A new approach to fluid–structure interaction within graphics hardware accelerated smooth particle hydrodynamics considering heterogeneous particle size distribution

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A corrective smooth particle method (CSPM) within smooth particle hydrodynamics (SPH) is used to study the deformation of an aircraft structure under high-velocity water-ditching impact load. The CSPM-SPH method features a new approach for the prediction of two-way fluid–structure interaction coupling. Results indicate that the implementation is well suited for modeling the deformation of structures under high-velocity impact into water as evident from the predicted stress and strain localizations in the aircraft structure as well as the integrity of the impacted interfaces, which show no artificial particle penetrations. To reduce the simulation time, a heterogeneous particle size distribution over a complex three-dimensional geometry is used. The variable particle size is achieved from a finite element mesh with variable element size and, as a result, variable nodal (i.e., SPH particle) spacing. To further accelerate the simulations, the SPH code is ported to a graphics processing unit using the OpenACC standard. The implementation and simulation results are described and discussed in this paper.

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  1. 1.

    Malan A, Oxtoby O (2013) An accelerated, fully-coupled, parallel 3d hybrid finite-volume fluid–structure interaction scheme. Comput Methods Appl Mech Eng 253:426–438

  2. 2.

    Hesch C, Gil A, Carreno AA, Bonet J (2012) On continuum immersed strategies for fluid–structure interaction. Comput Methods Appl Mech Eng 247:51–64

  3. 3.

    Koh HM, Kim JK, Park JH (1998) Fluid–structure interaction analysis of 3-D rectangular tanks by a variationally coupled BEM–FEM and comparison with test results. Earthq Eng Struct Dyn 27:109–124

  4. 4.

    Tong Z, Zhang Y, Zhang Z, Hua H (2007) Dynamic behavior and sound transmission analysis of a fluid–structure coupled system using the direct-BEM/FEM. J Sound Vib 299:645–655

  5. 5.

    Czygan O, Von Estorff O (2002) Fluid–structure interaction by coupling BEM and nonlinear FEM. Eng Anal Bound Elem 26:773–779

  6. 6.

    Soares D Jr, Von Estorff O, Mansur W (2005) Efficient non-linear solid–fluid interaction analysis by an iterative BEM/FEM coupling. Int J Numer Methods Eng 64:1416–1431

  7. 7.

    He Z, Liu G, Zhong Z, Zhang G, Cheng A (2011) A coupled ES-FEM/BEM method for fluid–structure interaction problems. Eng Anal Bound Elem 35:140–147

  8. 8.

    He T, Zhou D, Bao Y (2012) Combined interface boundary condition method for fluid–rigid body interaction. Comput Methods Appl Mech Eng 223:81–102

  9. 9.

    Heimbs S (2011) Computational methods for bird strike simulations: a review. Comput Struct 89:2093–2112

  10. 10.

    Georgiadis S, Gunnion AJ, Thomson RS, Cartwright BK (2008) Bird-strike simulation for certification of the Boeing 787 composite moveable trailing edge. Compos Struct 86:258–268

  11. 11.

    Smojver I, Ivančević D (2011) Bird strike damage analysis in aircraft structures using Abaqus/Explicit and coupled Eulerian Lagrangian approach. Compos Sci Technol 71:489–498

  12. 12.

    Smojver I, Ivančević D (2010) Numerical simulation of bird strike damage prediction in airplane flap structure. Compos Struct 92:2016–2026

  13. 13.

    Lucy LB (1977) A numerical approach to the testing of the fission hypothesis. Astron J 82:1013–1024

  14. 14.

    Gingold RA, Monaghan JJ (1977) Smoothed particle hydrodynamics: theory and application to non-spherical stars. Mon Not R Astron Soc 181:375–389

  15. 15.

    Monaghan J, Kocharyan A (1995) SPH simulation of multi-phase flow. Comput Phys Commun 87:225–235

  16. 16.

    Chen Z, Zong Z, Liu M, Zou L, Li H, Shu C (2015) An SPH model for multiphase flows with complex interfaces and large density differences. J Comput Phys 283:169–188

  17. 17.

    Tartakovsky AM, Panchenko A (2016) Pairwise force smoothed particle hydrodynamics model for multiphase flow: surface tension and contact line dynamics. J Comput Phys 305:1119–1146

  18. 18.

