Abstract
Fluid-structure interaction (FSI) is a class of mechanics-related problems with mutual dependence between the fluid and structure parts and it is observable nearly everywhere, in natural phenomena to many engineering systems. The primary challenges in developing numerical models with conventional grid-based methods are the inherent nonlinearity and time-dependent nature of FSI, together with possible large deformations and moving interfaces. Smoothed particle hydrodynamics (SPH) method is a truly Lagrangian and meshfree particle method that conveniently treats large deformations and naturally captures rapidly moving interfaces and free surfaces. Since its invention, the SPH method has been widely applied to study different problems in engineering and sciences, including FSI problems. This article presents a review of the recent developments in SPH based modeling techniques for solving FSI-related problems. The basic concepts of SPH along with conventional and higher order particle approximation schemes are first introduced. Then, the implementation of FSI in a pure SPH framework and the hybrid approaches of SPH with other grid-based or particle-based methods are discussed. The SPH models of FSI problems with rigid, elastic and flexible structures, with granular materials, and with extremely intensive loadings are demonstrated. Some discussions on several key techniques in SPH including the balance of accuracy, stability and efficiency, the treatment of material interface, the coupling of SPH with other methods, and the particle regularization and adaptive particle resolution are provided as concluding marks.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M. B. Liu, J. R. Shao, and H. Q. Li, Int. J. Numer. Meth. Fluids 74, 684 (2014).
F. R. Ming, A. M. Zhang, H. Cheng, and P. N. Sun, Ocean Eng. 165, 336 (2016).
J. R. Wright, and J. E. Cooper, Introduction to Aircraft Aeroelasticity and Loads (Wiley, Weinheim, 2007).
W. Shen, and Y. P. Zhao, J. Appl. Mech. 85, 031003 (2018).
M. B. Liu, and G. R. Liu, Arch. Comput. Methods Eng. 17, 25 (2010).
H.-J. Bungartz, Fluid-structure Interaction: Modelling, Simulation, Optimization (Springer-Verlag, Heidelberg, 2006).
J. F. Sigrist, Fluid-Structure Interaction: An Introduction to Finite Element Coupling (Wiley, Weinheim, 2015).
Y. C. Fung, An Introduction to the Theory of Aeroelasticity (John Wiley & Sons, Ltd., Hoboken, 1994).
M. B. Liu, and G. R. Liu, Particle Methods for Multi-Scale and Multi-Physics (World Scientific, Singapore, 2016).
M. Matsumoto, H. Shirato, T. Yagi, R. Shijo, A. Eguchi, and H. Tamaki, J. Wind Eng. Ind. Aerod. 91, 1547 (2003).
J. R. Shao, H. Q. Li, G. R. Liu, and M. B. Liu, Comput. Struct. 100–101, 18 (2012).
M. Luo, C. G. Koh, and W. Bai, Ocean Eng. 120, 52 (2016).
H. J.-P. Morand, and R. Ohayon, Fluid-Structure Interaction: Applied Numerical Methods (Wiley, Weinheim, 1995).
E. H. Dowell, and K. C. Hall, Annu. Rev. Fluid Mech. 33, 445 (2001).
W. Shyy, H. S. Udaykumar, M. M. Rao, and R. W. Smith, Computational Fluid Dynamics with Moving Boundaries (Dover Publications, New York, 2007).
G. Hou, J. Wang, and A. Layton, Commun. Commut. Phys. 12, 337 (2012).
G. R. Liu, and M. B. Liu, Smoothed Particle Hydrodynamics: A Meshfree Particle Method (World Scientific, Singapore, 2003).
