Sensitivity Study of Smoothed Particle Hydrodynamics

  • Kim, Yoo-Il (Department of Naval Architecture and Ocean Engineering, Seoul National University) ;
  • Nam, Bo-Woo (Department of Naval Architecture and Ocean Engineering, Seoul National University) ;
  • Kim, Yong-Hwan (Department of Naval Architecture and Ocean Engineering, Seoul National University)
  • Published : 2007.12.31

Abstract

Systematic sensitivity analysis of smoothed particle hydrodynamics method (SPH), a gridless Lagrangian particle method, was carried out in this study. Unlike traditional grid-based numerical schemes, systematic sensitivity study for computational parameters is very limited for SPH. In this study, the effect of computational parameters in SPH simulation is explored through two-dimensional dam-breaking and sloshing problem. The parameters to be considered are the speed of sound, the type of kernel function, the frequency of density re-initialization, particle number, smoothing length and pressure extraction method. Through a series of numerical test, detailed information was obtained about how SPH solution can be more stabilized and improved by adjusting computational parameters.

Keywords

References

  1. Colagrossi, A. 2005. A Meshless Lagrangian Method for Free-Surface and Interface Flows with Fragmentation. PhD Thesis University of Roma
  2. Colagrossi, A and M. Landrini. 2003. Numerical Simulation of Interfacial Flows by Smoothed Particle Hydrodynamics. Journal of Computational Physics, 191, 448-475 https://doi.org/10.1016/S0021-9991(03)00324-3
  3. Dalymple, R.A and B.D. Rogers. 2006. Numerical Modeling of Water Waves with the SPH Method. Coastal Engineering, 53, 141-147 https://doi.org/10.1016/j.coastaleng.2005.10.004
  4. Dilts, G. 1999. Moving-least-squares-particle Hydrodynamics - I. Consistency and Stability. International Journal for Numerical Methods in Engineering, 48, 1115-1155
  5. Dilts, G. 2000. Moving-least-squares-particle Hydrodynamics - II. Conservation and Boundaries. International Journal for Numerical Methods in Engineering, 48, 1504-1524
  6. Johnson, G.R. and S.R. Beissel. 1996. Normalized Smoothing Functions for SPH Impact Computations. International Journal for Numerical Methods in Engineering, 39, 2725-2741 https://doi.org/10.1002/(SICI)1097-0207(19960830)39:16<2725::AID-NME973>3.0.CO;2-9
  7. Liu, G.R. and M.B. Liu. 2003. Smoothed Particle Hydrodynamics -A Meshfree Particle Method-. World Scientific Publishing Co. Ltd
  8. Liu, M.B., G.R Liu. and K.Y. Lam. 2003. Constructing Smoothing Functions in Smoothed Particle Hydrodynamics with Applications. Journal of Computational and Applied Mathematics, 155, 263-284 https://doi.org/10.1016/S0377-0427(02)00869-5
  9. Liu, M.B. and G.R Liu. 2006. Restoring Particle Consistency in Smoothed Particle Hydrodynamics. Applied Numerical Mathematics, 56, 19-36 https://doi.org/10.1016/j.apnum.2005.02.012
  10. Li, S. and W.K. Liu. 2004. Meshfree Particle Methods. Springer
  11. Li, S. and W.K. Liu. 2002. Meshfree and Particle Methods and Their Applications. Appl. Mech. Rev., 55, 1-34 https://doi.org/10.1115/1.1431547
  12. Libersky, L.D. and A.G. Petschek. 1990. Smooth Particle Hydrodynamics with Strength of Materials. Advances in the Free Lagrangian Method, Lecture Notes in Physics, 395, 248-257
  13. Mas-Gallic, S. and P. Raviart. 1987. A Particle Method for First-order Symmetric Systems. Numer. Math., 51, 323-352 https://doi.org/10.1007/BF01400118
  14. Monaghan, J.J. 1992. Smoothed Particle Hydrodynamics. Annu. Rev. Astron. Astrophys., 543-574
  15. Monaghan, J.J. 1983. Shock Simulation by the Particle Method SPH. Journal of Computational Physics, 52, 374-389 https://doi.org/10.1016/0021-9991(83)90036-0
  16. Monaghan, J.J. 1994. Simulating free surface flow with SPH. Journal of Computational Physics, 110, 399-406 https://doi.org/10.1006/jcph.1994.1034
  17. Monaghan, J.J. 2000. SPH without a Tensile Instability. Journal of Computational Physics, 159, 290-311 https://doi.org/10.1006/jcph.2000.6439
  18. Monaghan, J.J. and A. Kos. 1999. Solitary Waves on a Cretan Beach. Journal of Waterway, Port, Coastal and Ocean Engineering, 145-154
  19. Nam, B.W. and Y. Kim. 2006. Simulation of Two-Dimensional Sloshing Flows by SPH Method. Proceedings of ISOPE-2006, San Francisco USA
  20. Oger, G., M. Doring, B. Alessandrini and P. Ferrant. 2005. Two-dimensional SPH Simulations of Wedge Water Entries. Journal of Computational Physics, 213, 803-822 https://doi.org/10.1016/j.jcp.2005.09.004
  21. Riffert, H, H. Herold, O. Flebbe and H. Ruder. 1995. Numerical Aspects of the Smoothed Particle Hydrodynamics Method for Simulating Accretion Disks. Computer Physics Communications, 89, 1-16 https://doi.org/10.1016/0010-4655(94)00182-2
  22. Shepard, D. 1968. A Two-Dimensional Interpolation Function for Irregularly-Spaced Data. Proceedings ofthe 23rd National Conference, ACM, 517-523
  23. Souto-Iglesias, L., L. Perez-Rojas and R. Zamora-Rodriguez. 2004. Simulation of Anti-roll Tanks and Sloshing type Problems with Smoothed Particle Hydrodynamics. Ocean Engineering, 31, 1169-1192 https://doi.org/10.1016/j.oceaneng.2003.09.002
  24. Swegel, J.W., D.L. Hicks and S.W. Attaway. 1995. Smoothed Particle Hydrodynamics Stability Analysis. Journal of Computational Physics, 116, 123-134 https://doi.org/10.1006/jcph.1995.1010
  25. Van Daalen, E.F.G. 1999. Two-dimensional free surface anti-roll tank simulations with a volume of fluid based Navier-Stokes solver. Report No. 15306-1-OE, MARIN