Advertisement

Journal of Hydrodynamics

, Volume 28, Issue 5, pp 731–745 | Cite as

On the modeling of viscous incompressible flows with smoothed particle hydro-dynamics

  • Mou-Bin Liu (刘谋斌)
  • Shang-ming Li (李上明)
Review article

Abstract

Smoothed particle hydrodynamics (SPH) is a Lagrangian, meshfree particle method and has been widely applied to different areas in engineering and science. Since its original extension to modeling free surface flows by Monaghan in 1994, SPH has been gradually developed into an attractive approach for modeling viscous incompressible fluid flows. This paper presents an overview on the recent progresses of SPH in modeling viscous incompressible flows in four major aspects which are closely related to the computational accuracy of SPH simulations. The advantages and disadvantages of different SPH particle approximation schemes, pressure field solution approaches, solid boundary treatment algorithms and particle adapting algorithms are described and analyzed. Some new perspectives and future trends in SPH modeling of viscous incompressible flows are discussed.

Keywords

smoothed particle hydrodynamics (SPH) viscous incompressible flow free surface flow fluid-structure interaction (FSI) 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Hipirt C., NICHOLS B. Volume of fluid (VOF) method for the dynamics of free boundaries[J]. Journal of Computational Physics, 1981, 39(1): 201–225.Google Scholar
  2. [2]
    SETHIAN J. Level set methods and fast marching methods[J]. Journal of Computing and Information Technology, 2003, 11(1): 1–2.MathSciNetGoogle Scholar
  3. [3]
    HU C., KASHIWAGI M. A CIP-based method for numerical simulations of violent free-surface flows[J]. Journal of Marine Science and Technology, 2004, 9(4): 143–157.Google Scholar
  4. [4]
    KOSHIZUKA S., OKA Y. Moving-particle semi-implicit method for fragmentation of incompressible fluid[J]. Nuclear Science and Engineering, 1996, 123(3): 421–434.Google Scholar
  5. [5]
    GINGOLD R. A., MONAGHAN J. J. Smoothed particle hydrodynamics-Theory and application to non-spherical stars[J]. Monthly Notices of The Royal Astronomical Society, 1977, 181(3): 375–389.zbMATHGoogle Scholar
  6. [6]
    LUCY L. B. A numerical approach to the testing of the fission hypothesis[J]. Astronomical Journal, 1977, 82(2): 1013–1024.Google Scholar
  7. [7]
    MONAGHAN J. J. Simulating free surface flows with SPH[J]. Journal of Computational Physics, 1994, 110(2): 399–406.zbMATHMathSciNetGoogle Scholar
  8. [8]
    LO Y. M. E., SHAO S. Simulation of near-shore solitary wave mechanics by an incompressible SPH method[J]. Applied Ocean Research, 2002, 24(5): 275–286.Google Scholar
  9. [9]
    SAMPATH R., MONTANARI N. and AKINCI N. et al. Large-scale solitary wave simulation with implicit incompressible SPH[J]. Journal of Ocean Engineering and Marine Energy, 2016, 2(3): 1–17.Google Scholar
  10. [10]
    GOMEZ-GESTEIRA M., DALRYMPLE R. A. Using a three-dimensional smoothed particle hydrodynamics method for wave impact on a tall structure[J]. Journal of Waterway Port Coastal And Ocean Engineering, 2004, 130(1): 63–69.Google Scholar
  11. [11]
    AMINI Y., EMDAD H. and FARID M. A new model to solve fluid—hypo-elastic solid interaction using the smoothed particle hydrodynamics (SPH) method[J]. European Journal of Mechanics-B/Fluids, 2011, 30(2): 184–194.zbMATHGoogle Scholar
  12. [12]
    CUMMINS S., SILVESTER T. and CLEARY P. W. Three-dimensional wave impact on a rigid structure using smoothed particle hydrodynamics[J]. International Journal for Numerical Methods in Fluids, 2012, 68(12): 1471–1496.MathSciNetzbMATHGoogle Scholar
  13. [13]
    MARUZEWSKI P., TOUZ D. L. and OGER G. et al. SPH high-performance computing simulations of rigid solids impacting the free-surface of water[J]. Journal of Hydraulic Research, 2010, 48(Suppl.): 126–134.Google Scholar