P. Brandimarte, Finite-Difference Methods for Partial Differential Equations (Wiley, Weinheim, 1960).
T. Liszka, and J. Orkisz, Comput. Struct. 11, 83 (1980).
T. N. Narasimhan, and P. A. Witherspoon, Water Resour. Res. 12, 57 (1976).
J. Kim, D. Kim, and H. Choi, J. Comput. Phys. 171, 132 (2001).
I. Demirdzic, and M. Peric, Int. J. Numer. Meth. Fluids 10, 771 (1990).
P. Jenny, S. H. Lee, and H. A. Tchelepi, J. Comput. Phys. 187, 47 (2003).
G. Strang, G. J. Fix, and D. S. Griffin, J. Appl. Mech. 41, 62 (1974).
J. R. Cho, and H. W. Lee, Comput. Methods Appl. Mech. Eng. 193, 2581 (2004).
S. Mitra, P. P. Upadhyay, and K. P. Sinhamahapatra, Int. J. Numer. Meth. Fluids 56, 1625 (2008).
K. Walayat, Z. Zhang, K. Usman, J. Chang, and M. Liu, Phys. Fluids 30, 103301 (2018).
D. Wan, and S. Turek, Int. J. Numer. Meth. Fluids 51, 531 (2006).
D. Wan, and S. Turek, J. Comput. Appl. Math. 203, 561 (2007).
O. C. Zienkiewicz, and R. L. Taylor, The Finite Element Method (McGraw-Hill, New York, 2000).
D. Liu, and P. Lin, J. Comput. Phys. 227, 3921 (2008).
A. E. P. Veldman, J. Gerrits, R. Luppes, J. A. Helder, and J. P. B. Vreeburg, J. Comput. Phys. 224, 82 (2007).
C. W. Hirt, and B. D. Nichols, J. Comput. Phys. 39, 201 (1981).
M. Sussman, P. Smereka, and S. Osher, J. Comput. Phys. 114, 146 (1994).
D. Peng, B. Merriman, S. Osher, H. Zhao, and M. Kang, J. Comput. Phys. 155, 410 (1999).
C. Farhat, and M. Lesoinne, Comput. Methods Appl. Mech. Eng. 182, 499 (2000).
M. Souli, A. Ouahsine, and L. Lewin, Comput. Methods Appl. Mech. Eng. 190, 659 (2000).
K. J. Bathe, and H. Zhang, Comput. Struct. 87, 604 (2009).
O. M. Faltinsen, and A. N. Timokha, J. Fluid Mech. 665, 457 (2010).
M. A. Noorian, R. D. Firouz-Abadi, and H. Haddadpour, Int. J. Numer. Meth. Engng. 89, 1652 (2012).
G. Fourey, C. Hermange, D. Le Touzé, and G. Oger, Comput. Phys. Commun. 217, 66 (2017).
A. W. Vreman, J. Fluid Mech. 796, 40 (2016).
A. W. Vreman, A Staggered Overset Grid Method for Resolved Simulation of Incompressible Flow Around Moving Spheres (Academic Press Professional, Inc., New York, 2017).
W. K. Liu, Y. Chen, S. Jun, J. S. Chen, T. Belytschko, C. Pan, R. A. Uras, and C. T. Chang, Arch. Comput. Methods Eng. 3, 3 (1996).