    Ming FR, Sun PN, Zhang AM (2017) Numerical investigation of rising bubbles bursting at a free surface through a multiphase SPH model. Meccanica 52:2665–2684

  19. 19.

    Tong M, Browne DJ (2014) An incompressible multi-phase smoothed particle hydrodynamics (SPH) method for modelling thermocapillary flow. Int J Heat Mass Transf 73:284–292

  20. 20.

    Morris JP, Fox PJ, Zhu Y (1997) Modeling low Reynolds number incompressible flows using SPH. J Comput Phys 136:214–226

  21. 21.

    Monaghan JJ (1994) Simulating free surface flows with SPH. J Comput Phys 110:399–406

  22. 22.

    Peng C, Xu G, Wu W, H-s Yu, Wang C (2017) Multiphase SPH modeling of free surface flow in porous media with variable porosity. Comput Geotech 81:239–248

  23. 23.

    Violeau D, Rogers BD (2016) Smoothed particle hydrodynamics (SPH) for free-surface flows: past, present and future. J Hydraul Res 54:1–26

  24. 24.

    Bankole AO, Dumbser M, Iske A, Rung T (2017) A meshfree semi-implicit smoothed particle hydrodynamics method for free surface flow. In: Griebel M, Schweitzer MA (eds) Meshfree methods for partial differential equations VIII. Springer, Berlin, pp 35–52

  25. 25.

    Abdelrazek AM, Kimura I, Shimizu Y (2016) Simulation of three-dimensional rapid free-surface granular flow past different types of obstructions using the SPH method. J Glaciol 62:335–347

  26. 26.

    Benz W, Asphaug E (1993) Explicit 3D continuum fracture modeling with smooth particle hydrodynamics. Lunar and planetary science conference

  27. 27.

    Benz W, Asphaug E (1995) Simulations of brittle solids using smooth particle hydrodynamics. Comput Phys Commun 87:253–265

  28. 28.

    Das R, Cleary P (2013) A mesh-free approach for fracture modelling of gravity dams under earthquake. Int J Fract 179:9–33

  29. 29.

    Monaghan J (2012) Smoothed particle hydrodynamics and its diverse applications. Annu Rev Fluid Mech 44:323–346

  30. 30.

    Caleyron F, Combescure A, Faucher V, Potapov S (2012) Dynamic simulation of damage–fracture transition in smoothed particles hydrodynamics shells. Int J Numer Methods Eng 90:707–738

  31. 31.

    Eghtesad A, Shafiei AR, Mahzoon M (2012) Study of dynamic behavior of ceramic-metal FGM under high velocity impact conditions using CSPM method. Appl Math Model 36:2724–2738

  32. 32.

    Eghtesad A, Shafiei AR, Mahzoon M (2011) Predicting fracture and fragmentation in ceramic using a thermo-mechanical basis. Theor Appl Fract Mech 56:68–78

  33. 33.

    Mehra V, Sijoy C, Mishra V, Chaturvedi S (2012) Tensile instability and artificial stresses in impact problems in SPH. In: Journal of physics: conference series. IOP Publishing, pp 012102

  34. 34.

    Johnson GR, Petersen EH, Stryk RA (1993) Incorporation of an SPH option into the EPIC code for a wide range of high velocity impact computations. Int J Impact Eng 14:385–394

  35. 35.

    Randles P, Libersky L (2000) Normalized SPH with stress points. Int J Numer Methods Eng 48:1445–1462

  36. 36.

    Chen J, Beraun J, Jih C (1999) An improvement for tensile instability in smoothed particle hydrodynamics. Comput Mech 23:279–287

  37. 37.

    Gao R, Ren B, Wang G, Wang Y (2012) Numerical modelling of regular wave slamming on subface of open-piled structures with the corrected SPH method. Appl Ocean Res 34:173–186

  38. 38.

    Xu F, Zhao Y, Yan R, Furukawa T (2013) Multidimensional discontinuous SPH method and its application to metal penetration analysis. Int J Numer Methods Eng 93:1125–1146

  39. 39.

    Korzilius S, Schilders W, Anthonissen M (2016) An improved CSPM approach for accurate second-derivative approximations with SPH. J Appl Math Phys 5:168

  40. 40.

    Eghtesad A, Shafiei A, Mahzoon M (2012) Study of dynamic behavior of ceramic–metal FGM under high velocity impact conditions using CSPM method. Appl Math Model 36:2724–2738

  41. 41.