  14. [14]
    GMEZ-GESTEIRA M., CERQUEIRO D. and CRESPO C. et al. Green water overtopping analyzed with a SPH model[J]. Ocean Engineering, 2005, 32(2): 223–238.Google Scholar
  15. [15]
    MARRONE S., COLAGROSSI A. and ANTUONO M. et al. An accurate SPH modeling of viscous flows around bodies at low and moderate Reynolds numbers[J]. Journal of Computational Physics, 2013, 245(1): 456–475.MathSciNetzbMATHGoogle Scholar
  16. [16]
    KHORASANIZADE S., SOUSA J. M. A detailed study of lid-driven cavity flow at moderate Reynolds numbers using Incompressible SPH[J]. International Journal for Numerical Methods in Fluids, 2014, 76(10): 653–668.MathSciNetGoogle Scholar
  17. [17]
    GOMEZ-GESTEIRA M., ROGERS B. D. and DALRYMPLE R. A. et al. State-of-the-art of classical SPH for free-surface flows[J]. Journal of Hydraulic Research, 2010, 48(Supp1): 6–27.Google Scholar
  18. [18]
    LIU W. K., CHEN Y. and JUN S. et al. Overview and applications of the reproducing kernel particle methods[J]. Archives of Computational Methods in Engineering, 1996, 3(1): 3–80.MathSciNetGoogle Scholar
  19. [19]
    LIU W. K., JUN S. and LI S. et al. Reproducing kernel particle methods for structural dynamics[J]. International Journal for Numerical Methods in Engineering, 1995, 38(10): 1655–1679.MathSciNetzbMATHGoogle Scholar
  20. [20]
    LIU G. R., LIU M. B. Smoothed particle hydrodynamics: A meshfree particle method[M]. Singapore: World Scientific, 2003.zbMATHGoogle Scholar
  21. [21]
    LIU M. B., LIU G. R. and LAM K. Y. Constructing smoothing functions in smoothed particle hydrodynamics with applications[J]. Journal of Computational and Applied Mathematics, 2003, 155(2): 263–284.MathSciNetzbMATHGoogle Scholar
  22. [22]
    CHEN J. K., BERAUN J. E. A generalized smoothed particle hydrodynamics method for nonlinear dynamic problems[J]. Computer Methods in Applied Mechanics and Engineering, 2000, 190(1): 225–239.zbMATHGoogle Scholar
  23. [23]
    BONET J., KULASEGARAM S. Correction and stabilization of smooth particle hydrodynamics methods with applications in metal forming simulations[J]. International Journal for Numerical Methods in Engineering, 2000, 47(6): 1189–1214.zbMATHGoogle Scholar
  24. [24]
    MONAGHAN J. J. On the problem of penetration in particle methods[J]. Journal of Computational Physics, 1989, 82(1): 1–15.zbMATHMathSciNetGoogle Scholar
  25. [25]
    MONAGHAN J. J. Smooth particle hydrodynamics[J]. Annual Review of Astronomy and Astrophsics, 1992, 30: 543–574.Google Scholar
  26. [26]
    LIND S., XU R. and STANSBY P. et al. Incompressible smoothed particle hydrodynamics for free-surface flows: A generalised diffusion-based algorithm for stability and validations for impulsive flows and propagating waves[J]. Journal of Computational Physics, 2012, 231(4): 1499–1523.MathSciNetzbMATHGoogle Scholar
  27. [27]
    XU R., STANSBY P. and LAURENCE D. Accuracy and stability in incompressible SPH (ISPH) based on the projection method and a new approach[J]. Journal of Computational Physics, 2009, 228(18): 6703–6725.MathSciNetzbMATHGoogle Scholar
  28. [28]
    CUMMINS S. J., RUDMAN M. An SPH projection method[J]. Journal of Computational Physics, 1999, 152(2): 584–607.MathSciNetzbMATHGoogle Scholar
  29. [29]
    RAFIEE A., THIAGARAJAN K. P. An SPH projection method for simulating fluid-hypoelastic structure interaction[J]. Computer Methods in Applied Mechanics and Engineering, 2009, 198(33): 2785–2795.zbMATHGoogle Scholar
  30. [30]
    CHEN Z., ZONG Z. and LIU M. B. et al. A comparative study of truly incompressible and weakly compressible SPH methods for free surface incompressible flows[J]. International Journal for Numerical Methods in Fluids, 2013, 73(9): 813–829.MathSciNetGoogle Scholar
  31. [31]