S. F. Li, and W. K. Liu, Appl. Mech. Rev. 55, 1 (2002).
G. R. Liu, and Y. T. Gu, An Introduction to Meshfree Methods and Their Programming (Springer, Heidelberg, 2005).
R. A. Gingold, and J. J. Monaghan, Mon. Not. R. Astron. Soc. 181, 375 (1977).
L. B. Lucy, Astron. J. 82, 1013 (1977).
J. J. Monaghan, Annu. Rev. Fluid Mech. 44, 323 (2012).
S. Koshizuka, and Y. Oka, Nucl. Sci. Eng. 123, 421 (1996).
S. Koshizuka, Comput. Fluid Dyn. J. 4, 29 (1995).
S. Shao, C. Ji, D. I. Graham, D. E. Reeve, P. W. James, and A. J. Chadwick, Coast. Eng. 53, 723 (2006).
Z. Chen, Z. Zong, M. B. Liu, and H. T. Li, Int. J. Numer. Meth. Fluids 73, 813 (2013).
A. J. Chorin, Math. Comp. 22, 745 (1968).
J. J. Monaghan, Annu. Rev. Astron. Astrophys. 30, 543 (1992).
A. Zhang, P. Sun, F. Ming, and A. Colagrossi, J. Hydrodyn. 29, 187 (2017).
D. Violeau, and B. D. Rogers, J. Hydraul. Res. 254, 1 (2016).
H. Gotoh, and A. Khayyer, Coast. Eng. J. 60, 79 (2018).
M. S. Shadloo, G. Oger, and D. Le Touzé, Comput. Fluids 136, 11 (2016).
Z. B. Wang, R. Chen, H. Wang, Q. Liao, X. Zhu, and S. Z. Li, Appl. Math. Model. 40, 9625 (2016).
J. J. Monaghan, J. Comput. Phys. 110, 399 (1994).
M. B. Liu, G. R. Liu, K. Y. Lam, and Z. Zong, Comput. Mech. 30, 106 (2003).
L. D. Libersky, A. G. Petschek, T. C. Carney, J. R. Hipp, and F. A. Allahdadi, J. Comput. Phys. 109, 67 (1993).
X. Y. Hu, and N. A. Adams, J. Comput. Phys. 227, 264 (2007).
A. Colagrossi, and M. Landrini, J. Comput. Phys. 191, 448 (2003).
R. A. Dalrymple, and B. D. Rogers, Coast. Eng. 53, 141 (2006).
S. Shao, and E. Y. M. Lo, Adv. Water Res. 26, 787 (2003).
Z. L. Zhang, D. L. Feng, T. Ma, and M. B. Liu, Eng. Anal. Bound. Elem. 98, 110 (2019).
A. Zhang, P. Sun, and F. Ming, Comput. Methods Appl. Mech. Eng. 294, 189 (2015).
J. K. Chen, and J. E. Beraun, Comput. Methods Appl. Mech. Eng. 190, 225 (2000).
M. B. Liu, and G. R. Liu, Appl. Numer. Math. 56, 19 (2006).
M. B. Liu, W. P. Xie, and G. R. Liu, Appl. Math. Model. 29, 1252 (2005).
R. C. Batra, and G. M. Zhang, J. Comput. Phys. 201, 172 (2004).
G. M. Zhang, and R. C. Batra, Comput. Mech. 34, 137 (2004).
J. Fang, R. G. Owens, L. Tacher, and A. Parriaux, J. Non-Newton. Fluid Mech. 139, 68 (2006).
J. Fang, and A. Parriaux, J. Comput. Phys. 227, 8894 (2008).
D. Asprone, F. Auricchio, and A. Reali, Int. J. Numer. Meth. Fluids 65, 1376 (2011).
D. Asprone, F. Auricchio, A. Montanino, and A. Reali, Int. J. Numer. Meth. Eng. 99, 1 (2014).
Z. L. Zhang, and M. B. Liu, Appl. Math. Model. 60, 606 (2018).
Z. L. Zhang, K. Walayat, J. Z. Chang, and M. B. Liu, Int. J. Numer. Meth. Eng. 116, 530 (2018).
C. Huang, J. M. Lei, M. B. Liu, and X. Y. Peng, Int. J. Numer. Meth. Fluids 78, 691 (2015).
C. Huang, J. M. Lei, M. B. Liu, and X. Y. Peng, Int. J. Numer. Meth. Fluids 81, 377 (2016).
J. Ren, T. Jiang, W. Lu, and G. Li, Comput. Phys. Commun. 205, 87 (2016).
G. Oger, D. Le Touzé, D. Guibert, M. de Leffe, J. Biddiscombe, J. Soumagne, and J. G. Piccinali, Comput. Phys. Commun. 200, 1 (2016).
