama, K., Ii, S. and Matsumoto, Y., “A review of Full Eulerian Methods for Fluid Structure Interaction Problems,” Journal of Applied Mechanics, 79, pp. 17 (2012).Google Scholar
15.Gao, T. and Hu, H. H., “Deformation of Elastic Particles in Viscous Shear Flow,” Journal of Computational Physics, 228, pp. 21322151 (2009).Google Scholar
16.Pita, C. M. and Felicelli, S. D., “A Fluid-Structure Interaction Method for Highly Deformable Solids,” Computers & Structures, 88, pp. 255262 (2010).Google Scholar
17.Shen, L. and Chan, E. S., “Numerical Simulation of Fluid-Structure Interaction Using a Combined Volume of Fluid and Immersed Boundary Method,” Ocean Engineering, 35, pp. 939952 (2008).CrossRefGoogle Scholar
18.Zhang, C., Zhang, W., Lin, N., Tang, Y., Zhao, C., Gu, J., Lin, W., Chen, X. and Qiu, A., “A Two-Phase Flow Model Coupling with Volume of Fluid and Immersed Boundary Methods for Free Surface and Moving Structure Problems,” Ocean Engineering, 74, pp. 107124 (2013).Google Scholar
19.Uzunoğlu, B., Tan, M. and Price, W. G., “Low-Reynolds-Number Flow Around an Oscillating Circular Cylinder Using a Cell Viscous Boundary Element Method,” International Journal for Numerical Methods in Engineering, 50, pp. 23172338 (2001).Google Scholar
20.Yang, J. and Balaras, E., “An Embedded-Boundary Formulation for Large-Eddy Simulation of Turbulent Flows Interacting with Moving Boundaries,” Journal of Computational Physics, 215, pp. 1240 (2006).CrossRefGoogle Scholar
21.Pham, A. H., Lee, C. Y., Seo, J. H., Chun, H. H., Kim, H. J., Yoon, H. S., Kim, J. H., Park, D. W. and Park, I. R., “Laminar Flow Past an Oscillating Circular Cylinder in Cross Flow,” Journal of Marine Science and Technology, 18, pp. 361368 (2010).Google Scholar
22.Morse, T. L. and Williamson, C. H. K., “Prediction of Vortex-Induced Vibration Response by Employing Controlled Motion,” Journal of Fluid Mechanics, 634, pp. 539 (2009).Google Scholar
23.Bearman, P. W., “Understanding and Predicting Vortex-Induced Vibrations,” Journal of Fluid Mechanics, 634, pp. 14 (2009).Google Scholar
24.Mittal, R. and Iaccarino, G., “Immersed Boundary Methods,” Annual Review of Fluid Mechanics, 37, pp. 239261 (2005).Google Scholar
25.Peskin, C. S., “Numerical Analysis of Blood Flow in the Heart,” Journal of Computational Physics, 25, pp. 220252 (1977).Google Scholar
26.Peskin, C. S., “The Immersed Boundary Method,” Acta Numerica, pp. 479517 (2002).Google Scholar
27.Lai, M. C. and Peskin, C. S., “An Immersed Boundary Method with Formal Second-Order Accuracy and Reduced Numerical Viscosity,” Journal of Computational Physics, 160, pp. 705719 (2000).CrossRefGoogle Scholar
28.Uhlmann, M., “An Immersed Boundary Method with Direct Forcing for the Simulation of Particulate Flows,” Journal of Computational Physics, 209, pp. 448476 (2005).Google Scholar
29.Kim, D. and Choi, H., “Immersed Boundary Method for Flow Around an Arbitrarily Moving Body,” Journal of Computational Physics, 212, pp. 662680 (2006).CrossRefGoogle Scholar
30.Choi, J. I., Oberoi, R. C., Edwards, J. R. and Rosati, J. A., “An Immersed Boundary Method for Complex Incompressible Flows,” Journal of Computational Physics, 224, pp. 757784 (2007).Google Scholar
31.Taira, K. and Colonius, T., “The Immersed Boundary Method: A. Projection Approach,” Journal of Computational Physics, 225, pp. 21182137 (2007).Google Scholar
32.Xu, S. and Wang, Z. J., “A 3D Immersed Interface Method for Fluid-Solid Interaction,” Computer Methods in Applied Mechanics and Engineering, 197, pp. 20682086 (2008).Google Scholar
33.Bonfigli, G., “High-Order Finite-Difference Implementation of the Immersed-Boundary Technique for Incompressible Flows,” Computers & Fluids, 46, pp. 211 (2011).CrossRefGoogle Scholar
34.Chaudhuri, A., Hadjadj, A. and Chinnayya, A., “On the Use of Immersed Boundary Methods for Shock/Obstacle Interactions,” Journal of Computational Physics, 230, pp. 17311748 (2011).Google Scholar
35.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, pp. 22062228 (2007).Google Scholar
36.Song, C., Shin, S. J., Sung, H. J. and Chang, K. S., “Dynamic Fluid-Structure Interaction of an Elastic Capsule in a Viscous Shear Flow at Moderate Reynolds Number,” Journal of Fluids and Structures, 27, pp. 438455 (2011).Google Scholar
37.Xu, S., “The Immersed Interface Method for Simulating Prescribed Motion of Rigid Objects in an Incompressible Viscous Flow,” Journal of Computational Physics, 227, pp. 50455071 (2008).Google Scholar
38.Liao, C. C., Chang, Y. W., Lin, C. A. and McDonough, J. M., “Simulating Flows with Moving Rigid Boundary Using Immersed-Boundary Method,” Computers & Fluids, 39, pp. 152167 (2010).Google Scholar
39.Glowinski, R., Pan, T. W., Hesla, T. I., Joseph, D. D. and Périauxz, J., “A Fictitious Domain Approach to the Direct Numerical Simulation of Incompressible Viscous Flow Past Moving Rigid Bodies: Application to Particulate Flow,” Journal of Computational Physics, 169, pp. 363426 (2001).Google Scholar
40.Coquerelle, M. and Cottet, G H., “A Vortex Level Set Method for the Two-Way Coupling of an Incompressible Fluid with Colliding Rigid Bodies,” Journal of Computational Physics 227, pp. 91219137 (2008).Google Scholar
41.Horowitz, M. and Williamson, C. H. K., “Dynamics of a Rising and Falling Cylinder,” Journal of Fluids and Structures, 22, pp. 837843 (2006).Google Scholar
42.Horowitz, M. and Williamson, C. H. K., “Vortex-Induced Vibration of a Rising and Falling Cylinder,” Journal of Fluid Mechanics, 662, pp. 352383 (2010).Google Scholar
43.Bergmann, M. and Iollo, A., “Modeling and Simulation of Fish-Like Swimming,” Journal of Computational Physics, 230, pp. 329348 (2011).Google Scholar
44.Sugiyama, K., Ii, S., Takeuchi, S., Takagi, S. and Matsumoto, Y., “A Full Eulerian Finite Difference Approach for Solving Fluid-Structure Coupling Problems,” Journal of Computational Physics, 230 pp. 596627 (2011).Google Scholar