    LIU Mou-bin, SHAO Jia-ru. and CHANG Jian-zhong. On the treatment of solid boundary in smoothed particle hydro-dynamics[J]. Science China Technological Sciences, 2012, 55(1): 244–254.Google Scholar
  32. [32]
    MONAGHAN J. J. Smoothed particle hydrodynamics[J]. Reports on Progress in Physics, 2005, 68(8): 1703–1759.MathSciNetGoogle Scholar
  33. [33]
    LIU M. B., XIE W. P. and LIU G. R. Modeling incompressible flows using a finite particle method[J]. Applied Mathematical Modelling, 2005, 29(12): 1252–1270.zbMATHGoogle Scholar
  34. [34]
    LIU M. B., LIU G. R. Restoring particle consistency in smoothed particle hydrodynamics[J]. Applied Numerical Mathematics, 2006, 56(1): 19–36.MathSciNetzbMATHGoogle Scholar
  35. [35]
    LIU M. B., LIU G. R. Smoothed particle hydrodynamics (SPH): An overview and recent developments[J]. Archives of Computational Methods in Engineering, 2010, 17(1): 25–76.MathSciNetzbMATHGoogle Scholar
  36. [36]
    DILTS G. A. Moving-least-squares-particle hydrodynamics-I. Consistency and stability[J]. International Journal for Numerical Methods in Engineering, 1999, 44(8): 1115–1155.MathSciNetzbMATHGoogle Scholar
  37. [37]
    RANDLES P. W., LIBERSKY L. D. Smoothed particle hydrodynamics: Some recent improvements and applications[J]. Computer Methods in Applied Mechanics and Engineering, 1996, 139(1–4): 375–408.MathSciNetzbMATHGoogle Scholar
  38. [38]
    LIU Mou-bin, CHANG Jian-zhong. Particle distribution and numerical stability in smoothed particle hydrodynamics[J]. Acta Physica Sinica, 2010, 59(6): 3654–3662 (in Chinese).Google Scholar
  39. [39]
    FANG J., PARRIAUX A. and RENTSCHLER M. et al. Improved SPH methods for simulating free surface flows of viscous fluids[J]. Applied Numerical Mathematics, 2009, 59(2): 251–271.MathSciNetzbMATHGoogle Scholar
  40. [40]
    HUANG C., LEI J. M. and LIU M. B. et al. A kernel gradient free (KGF) SPH method[J]. International Journal for Numerical Methods in Fluids, 2015, 78(11): 691–707.MathSciNetGoogle Scholar
  41. [41]
    SHAO J. R., LI H. Q. and LIU G. R. et al. An improved SPH method for modeling liquid sloshing dynamics[J]. Computers and Structures, 2012, 100–101(6): 18–26.Google Scholar
  42. [42]
    COLAGROSSI A., LANDRINI M. Numerical simulation of interfacial flows by smoothed particle hydrodynamics[J]. Journal of Computational Physics, 2003, 191(2): 448–475.zbMATHGoogle Scholar
  43. [43]
    LIU M. B., SHAO J. R. and LI H. Q. An SPH model for free surface flows with moving rigid objects[J]. International Journal for Numerical Methods in Fluids, 2014, 74(9): 684–697.MathSciNetGoogle Scholar
  44. [44]
    KOSHIZUKA S., NOBE A. and OKA Y. Numerical analysis of breaking waves using the moving particle semi-implicit method[J]. International Journal For Numerical Methods In Fluids, 1998, 26(7): 751–769.zbMATHGoogle Scholar
  45. [45]
    LIU X., XU H. and SHAO S. et al. An improved incompressible SPH model for simulation of wave-structure interaction[J]. Computers and Fluids, 2013, 71: 113–123.MathSciNetzbMATHGoogle Scholar
  46. [46]
    BCKMANN A., SHIPLIOVA O. and SKEIE G. Incompressible SPH for free surface flows[J]. Computers and Fluids, 2012, 67: 138–151.MathSciNetGoogle Scholar
  47. [47]
    LEE E.-S., MOULINEC C. and XU R. et al. Comparisons of weakly compressible and truly incompressible algorithms for the SPH mesh free particle method[J]. Journal of Computational Physics, 2008, 227(18): 8417–8436.MathSciNetzbMATHGoogle Scholar
  48. [48]
    SHADLOO M. S., ZAINALI A. and YILDIZ M. et al. A robust weakly compressible SPH method and its comparison with an incompressible SPH[J]. International Journal for Numerical Methods in Engineering, 2012, 89(8): 939–956.MathSciNetzbMATHGoogle Scholar
  49. [49]
    SHAKIBAEINIA A., JIN Y.-C. A weakly compressible MPS method for modeling of open-boundary free-surface flow[J]. International Journal for Numerical Methods in Fluids, 2010, 63(10): 1208–1232MathSciNetzbMATHGoogle Scholar