A. Ferrari, M. Dumbser, E. F. Toro, and A. Armanini, Comput. Fluids 38, 1203 (2009).
A. Zhang, X. Cao, F. Ming, and Z. F. Zhang, Appl. Ocean Res. 42, 24 (2013).
H. Wen, B. Ren, P. Dong, and Y. Wang, Appl. Ocean Res. 59, 366 (2016).
J. L. Cercos-Pita, Comput. Phys. Commun. 192, 295 (2015).
Q. Xiong, B. Li, and J. Xu, Comput. Phys. Commun. 184, 1701 (2013).
D. Winkler, M. Meister, M. Rezavand, and W. Rauch, Comput. Phys. Commun. 213, 165 (2017).
S. M. Longshaw, and B. D. Rogers, Adv. Eng. Softw. 83, 31 (2015).
S. Børve, M. Omang, and J. Trulsen, J. Comput. Phys. 208, 345 (2005).
G. Oger, M. Doring, B. Alessandrini, and P. Ferrant, J. Comput. Phys. 213, 803 (2006).
R. Vacondio, B. D. Rogers, P. K. Stansby, and P. Mignosa, Adv. Water Res. 58, 10 (2013).
R. Vacondio, B. D. Rogers, P. K. Stansby, P. Mignosa, and J. Feldman, Comput. Methods Appl. Mech. Eng. 256, 132 (2013).
R. Vacondio, B. D. Rogers, and P. K. Stansby, Int. J. Numer. Meth. Fluids 69, 1377 (2012).
D. A. Barcarolo, D. Le Touzé, G. Oger, and F. de Vuyst, J. Comput. Phys. 273, 640 (2014).
P. N. Sun, A. Colagrossi, S. Marrone, and A. M. Zhang, Comput. Methods Appl. Mech. Eng. 315, 25 (2017).
L. Chiron, G. Oger, M. de Leffe, and D. Le Touzé, J. Comput. Phys. 354, 552 (2018).
J. Feldman, and J. Bonet, Int. J. Numer. Meth. Eng. 72, 295 (2007).
Y. R. López, D. Roose, and C. Recarey Morfa, Comput. Mech. 51, 731 (2013).
S. Koshizuka, A. Nobe, and Y. Oka, Int. J. Numer. Meth. Fluids 26, 751 (1998).
E. S. Lee, C. Moulinec, R. Xu, D. Violeau, D. Laurence, and P. Stansby, J. Comput. Phys. 227, 8417 (2008).
A. Khayyer, H. Gotoh, and S. D. Shao, Coast. Eng. 55, 236 (2008).
H. Gotoh, A. Khayyer, H. Ikari, T. Arikawa, and K. Shimosako, Appl. Ocean Res. 46, 104 (2008).
A. Skillen, S. Lind, P. K. Stansby, and B. D. Rogers, Comput. Methods Appl. Mech. Eng. 265, 163 (2013).
M. Antuono, A. Colagrossi, S. Marrone, and D. Molteni, Comput. Phys. Commun. 181, 532 (2010).
M. Antuono, A. Colagrossi, and S. Marrone, Comput. Phys. Commun. 183, 2570 (2012).
J. P. Vila, Math. Model. Methods Appl. Sci. 9, 161 (1999).
S. I. Inutsuka, J. Comput. Phys. 179, 238 (2002).
J. J. Monaghan, J. Comput. Phys. 136, 298 (1997).
P. Omidvar, P. K. Stansby, and B. D. Rogers, Int. J. Numer. Meth. Fluids 72, 427 (2013).
P. K. Koukouvinis, J. S. Anagnostopoulos, and D. E. Papantonis, Int. J. Numer. Meth. Fluids 71, 1152 (2013).
L. Han, and X. Hu, J. Hydrodyn. 30, 62 (2018).
A. Rafiee, and K. P. Thiagarajan, Comput. Methods Appl. Mech. Eng. 198, 2785 (2009).
M. Liu, J. Shao, and H. Li, J. Hydrodyn. 25, 673 (2013).
