Combined SPH-DEM modeling of solid-fluid interactions

Document Type : Research Paper


1 Faculty of Engineering, Tarbiat Modares University, Jalal Ale Ahmad Highway, P.O. Box 14115-143, Tehran, Iran

2 Department of Civil and Environmental Engineering, Tarbiat Modares University, Jalal Ale Ahmad Highway, P.O. Box 14115-397, Tehran, Iran



Evaluation of Solid-Fluid interaction is of high significance in all engineering fields. In this paper, the Smoothed Particle Hydrodynamics (SPH) and the Discrete Element Method (DEM) were employed to simulate solids and fluids, respectively. As for the simulation of water behavior, first, a single-phase “dam break” experiment is modeled by the SPH. In this model, variable smoothing length and an almost novel boundary method were utilized which resulted in a tremendous boost in its resemblance to the experiment. To couple these methods (SPH and DEM), three approaches were proposed and validated against a famous experimental test named “dam break with an elastic gate test”. Finally, to be sure of the correctness of these approaches, an elastic plate under a water column in the hydrostatic condition was simulated and the error was 2 percent in comparison with the analytical solution. In pursuit of having short run-times, parallel computing on GPU (CUDA) was employed, and a robust nearest neighbor search (NNS) algorithm was modified and developed.


  1. Krevor SCM, Pini R, Li B, Benson SM. Capillary heterogeneity trapping of CO2 in a sandstone rock at reservoir conditions. Geophysical Research Letters 2011; 38(15). doi: 10.1029/2011gl048239.
  2. Fakhimi A, Lanari M. DEM–SPH simulation of rock blasting. Computers and Geotechnics 2014; 55: 158-164. doi:
  3. Wu K, Yang D, Wright N. A coupled SPH-DEM model for fluid-structure interaction problems with free-surface flow and structural failure. Computers and Structures 2016; 177: 141-161. doi:
  4. Liang Q. Flood simulation using a well-balanced shallow flow model. Journal of hydraulic engineering 2010; 136(9): 669-675.
  5. Gong Gb, Zha Xx. DEM simulation of liquefaction for cohesionless media at grain scale. Journal of Central South University 2012; 19(9): 2643-2649. doi: 10.1007/s11771-012-1322-9.
  6. Müller M, Schirm S, Teschner M. Interactive blood simulation for virtual surgery based on smoothed particle hydrodynamics. Technology and Health Care 2004; 12(1): 25-31.
  7. Liu Mb, Huang C, Zhang Am. Modelling incompressible flows and fluid-structure interaction problems with smoothed particle hydrodynamics: Briefing on the 2017 SPHERIC Beijing International Workshop. Journal of Hydrodynamics 2018; 30(1): 34-37. doi: 10.1007/s42241-018-0003-z.
  8. Sadrnejad S, Ghasemzadeh H, Taheri E. Multiscale multiphysic mixed geomechanical model in deformable porous media. International Journal for Multiscale Computational Engineering 2014; 12(6).
  9. Taheri E, Sadrnejad S, Ghasemzadeh H. Multiscale geomechanical model for a deformable oil reservoir with surrounding rock effects. International journal for multiscale computational engineering 2015; 13(6).
  10. Ghoreishian Amiri SA, Sadrnejad SA, Ghasemzadeh H. A hybrid numerical model for multiphase fluid flow in a deformable porous medium. Applied Mathematical Modelling 2017; 45: 881-899. doi:
  11. Ghoreishian Amiri SA, Taheri E, Lavasan AA. A hybrid finite element model for non-isothermal two-phase flow in deformable porous media. Computers and Geotechnics 2021; 135: 104199. doi:
  12. Oger G, Doring M, Alessandrini B, Ferrant P. Twodimensional SPH simulations of wedge water entries. Journal of Computational Physics 2006; 213(2): 803-822. doi:
  13. Vandamme J, Zou Q, Reeve DE. Modeling Floating Object Entry and Exit Using Smoothed Particle Hydrodynamics. Journal of Waterway, Port, Coastal, and Ocean Engineering 2011; 137(5): 213-224. doi:10.1061/(ASCE)WW.1943-5460.0000086.
  14. Tang Y, Jiang Q, Zhou C. A Lagrangian-based SPH-DEM model for fluid–solid interaction with free surface flow in two dimensions. Applied Mathematical Modelling 2018; 62: 436-460. doi:
  15. Ren B, Jin Z, Gao R,Wang Yx, Xu Zl. SPH-DEM modeling of the hydraulic stability of 2D blocks on a slope. Journal of Waterway, Port, Coastal, and Ocean Engineering 2013; 140(6): 04014022.
  16. Zhu X, Faltinsen OM, Hu C.Water entry and exit of a horizontal circular cylinder. Journal of Offshore Mechanics and Arctic Engineering 2007; 129(4): 253–264.
  17. Tan H, Chen S. A hybrid DEM-SPH model for deformable landslide and its generated surge waves. Advances in Water Resources 2017; 108: 256-276. doi:
  18. Antoci C, Gallati M, Sibilla S. Numerical simulation of fluid–structure interaction by SPH. Computers and Structures 2007; 85(11): 879-890. doi:
  19. Liu Mb, Shao Jr, Li Hq. Numerical simulation of hydroelastic problems with smoothed particle hydrodynamics method. Journal of Hydrodynamics 2013; 25(5): 673-682. doi: 10.1016/S1001-6058(13)60412-6.