  50. [50]
    ZIENKIEWICZ O. C., TAYLOR R. L. The finite element method[M]. Oxford, UK: Butterworth-Heinemann, 2000.zbMATHGoogle Scholar
  51. [51]
    HIRSCH C. Numerical computation of internal and external flows: Fundamentals of numerical discretization[M]. New York, USA: John Wiley and Sons, 1988.zbMATHGoogle Scholar
  52. [52]
    AGERTZ O., MOORE B. and STADEL J. et al. Fundamental differences between SPH and grid methods[J]. Monthly Notices of The Royal Astronomical Society, 2007, 380(3): 963–978.zbMATHGoogle Scholar
  53. [53]
    SCHUSSLER M., SCHMITT D. Comments on smoothed particle hydrodynamics[J]. Astronomy and Astrophysics, 1981, 97: 373–379.Google Scholar
  54. [54]
    HERNQUIST L. Some cautionary remarks about smoothed particle hydrodynamics[J]. Astrophysical Journal, 1993, 404(2): 717–722.Google Scholar
  55. [55]
    NGUYEN V. P., RABCZUK T. and BORDAS S. et al. Meshless methods: A review and computer implementation aspects[J]. Mathematics and Computers in Simulation, 2008, 79(3): 763–813.MathSciNetzbMATHGoogle Scholar
  56. [56]
    REVENGA M., ZUNIGA I. and ESPANOL P. Boundary models in DPD[J]. International Journal of Modern Physics C, 1998, 9(8): 1319–1328.Google Scholar
  57. [57]
    MONAGHAN J. J. Simulating free-surface flows with SPH[J]. Journal of Computational Physics, 1994, 110(2): 399–406.zbMATHMathSciNetGoogle Scholar
  58. [58]
    LIU M. B., LIU G. R. Particle methods for multiscale and multiphysics[M]. Singapore: World Scientific, 2015.Google Scholar
  59. [59]
    ROGERS B., DALRYMPLE R. SPH modeling of tsunami waves[J]. Advanced Numerical Models for Simulating Tsunami Waves and Runup, 2007, 10: 75–100.Google Scholar
  60. [60]
    LIU M. B., LIU G. R. Smoothed particle hydrodynamics (SPH): An overview and recent developments[J]. Archives of Computational Methods in Engineering, 2010, 17(1): 25–76.MathSciNetzbMATHGoogle Scholar
  61. [61]
    GONG Kai, LIU Hua and WANG Ben-long. Water entry of a wedge based on SPH model with an improved boundary treatment[J]. Journal of Hydrodynamics, 2009, 27(6): 750–757.Google Scholar
  62. [62]
    LIBERSKY L. D., PETSCHEK A. G. and CARNEY T. C. et al. High-strain lagrangian hydrodynamics-A three-dimensional SPH code for dynamic material responses[J]. Journal of Computational Physics, 1993, 109(1): 67–75.zbMATHGoogle Scholar
  63. [63]
    COLAGROSSI A., LANDRINI M. Numerical simulation of interfacial flows by smoothed particle hydrodynamics[J]. Journal of computational physics, 2003, 191(2): 448–475.zbMATHGoogle Scholar
  64. [64]
    MORRIS J., FOX P. and ZHU Y. Modeling low Reynolds number incompressible flows using SPH[J]. Journal of Computational Physics, 1997, 136(1): 214–226.zbMATHGoogle Scholar
  65. [65]
    MARRONE S., COLAGROSSI A. Delta SPH model for simulating violent impact flows[J]. Computer Methods in Applied Mechanics and Engineering, 2011, 200(13–16): 1526–1542.MathSciNetzbMATHGoogle Scholar
  66. [66]
    KOUMOUTSAKOS P. Multiscale flow simulations using particles[J], Annual Review of Fluid Mechanics, 2005, 37(1): 457–487.MathSciNetzbMATHGoogle Scholar
  67. [67]
    LIU M. B., LIU G. R. and ZONG Z. et al. Computer simulation of high explosive explosion using smoothed particle hydrodynamics methodology[J]. Computers and Fluids, 2003, 32(3): 305–322.zbMATHGoogle Scholar
  68. [68]
    MOIN P., MAHESH K. Direct numerical simulation: A tool in turbulence research[J]. Annual Review of Fluid Mechanics, 1998, 30(1): 539–578.MathSciNetGoogle Scholar
  69. [69]
    SHAO S. Incompressible SPH simulation of wave breaking and overtopping with turbulence modelling[J]. International Journal for Numerical Methods in Fluids, 2006, 50(5): 597–621.MathSciNetzbMATHGoogle Scholar
  70. [70]
    LIN P., LIU P. L. F. A numerical study of breaking waves in the surf zone[J], Journal of Fluid Mechanics, 1998, 359(1): 239–264.zbMATHGoogle Scholar