F. R. Ming, A. M. Zhang, and X. Y. Cao, Acta Mech. Sin. 29, 241 (2013).
F. R. Ming, A. M. Zhang, and S. P. Wang, Int. J. Appl. Mech. 07, 1550032 (2015).
V. Mehra, and S. Chaturvedi, J. Comput. Phys. 212, 318 (2006).
A. M. Zhang, W. S. Yang, and X. L. Yao, Appl. Ocean Res. 34, 10 (2012).
M. B. Liu, Z. L. Zhang, and D. L. Feng, Comput. Mech. 60, 513 (2017).
P. W. Randles, and L. D. Libersky, Comput. Methods Appl. Mech. Eng. 139, 375 (1996).
M. B. Liu, G. R. Liu, Z. Zong, and K. Y. Lam, Comput. Fluids 32, 305 (2003).
D. L. Feng, M. B. Liu, H. Q. Li, and G. R. Liu, Comput. Fluids 86, 77 (2013).
M. B. Liu, G. R. Liu, K. Y. Lam, and Z. Zong, Shock Waves 12, 509 (2003).
M. B. Liu, G. R. Liu, and K. Y. Lam, Shock Waves 15, 21 (2006).
Z. L. Zhang, and M. B. Liu, Eng. Anal. Bound. Elem. 83, 141 (2017).
Z. L. Zhang, D. L. Feng, and M. B. Liu, J. Manuf. Proc. 35, 169 (2018).
Z. L. Zhang, T. Ma, M. B. Liu, and D. Feng, Int. J. Comput. Methods 16, 1846001 (2019).
A. Zhang, W. S. Yang, C. Huang, and F. Ming, Comput. Fluids 71, 169 (2013).
F. R. Ming, A. M. Zhang, Y. Z. Xue, and S. P. Wang, Ocean Eng. 117, 359 (2016).
P. Wang, A. M. Zhang, F. Ming, P. Sun, and H. Cheng, J. Fluid Mech. 860, 81 (2019).
S. Marrone, A. Di Mascio, and D. Le Touzé, J. Comput. Phys. 310, 161 (2016).
L. Chiron, S. Marrone, A. Di Mascio, and D. Le Touzé, J. Comput. Phys. 364, 111 (2018).
D. Hu, T. Long, Y. Xiao, X. Han, and Y. Gu, Comput. Methods Appl. Mech. Eng. 276, 266 (2014).
T. Long, D. Hu, D. Wan, C. Zhuang, and G. Yang, J. Comput. Phys. 350, 166 (2017).
Z. Li, J. Leduc, J. Nunez-Ramirez, A. Combescure, and J. C. Marongiu, Comput. Mech. 55, 697 (2015).
Q. Yang, V. Jones, and L. McCue, Ocean Eng. 55, 136 (2012).
K. Wu, D. Yang, and N. Wright, Comput. Struct. 177, 141 (2016).
L. C. Qiu, Ind. Eng. Chem. Res. 52, 11313 (2013).
Y. Tang, Q. Jiang, and C. Zhou, Appl. Math. Model. 62, 436 (2018).
X. Yang, and M. Liu, Commun. Comput. Phys. 22, 1015 (2017).
X. Yang, M. Liu, and S. Peng, Phys. Rev. E 90, 063011 (2014).
X. Yang, M. Liu, S. Peng, and C. Huang, Coast. Eng. 108, 56 (2016).
J. J. Monaghan, and J. C. Lattanzio, Astron. Astrophys. 149, 135 (1985).
A. Colagrossi, M. Antuono, and D. Le Touzé, Phys. Rev. E 79, 056701 (2009).
Z. L. Zhang, T. Ma, D. L. Feng, and M. B. Liu, Int. J. Comput. Methods 15, 1844004 (2018).
J. D. Anderson, Computational Fluid Dynamics: The Basics With Applications (McGraw Hill, New York, 2002).
H. U. Mair, Shock Vib. 6, 81 (1999).
R. Car, and M. Parrinello, Phys. Rev. Lett. 55, 2471 (1985).
H. J. C. Berendsen, J. P. M. Postma, W. F. van Gunsteren, A. DiNola, and J. R. Haak, J. Chem. Phys. 81, 3684 (1984).