    Rabczuk T, Gracie R, Song J-H, Belytschko T (2010) Immersed particle method for fluid–structure interaction. Int J Numer Methods Eng 22:48

  42. 42.

    Gong K, Shao S, Liu H, Wang B, Tan S-K (2016) Two-phase SPH simulation of fluid–structure interactions. J Fluids Struct 65:155–179

  43. 43.

    Dai Z, Huang Y, Cheng H, Xu Q (2017) SPH model for fluid–structure interaction and its application to debris flow impact estimation. Landslides 14:917–928

  44. 44.

    Stasch J, Avci B, Wriggers P (2016) Numerical simulation of fluid–structure interaction problems by a coupled SPH–FEM approach. PAMM 16:491–492

  45. 45.

    Liu X, Shao S, Lin P, Tan S (2016) 2D numerical ISPH wave tank for complex fluid–structure coupling problems. Int J Offshore Polar Eng 26:26–32

  46. 46.

    Groenenboom P, Siemann M (2016) Fluid-structure interaction by the mixed SPH-FE method with application to aircraft ditching. Int J Multiphys 9:249–265

  47. 47.

    Zhu B, Gu L, Peng X, Zhou Z (2010) A point-based simulation framework for minimally invasive surgery. In: International symposium on biomedical simulation. Springer, Berlin, pp 130–138

  48. 48.

    Pan W, Li D, Tartakovsky AM, Ahzi S, Khraisheh M, Khaleel M (2013) A new smoothed particle hydrodynamics non-Newtonian model for friction stir welding: process modeling and simulation of microstructure evolution in a magnesium alloy. Int J Plast 48:189–204

  49. 49.

    Ma A, Hartmaier A (2016) A crystal plasticity smooth-particle hydrodynamics approach and its application to equal-channel angular pressing simulation. Model Simul Mater Sci Eng 24:085011

  50. 50.

    Liu G-R, Liu MB (2003) Smoothed particle hydrodynamics: a meshfree particle method. World Scientific, Singapore

  51. 51.

    Monaghan J, Gingold R (1983) Shock simulation by the particle method SPH. J Comput Phys 52:374–389

  52. 52.

    Rice W, Paardekooper S-J, Forgan D, Armitage P (2014) Convergence of simulations of self-gravitating accretion discs-II. Sensitivity to the implementation of radiative cooling and artificial viscosity. Mon Not R Astron Soc 438:1593–1602

  53. 53.

    Li X, Zhang T, Zhang Y, Liu G (2014) Artificial viscosity in smoothed particle hydrodynamics simulation of sound interference. In: Proceedings of meetings on acoustics 168ASA ASA, p 040005

  54. 54.

    Li X, Zhang T, Zhang YO (2015) Time domain simulation of sound waves using smoothed particle hydrodynamics algorithm with artificial viscosity. Algorithms 8:321–335

  55. 55.

    Monaghan J (1989) On the problem of penetration in particle methods. J Comput Phys 82:1–15

  56. 56.

    Takahashi T, Fujishiro I, Nishita T (2014) A velocity correcting method for volume preserving viscoelastic fluids. In: Proceedings of the computer graphics international

  57. 57.

    Maindl TI (2013) SPH for simulating impacts and collisions. University of Vienna, Vienna

  58. 58.

    Deb D, Pramanik R (2013) Failure process of brittle rock using smoothed particle hydrodynamics. J Eng Mech 139:1551–1565

  59. 59.

    Monaghan JJ (1992) Smoothed particle hydrodynamics. Annu Rev Astron Astrophys 30:543–574

  60. 60.

    Imaeda Y, S-i Inutsuka (2002) Shear flows in smoothed particle hydrodynamics. Astrophys J 569:501

  61. 61.

    Paiva A, Petronetto F, Lewiner T, Tavares G (2009) Particle-based viscoplastic fluid/solid simulation. Comput Aided Des 41:306–314

  62. 62.

    Crespo AJC, Domínguez JM, Rogers BD, Gómez-Gesteira M, Longshaw S, Canelas R, Vacondio R, Barreiro A, García-Feal O (2015) DualSPHysics: open-source parallel CFD solver based on smoothed particle hydrodynamics (SPH). Comput Phys Commun 187:204–216

  63. 63.