  71. [71]
    JOHNSON G. R. Linking of Lagrangian particle methods to standard finite element methods for high velocity impact computations[J]. Nuclear Engineering and Design, 1994, 150(2–3): 265–274.Google Scholar
  72. [72]
    JOHNSON G. R., STRYK R. A. and BEISSEL S. R. SPH for high velocity impact computations[J]. Computer Methods in Applied Mechanics and Engineering, 1996, 139(1): 347–373.zbMATHGoogle Scholar
  73. [73]
    HU D., LONG T. and XIAO Y. et al. Fluid-structure interaction analysis by coupled FE-SPH model based on a novel searching algorithm[J]. Computer Methods in Applied Mechanics and Engineering, 2014, 276: 266–286.MathSciNetzbMATHGoogle Scholar
  74. [74]
    ZHANG A. M., MING F. R. and WANG S. P. Coupled SPHS-BEM method for transient fluid-structure interaction and applications in underwater impacts[J]. Applied Ocean Research, 2013, 43(10): 223–233.Google Scholar
  75. [75]
    LEE C. J. K., NOGUCHI H. and KOSHIZUKA S. Fluid shell structure interaction analysis by coupled particle and finite element method[J]. Computers and Structures, 2007, 85(11–14): 688–697.Google Scholar
  76. [76]
    MARRONE S., MASCIO A. D. and TOUZE D. L. Coupling of smoothed particle hydrodynamics with finite volume method for free surface flows[J]. Journal of Computational Physics, 2016, 310(3): 161–180.MathSciNetzbMATHGoogle Scholar
  77. [77]
    CUNDALL P. A., STRACK O. D. L. A discrete numerical model for granular assemblies[J]. Geotechnique, 1979, 29(1): 47–65.Google Scholar
  78. [78]
    ZEGHAL M., SHAMY U. E. Coupled continuum-discrete model for saturated granular soils[J]. Journal of Engineering Mechanics, 2005, 131(4): 413–426.Google Scholar
  79. [79]
    CLEARY P. W., PRAKASH M. Discrete-element modelling and smoothed particle hydrodynamics: Potential in the environmental sciences[J]. Philosophical Transactions: Mathematical, Physical and Engineering Sciences, 2004, 362(1822): 2003–2030.MathSciNetzbMATHGoogle Scholar
  80. [80]
    SILLING S. A., ASKARI E. A meshfree method based on the peridynamic model of solid mechanics[J]. Computers and Structures, 2005, 83(17): 1526–1535.Google Scholar
  81. [81]
    FAN H., BERGEL G. L. and LI S. A hybrid peridynamics?SPH simulation of soil fragmentation by blast loads of buried explosive[J]. International Journal of Impact Engineering, 2015, 86: 14–27.Google Scholar
  82. [82]
    CAI Y., ZHU H. A local search algorithm for natural neighbours in the natural element method[J]. International Journal of Solids and Structures, 2005, 42(23): 6059–6070.zbMATHGoogle Scholar
  83. [83]
    BATRA R. C., ZHANG G. M. Search algorithm, and simulation of elastodynamic crack propagation by modified smoothed particle hydrodynamics (MSPH) method[J]. Computational Mechanics, 2007, 40(3): 531–546.zbMATHGoogle Scholar
  84. [84]
    VALDEZ-BALDERAS D., DOM NGUEZ J. M. and ROGERS B. D. et al. Towards accelerating smoothed particle hydrodynamics simulations for free-surface flows on multi-GPU clusters[J]. Journal of Parallel And Distributed Computing, 2013, 73(11): 1483–1493.Google Scholar
  85. [85]
    DOM NGUEZ J. M. and CRESPO A. J. et al. Optimization strategies for CPU and GPU implementations of a smoothed particle hydrodynamics method[J]. Computer Physics Communications, 2013, 184((3): 617–627.Google Scholar

Copyright information

© China Ship Scientific Research Center 2016

Authors and Affiliations

  • Mou-Bin Liu (刘谋斌)
    • 1
    • 2
    • 3
  • Shang-ming Li (李上明)
    • 4
  1. 1.College of EngineeringPeking UniversityBeijingChina
  2. 2.Institute of Ocean ResearchPeking UniversityBeijingChina
  3. 3.State Key Laboratory for Turbulence and Complex systemsPeking UniversityBeijingChina
  4. 4.Institute of Systems EngineeringChina Academy of Engineering Physics (CAEP)MianyangChina

Personalised recommendations