S. Yamamoto, Y. Maruyama, and S. Hyodo, J. Chem. Phys. 116, 5842 (2002).
R. D. Groot, and P. B. Warren, J. Chem. Phys. 107, 4423 (1997).
M. S. Shadloo, A. Zainali, M. Yildiz, and A. Suleman, Int. J. Numer. Meth. Eng. 89, 939 (2012).
D. H. Zhang, Y. X. Shi, C. Huang, Y. L. Si, and W. Li, J. Mar. Sci. Technol. 24, 73 (2019).
P. N. Sun, A. Colagrossi, S. Marrone, M. Antuono, and A. M. Zhang, Comput. Phys. Commun. 224, 63 (2018).
F. Macia, M. Antuono, L. M. Gonzalez, and A. Colagrossi, Prog. Theor. Phys. 125, 1091 (2011).
S. Adami, X. Y. Hu, and N. A. Adams, J. Comput. Phys. 231, 7057 (2012).
J. J. Monaghan, and J. B. Kajtar, Comput. Phys. Commun. 180, 1811 (2009).
B. D. Rogers, and R. A. Dalrymple, SPH Modeling of Tsunami Waves (World scientific, Singapore, 2008).
S. Kulasegaram, J. Bonet, R. W. Lewis, and M. Profit, Comput. Mech. 33, 316 (2004).
M. Ferrand, D. R. Laurence, B. D. Rogers, D. Violeau, and C. Kassiotis, Int. J. Numer. Meth. Fluids 71, 446 (2013).
A. Amicarelli, G. Agate, and R. Guandalini, Int. J. Numer. Meth. Eng. 95, 419 (2013).
A. Leroy, D. Violeau, M. Ferrand, and C. Kassiotis, J. Comput. Phys. 261, 106 (2014).
Z. Chen, Z. Zong, M. B. Liu, L. Zou, H. T. Li, and C. Shu, J. Comput. Phys. 283, 169 (2015).
S. Adami, X. Y. Hu, and N. A. Adams, J. Comput. Phys. 229, 5011 (2010).
N. Grenier, M. Antuono, A. Colagrossi, D. Le Touzé, and B. Alessandrini, J. Comput. Phys. 228, 8380 (2009).
T. Belytschko, Y. Krongauz, J. Dolbow, and C. Gerlach, Int. J. Numer. Meth. Eng. 43, 785 (2015).
M. B. Liu, J. R. Shao, and J. Z. Chang, Sci. China Technol. Sci. 55, 244 (2012).
Z. Li, J. Leduc, A. Combescure, and F. Leboeuf, Comput. Fluids 103, 6 (2014).
G. Fourey, G. Oger, D. Touzé, and B. Alessandrini, in IOP Conference Series: Materials Science and Engineering 10 (IOP Publishing, Bristol, 2010), p. 012041.
P. H. L. Groenenboom, and B. K. Cartwright, J. Hydraul. Res. 48, 61 (2010).
T. Belytschko, W. K. Liu, and B. Moran, Nonlinear Finite Elements for Continua and Structures (John Wiley & Sons Inc., Hoboken, 2014).
S. W. Attaway, M. W. Heinstein, and J. W. Swegle, Nucl. Eng. Des. 150, 199 (1994).
Z. Zhang, H. Qiang, and W. Gao, Eng. Struct. 33, 255 (2011).
T. De Vuyst, R. Vignjevic, and J. C. Campbell, Int. J. Impact Eng. 31, 1054 (2005).
E. A. Fadlun, R. Verzicco, P. Orlandi, and J. Mohd-Yusof, J. Comput. Phys. 161, 35 (2000).
R. Mittal, and G. Iaccarino, Annu. Rev. Fluid Mech. 37, 239 (2005).
M. Neuhauser, and J.-C. Marongiu, in Proceedings of 9th SPHERIC International Workshop (SPH European Research Interest Community, Paris, 2014).