  20. Zhang G, Wang S, Sui Z, Sun L, Zhang Z, Zong Z. Coupling of SPH with smoothed point interpolation method for violent fluid-structure interaction problems. Engineering Analysis with Boundary Elements 2019; 103: 1-10. doi:
  21. Cundall PA, Strack ODL. A discrete numerical model for granular assemblies. Géotechnique 1979; 29(1): 47-65. doi: 10.1680/geot.1979.29.1.47.
  22. Potyondy DO, Cundall PA. A bonded-particle model for rock. International Journal of Rock Mechanics and Mining Sciences 2004; 41(8): 1329-1364. doi:
  23. Bazgard A, Cundall PA, Davies TR. Dynamic analysis of mountain response using PFC3D and FLAC3D. In: ; 2011.
  24. Tavarez FA, Plesha ME. Discrete element method for modelling solid and particulate materials. International journal for numerical methods in engineering 2007; 70(4): 379-404.
  25. André D, Iordanoff I, Charles Jl, Néauport J. Discrete element method to simulate continuous material by using the cohesive beam model. Computer Methods in Applied Mechanics and Engineering 2012; 213-216: 113-125. doi:
  26. Fakhimi A. A hybrid discrete–finite element model for numerical simulation of geomaterials. Computers and Geotechnics 2009; 36(3): 386-395. doi:
  27. Itasca Consulting Group I. PFC 6.0 documentation. 2018.
  28. Gingold RA, Monaghan JJ. Smoothed particle hydrodynamics: theory and application to non-spherical stars. Monthly notices of the royal astronomical society 1977; 181(3): 375-389.
  29. Lucy LB. A numerical approach to the testing of the fission hypothesis. The astronomical journal 1977; 82: 1013-1024.
  30. Campbell PM. Some new algorithms for boundary value problems in smooth particle hydrodynamics. report, MISSION RESEARCH CORP ALBUQUERQUE NM; 1989.
  31. Monaghan J. On the problem of penetration in particle methods. Journal of Computational physics 1989; 82: 1-15.
  32. Monaghan JJ. Simulating Free Surface Flows with SPH. Journal of Computational Physics 1994; 110(2): 399-406. doi:
  33. Morris JP, Fox PJ, Zhu Y. Modeling Low Reynolds Number Incompressible Flows Using SPH. Journal of Computational Physics 1997; 136(1): 214-226. doi:
  34. Monaghan JJ. SPH without a Tensile Instability. Journal of Computational Physics 2000; 159(2): 290-311. doi:
  35. Crespo A, Gómez-Gesteira M, Dalrymple RA. Boundary conditions generated by dynamic particles in SPH methods. 2007.
  36. Adami S, Hu XY, Adams NA. A generalized wall boundary condition for smoothed particle hydrodynamics. Journal of Computational Physics 2012; 231(21): 7057-7075. doi:
  37. Liu S, Nistor I, Mohammadian M. Evaluation of the Solid Boundary Treatment Methods in SPH. International Journal of Ocean and Coastal Engineering 2018; 1(02): 1840002.
  38. Chiron L, Leffe dM, Oger G, Le Touzé D. Fast and accurate SPH modelling of 3D complex wall boundaries in viscous and non viscous flows. Computer Physics Communications 2019; 234: 93-111. doi:
  39. Robinson M, Ramaioli M, Luding S. Fluid–particle flow simulations using two-way-coupled mesoscale SPH–DEM and validation. International Journal of Multiphase Flow 2014; 59: 121-134. doi:
  40. He Y, Bayly AE, Hassanpour A, Muller F, Wu K, Yang D. A GPU-based coupled SPH-DEM method for particle-fluid flow with free surfaces. Powder Technology 2018; 338: 548-562. doi:
  41. Sun X, Sakai M, Yamada Y. Three-dimensional simulation of a solid–liquid flow by the DEM–SPH method. Journal of Computational Physics 2013; 248: 147-176. doi:
  42. Jonsson P, Jonsén P, Andreasson P, Lundström TS, Hellström JGI. Modelling dam break evolution over a wet bed with smoothed particle hydrodynamics: A parameter study. Engineering 2015; 7(05): 248.
  43. O’Sullivan C. Particulate Discrete Element Modelling: A Geomechanics Perspective. CRC Press . 2014.
  44. Cundall PA. Distinct element models of rock and soil structure. Analytical and Computational Methods in Engineering Rock Mechanics 1987: 129-163.
  45. Gui-rong L. Smoothed Particle Hydrodynamics: A Meshfree Particle Method. World Scientific Publishing Company . 2003.
  46. Zheng J, An X, Huang M. GPU-based parallel algorithm for particle contact detection and its application in self-compacting concrete flow simulations. Computers and Structures 2012; 112-113: 193-204. doi:
  47. Khayyer A, Gotoh H, Falahaty H, Shimizu Y. An enhanced ISPH–SPH coupled method for simulation of incompressible fluid–elastic structure interactions. Computer Physics Communications 2018; 232: 139-164. doi:
  48. Liu Mb, Shao Jr, Li Hq. Numerical simulation of hydroelastic problems with smoothed particle hydrodynamics method. Journal of Hydrodynamics 2013; 25(5): 673-682. doi: 10.1016/S1001-6058(13)60412-6.
  49. Fourey G, Hermange C, Le Touzé D, Oger G. An efficient FSI coupling strategy between Smoothed Particle Hydrodynamics and Finite Element methods. Computer Physics Communications 2017; 217: 66-81. doi:
  50. Fakhimi A, Villegas T. Calibration of a discrete element model for rock failure envelope and tensile strength 2004: 383-390.