    Paredes RJ, Imas L (2014) Application of multiphase SPH to fluid structure interaction problems. In: 9th international SPHERIC workshop. CNAM Paris, France

  64. 64.

    Dyka C, Ingel R (1995) An approach for tension instability in smoothed particle hydrodynamics (SPH). Comput Struct 57:573–580

  65. 65.

    Monaghan JJ (2000) SPH without a tensile instability. J Comput Phys 159:290–311

  66. 66.

    Korzilius S, Schilders W, Anthonissen M (2015) An improved CSPM approximation for multi-dimensional second-order derivatives. In: Proceedings of the 10th international SPHERIC workshop

  67. 67.

    Chen J, Beraun J, Carney T (1999) A corrective smoothed particle method for boundary value problems in heat conduction. Int J Numer Methods Eng 46:231–252

  68. 68.

    Crespo AJC (2008) Application of the smoothed particle hydrodynamics model SPHysics to free surface hydrodynamics. Universidade de Vigo, Vigo

  69. 69.

    Davison L (2008) Fundamentals of shock wave propagation in solids. Springer, Berlin

  70. 70.

    Ben-Dor G, Igra O, Elperin T (2000) Handbook of shock waves, three volume set. Academic Press, New York

  71. 71.

    Zharkov VN, Kalinin VA, Tybulewicz A (1971) Equations of state for solids at high pressures and temperatures. Springer, Berlin

  72. 72.

    Raizer YP (2002) Physics of shock waves and high-temperature hydrodynamic phenomena. Courier Corporation, North Chelmsford

  73. 73.

    Goda T (2017) Numerical study on seepage-induced failure of Caisson type breakwaters using a stabilized ISPH. TVVR 17/5007

  74. 74.

    Zheng X, Shao S, Khayyer A, Duan W, Ma Q, Liao K (2017) Corrected first-order derivative ISPH in water wave simulations. Coast Eng J 59:1750010

  75. 75.

    Pahar G, Dhar A (2017) Coupled incompressible smoothed particle hydrodynamics model for continuum-based modelling sediment transport. Adv Water Resour 102:84–98

  76. 76.

    Johnson GR, Cook WH (1983) A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. In: Proceedings of the 7th international symposium on ballistics. The Hague, The Netherlands, pp 541–547

  77. 77.

    SolidWorks I (2002) Solidworks Corporation, Concord

  78. 78.

    Amini Y, Emdad H, Farid M (2011) A new model to solve fluid–hypo-elastic solid interaction using the smoothed particle hydrodynamics (SPH) method. Eur J Mech B Fluids 30:184–194

  79. 79.

    Yang Q, Jones V, McCue L (2012) Free-surface flow interactions with deformable structures using an SPH-FEM model. Ocean Eng 55:136–147

  80. 80.

    Rafiee A, Thiagarajan KP (2009) An SPH projection method for simulating fluid–hypoelastic structure interaction. Comput Methods Appl Mech Eng 198:2785–2795

  81. 81.


  82. 82.


  83. 83.


  84. 84.

    CAPS OpenACC Compiler (2012) The fastest way to many-core programming.

  85. 85.

    OpenACC (2012) OpenACC accelerator directives.

  86. 86.

    Lebacki B, Wolfe M, Miles D (2012) The pgi fortran and c99 openacc compilers. Cray User Group, Redmond

  87. 87.

    Using OpenACC with MPI Tutorial—PGI Compilers.

  88. 88.

    Wienke S, Springer P, Terboven C, an Mey D (2012) OpenACC—first experiences with real-world applications. In: European conference on parallel processing. Springer, Berlin, pp 859–870

  89. 89.

    Herdman J, Gaudin W, McIntosh-Smith S, Boulton M, Beckingsale DA, Mallinson A, Jarvis SA (2012) Accelerating hydrocodes with OpenACC, OpenCL and CUDA. In: High performance computing, networking, storage and analysis (SCC), 2012 SC companion. IEEE, pp 465–471

  90. 90.

    Hart A, Ansaloni R, Gray A (2012) Porting and scaling OpenACC applications on massively-parallel, GPU-accelerated supercomputers. Eur Phys J Spec Top 210:5–16

  91. 91.

    Farber R (2016) Parallel programming with OpenACC. Newnes, London

  92. 92.