E. Napoli, M. De Marchis, C. Gianguzzi, B. Milici, and A. Monteleone, Comput. Methods Appl. Mech. Eng. 310, 674 (2016).
F. Chen, H. Qiang, and W. Gao, Comput. Chem. Eng. 77, 135 (2015).
F. Chen, H. Qiang, H. Zhang, and W. Gao, Int. J. Numer. Meth. Eng. 109, 73 (2017).
D. Zhou, and R. H. Wagoner, J. Mater. Proc. Tech. 50, 1 (1995).
K.-I. Tsubota, S. Wada, and T. Yamaguchi, J. Mater. Proc. Technol. 1, 159 (2006).
S. M. Hosseini, and J. J. Feng, Chem. Eng. Sci. 64, 4488 (2009).
P. W. Cleary, Miner. Eng. 73, 85 (2015).
B. Ren, Z. Jin, R. Gao, Y. Wang, and Z. Xu, J. Waterw. Port Coast. Ocean Eng. 140, 04014022 (2014).
M. Robinson, M. Ramaioli, and S. Luding, Int. J. Multiphase Flow 59, 121 (2014).
A. M. Zhang, F. R. Ming, and S. P. Wang, Appl. Ocean Res. 43, 223 (2013).
K. Gong, S. Shao, H. Liu, B. Wang, and S. K. Tan, J. Fluids Struct. 65, 155 (2016).
X. Liu, H. Xu, S. Shao, and P. Lin, Comput. Fluids 71, 113 (2013).
L. Wang, F. Xu, Y. Yang, and J. Wang, Eng. Anal. Bound. Elem. 100, 140 (2019).
T. Ye, D. Pan, C. Huang, M. Liu, Phys. Fluids 31 (2019).
J. Shao, S. Li, Z. Li, and M. Liu, Eng. Comput. 32, 1172 (2015).
H. Akyildız, and U. N. Erdem, Ocean Eng. 33, 2135 (2006).
O. M. Faltinsen, O. F. Rognebakke, I. A. Lukovsky, and A. N. Timokha, J. Fluid Mech. 407, 201 (2000).
M. Greenhow, and S. Moyo, Philos. Trans. R. Soc. London. Ser. A-Math. Phys. Eng. Sci. 355, 551 (1997).
P. Lin, Comput. Fluids 36, 549 (2007).
P. A. Tyvand, and T. Miloh, J. Fluid Mech. 286, 67 (1995).
G. Oger, L. Brosset, P. M. Guilcher, E. Jacquin, J. B. Deuff, and D. L. Touzé, Int. J. Offshore Polar Eng. 20, 181 (2010).
C. Antoci, M. Gallati, and S. Sibilla, Comput. Struct. 85, 879 (2007).
S. C. Hwang, A. Khayyer, H. Gotoh, and J. C. Park, J. Fluids Struct. 50, 497 (2014).
A. Khayyer, H. Gotoh, H. Falahaty, and Y. Shimizu, Comput. Phys. Commun. 232, 139 (2018).
Y. M. Scolan, J. Sound Vib. 277, 163 (2004).
J. C. Liao, D. N. Beal, G. V. Lauder, and M. S. Triantafyllou, Science 302, 1566 (2003).
T. Y. Wu, Annu. Rev. Fluid Mech. 43, 25 (2011).
S. Vogel, J. Exp. Bot. 40, 941 (1989).
F. Gosselin, E. de Langre, and B. A. Machado-Almeida, J. Fluid Mech. 650, 319 (2010).
S. Alben, M. Shelley, and J. Zhang, Nature 420, 479 (2002).
S. Alben, M. Shelley, and J. Zhang, Phys. Fluids 16, 1694 (2004).
W. Hu, Q. Tian, and H. Hu, Nonlin. Dyn. 75, 653 (2014).
W. Hu, Q. Tian, and H. Y. Hu, Sci. China-Phys. Mech. Astron. 61, 044711 (2018).
L. A. Miller, A. Santhanakrishnan, S. Jones, C. Hamlet, K. Mertens, and L. Zhu, J. Exp. Biol. 215, 2716 (2012).
L. Zhu, J. Fluid Mech. 587, 217 (2007).
R. Y. Yakoub, and A. A. Shabana, J. Mech. Des. 123, 614 (2001).
R. Glowinski, T. W. Pan, T. I. Hesla, and D. D. Joseph, Int. J. Multiphase Flow 25, 755 (1999).
B. K. Mishra, and R. K. Rajamani, Appl. Math. Model. 16, 598 (1992).
S. B. Pillapakkam, and P. Singh, J. Comput. Phys. 174, 552 (2001).
G. J. Wagner, S. Ghosal, and W. K. Liu, Int. J. Numer. Meth. Engng. 56, 1261 (2003).
N. Tofighi, M. Ozbulut, A. Rahmat, J. J. Feng, and M. Yildiz, J. Comput. Phys. 297, 207 (2015).
M. R. Hashemi, R. Fatehi, and M. T. Manzari, Int. J. Non-Lin. Mech. 47, 626 (2012).
X. Bian, and M. Ellero, Comput. Phys. Commun. 185, 53 (2014).
S. Turek, D. Wan, and L. S. Rivkind, Lect. Notes Comput. Sci. Eng. 35, 37 (2003).
R. Glowinski, T. W. Pan, T. I. Hesla, D. D. Joseph, and J. Périaux, J. Comput. Phys. 169, 363 (2001).
G. He, G. Jin, and Y. Yang, Annu. Rev. Fluid Mech. 49, 51 (2017).
Z. L. Zhang, K. Walayat, C. Huang, J. Z. Chang, and M. B. Liu, Int. J. Heat Mass Transfer 128, 1245 (2019).
J. W. Swegle, and S. W. Attaway, Comput. Mech. 17, 151 (1995).
Y. Wang, H. G. Beom, M. Sun, and S. Lin, Int. J. Impact Eng. 38, 51 (2011).
S. A. A. A. Mousavi, and S. T. S. Al-Hassani, Mater. Des. 29, 1 (2008).
S. R. Reid, Int. J. Mech. Sci. 16, 399 (1974).
G. R. Cowan, O. R. Bergmann, and A. H. Holtzman, Metall. Mater. Trans. B 2, 3145 (1971).
M. Katayama, A. Takeba, S. Toda, and S. Kibe, Int. J. Impact Eng. 23, 443 (1999).
M. N. Raftenberg, in Twelfth Army Symposium on Solid Mechanics Proceedings, Watertown, USA November 4–7, 1991, edited by S. C. Chou (1992).
J. J. Monaghan, J. Comput. Phys. 159, 290 (2000).
N. Tsuruta, A. Khayyer, and H. Gotoh, Comput. Fluids 82, 158 (2013).
R. Xu, P. Stansby, and D. Laurence, J. Comput. Phys. 228, 6703 (2009).
S. J. Lind, R. Xu, P. K. Stansby, and B. D. Rogers, J. Comput. Phys. 231, 1499 (2012).
P. Omidvar, P. K. Stansby, and B. D. Rogers, Wave Body Interaction in 2D Using Smoothed Particle Hydrodynamics (SPH) With Variable Particle Mass (John Wiley & Sons, Hoboken, 2012).
S. Kitsionas, and A. P. Whitworth, Mon. Not. R. Astron. Soc. 330, 129 (2002).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Liu, M., Zhang, Z. Smoothed particle hydrodynamics (SPH) for modeling fluid-structure interactions. Sci. China Phys. Mech. Astron. 62, 984701 (2019). https://doi.org/10.1007/s11433-018-9357-0
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11433-018-9357-0