    Hiermaier S, Könke D, Stilp A, Thoma K (1997) Computational simulation of the hypervelocity impact of Al-spheres on thin plates of different materials. Int J Impact Eng 20:363–374

  93. 93.

  94. 94.

    Henderson A, Ahrens J, Law C (2004) The ParaView guide. Kitware, Clifton Park

  95. 95.

    Knezevic M, Crapps J, Beyerlein IJ, Coughlin DR, Clarke KD, McCabe RJ (2016) Anisotropic modeling of structural components using embedded crystal plasticity constructive laws within finite elements. Int J Mech Sci 105:227–238

  96. 96.

    Knezevic M, Kalidindi SR, Fullwood D (2008) Computationally efficient database and spectral interpolation for fully plastic Taylor-type crystal plasticity calculations of face-centered cubic polycrystals. Int J Plast 24:1264–1276

  97. 97.

    Knezevic M, McCabe RJ, Tomé CN, Lebensohn RA, Chen SR, Cady CM, Gray Iii GT, Mihaila B (2013) Modeling mechanical response and texture evolution of \(\alpha \)-uranium as a function of strain rate and temperature using polycrystal plasticity. Int J Plast 43:70–84

  98. 98.

    Knezevic M, Kalidindi SR (2017) Crystal plasticity modeling of microstructure evolution and mechanical fields during processing of metals using spectral databases. JOM 69:830–838

  99. 99.

    Zecevic M, Beyerlein IJ, McCabe RJ, McWilliams BA, Knezevic M (2016) Transitioning rate sensitivities across multiple length scales: microstructure–property relationships in the Taylor cylinder impact test on zirconium. Int J Plast 84:138–159

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This work is based upon a project supported by the US National Science Foundation under grant no. CMMI-1650641. The authors gratefully acknowledge this support.

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Correspondence to Marko Knezevic.

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Supplementary material 1 (mp4 4278 KB)

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Supplementary material 1 (mp4 4278 KB)

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Supplementary material 3 (mp4 6106 KB)


Appendix A

The % time spent in subroutines ordered from top to bottom as identified using PGPROF:

  1. 1.

    Subroutine Direct_find (neighbor search subroutine, 38% of total execution time)

  2. 2.

    Subroutine Int_Force (force calculation subroutine, 23% of total execution time)

  3. 3.

    Subroutine Time_Intg (time integration subroutine, 12% of total execution time)

  4. 4.

    Main program SPH (main program, 9% of total execution time)

  5. 5.

    Subroutine Cont_Density (continuity subroutine including the CSPM modification, 8% of total execution time)

  6. 6.

    Subroutine H_Upgrade (update smoothing length subroutine, 5% of total execution time)

  7. 7.

    Other subroutines (5% of total execution time)

In this work, subroutines 1–5 were ported to GPU.

Appendix B

  1. (i)

    Neighbor particles search within computational domain:

  1. (ii)

    Force calculation:

  1. (iii)

    Time integration:

  1. (iv)


  1. (v)

    SPH main program:


A loop from the continuity subroutine is presented below to better illustrate how the OpenACC data and kernels directives can be used to run the loop in parallel on GPU. The “reduction” and “private” clauses ensure that there are no race conditions while accessing the summation over the scalar “vcc” using the GPU threads. Additionally, “copyin” clauses show the arrays data input from CPU (host) to the device (GPU).


In above loop, “x”, “vx”, “rho”, “drhodt”, “pair_i”, “pair_j”, “niac”, “dwdx”, and “dim” represent particle position, velocity, density, time rate of density, neighbor particle “i” interacting with particle “j”, neighbor particle “j” interacting with particle “i”, gradient of kernel function, total number of interacting pairs, and domain dimension, respectively.

Supplementary material

Movies showing the evolution of pressure, equivalent plastic strain, and von Mises stress during aircraft water ditching at an angle of \(60{^{\circ }}\).

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Eghtesad, A., Knezevic, M. A new approach to fluid–structure interaction within graphics hardware accelerated smooth particle hydrodynamics considering heterogeneous particle size distribution. Comp. Part. Mech. 5, 387–409 (2018) doi:10.1007/s40571-017-0176-1

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  • Smooth particle hydrodynamics
  • Heterogeneous particle size distribution
  • Fluid–structure interaction
  • Graphics processing unit
  • OpenACC