A 2D incompressible smoothed particle hydrodynamics (SPH) method is implemented to simulate the impact flows associated with complex free surface. In the incompressible SPH framework, pressure Poisson equation (PPE) based on the projection method is solved using a semi-implicit scheme to evaluate the correct pressure distribution. In this procedure, the PPE comprises the divergence-free velocity condition and density-invariance condition with a relaxation parameter. To test the accuracy and efficiency of the proposed incompressible SPH method, it was applied to several sample problems with largely distorted free surface, including 2D dam-break over horizontal and inclined planes with different inclination angles, as well as the water entry of a circular cylinder into a tank. We mainly focused on the time history of impact pressure on various positions of the solid boundary and temporal evolution of free surface profiles. The results showed reasonably good agreement with experimental data. However, further improvement is needed for extremely high impact flow.
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M. Greenhow and W. Lin, Non-linear free surface effects: experiments and theory, Report Number 83-19, Department of Ocean Engineering, MIT (1983).
R. Zhao, O. Faltinsen and J. Aarsnes, Water entry of arbitrary two-dimensional sections with and without flow separation, 21th Symposium on Naval Hydrodynamics, Trondheim, Norway (1997) 408–423.
P. Tyv and T. Miloh, Free-surface flow due to impulsive motion of a submerged circular cylinder, J. Fluid Mech., 286 (1995) 67–101.
M. Greenhow and S. Moyo, Water entry and exit of horizontal circular cylinders, Philos. TR Soc. A355 (1997) 551–563.
C. W. Hirt and B. D. Nichols, Volume of fluid (VOF) method for dynamics of free boundaries, J. Compt. Phys., 39 (1981) 201–225.
M. Sussman, P. Smereka and S. Osher, A level set approach for computing solutions to incompressible two-phase flow, J. Compt. Phys., 114 (1994) 146–159.
H. Miyata and Park, J. C. Chap.5. Wave breaking simulation. In: Rahman, M. (Ed.), Potential Flow of Fluids, Comp. Mech. Pub., UK (1995) 149–176.
KMT Kleefsman, G. Fekken, AEP Veldman, B. Iwanowski and B. Buchner, A volume-of-fluid based simulation method for wave impact problems, J. Compt. Phys., 206 (2005) 363–393.
R. Panahi, E. Jahanbakhsh and MS Seif, Development of a VoF-fractional step solver for floating body motion simulation, Appl. Ocean Res., 28 (2006) 171–181.
P. Lin, A fixed-grid model for simulation of a moving body in free surface flows, Comput.&Fluids, 36 (2007) 549–561.
L. B. Lucy, A numerical approach to the testing of the fusion process, Astron J., 88 (1977) 1013–1024.
R. A. Gingold and J. J. Monaghan, Smoothed particle hydrodynamics: theory and application to non-spherical stars, Mon. Not. R.Astron Soc., 181 (1977) 375–389.
G. Oger, M. Doring, B. Alessandrini and P. Ferrant, Two-dimensional SPH simulations of wedge water entries, J. Compt. Phys., 213 (2006) 803–822.
H. Liu, K. Gong and B. L. Wang, Modelling water entry of a wedge by multiphase SPH method, SPHERIC Newsletter, 9 (2009).
G. Kai, L. Hua and W. Ben-long, Water entry of a wedge based on SPH model with an improved boundary treatment, J.Hydrodyn., 21(6) (2009) 750–757.
M. Antuono, A. Colagrossi, S. Marrone and D. Molteni, Free-surface flows solved by means of SPH schemes with numerical diffusive terms, Comput. Phys. Commun., 181(3) (2010) 532–549.
A. Colagrossi, M. Antuono, D. Le Touzé, Theoretical considerations on the free surface role in the SPH model, Phys. Rev. E, 79(5) (2009) 1–13. 056701.
S. Marrone, M. Antuono, A. Colagrossi, G. Colicchio, D. Le Touzé and G. Graziani, d-SPH model for simulating violent impact flows, Comput. Method Appl. M., 200 (2011) 13–16: 1526–1542.
F. Macià, M. Antuono, L. M. Gonzàlez and A. Colagrossi, Theoretical analysis of the no-slip boundary condition enforcement in SPH methods, Prog. Theor. Phys., 125(6) (2011) 1091–1121.
M. Antuono, A. Colagrossi, S. Marrone and C. Lugni, Propagation of gravity waves through an SPH scheme with numerical diffusive terms, Comp. Phys. Comm., 182(4) (2011) 866–877.
S. Marrone, A. Colagrossi, M. Antuono, C. Lugni and M. P. Tulin, A 2D+t SPH model to study the breaking wave pattern generated by fast ships, J. Fluids Struct., 27(8) (2011) 1199–1215.
A. Colagrossi, M. Antuono, A. Souto-Iglesias and D. Le Touzé, Theoretical Analysis and numerical verification of the consistency of viscous SPH formulation in simulating free-surface flows, Phys. Rev. E, 84 (2011) 026705.
M. Landrini, A. Colagrossi, M. Greco and M. P. Tulin, The fluid mechanics of splashing bow waves on ships: A hybrid-BEM-SPH analysis, Ocean Eng., 53 (2012) 111–127.
M. Antuono, A. Colagrossi and S. Marrone, Numerical diffusive terms in weakly-compressible SPH schemes, Comput. Phys.Commun., 183 (2012) 2570–2580.
I. Federico, S. Marrone, A. Colagrossi, F. Aristodemo and M. Antuono, Simulating 2D open-channel flows through an SPH model, Eur. J. Mech. B/Fluids, 34 (2012) 35–46.
A. Colagrossi, B. Bouscasse, M. Antuono and S. Marrone, Particle packing algorithm for SPH schemes, Comput. Phys.Commun., 183 (2012) 1641–1653.
S. J. Cummins and M. Rudman, An SPH projection method. J. Comput. Phys., 152(2) (1999) 584–607.
S. D. Shao and EYM. Lo, Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface, Adv. Water Res., 26 (2003) 787–800.
E. S. Lee, D. Laurence, P. K. Stansby, D. Violeau and C. Moulinec, 2D flow past a square cylinder in a closed channel, SPHERIC Newsletter, 3 (2006).
M. Ellero, M. Serrano and P. Espanol, Incompressible smoothed particle hydrodynamics, J.Comput. Phys., 226 (2007) 1731–1752.
E. S. Lee, C. Moulinec, R. Xu, D. Violeau, D. Laurence and P. Stansby, Comparisons of weakly compressible and truly incompressible algorithms for the SPH mesh free particle method, J. Comput. Phys., 227(18) (2008) 8417–8436.
A. Khayyer, H. Gotoh and S. Shao, Corrected incompressible SPH method for accurate water-surface tracking in breaking waves, Coast. Eng., 55 (2008) 236–250.
A. Khayyer, H. Gotoh and S. Shao, Enhanced predictions of wave impact pressure by improved incompressible SPH methods, Appl.Ocean Res., 31 (2009) 111–131.
X. Y. Hu and N. A. Adams, An incompressible multi-phase SPH method, J. of Comput. Phys., 227 (2007) 264–278.
M. Asai, A. M. Aly, Y. Sonoda and Y. Sakai, A Stabilized Incompressible SPH method by relaxing the Density invariance condition, J. Appl. Math., (2012); 2012: 24. doi: 10.1155/2012/139583.
A. M. Aly, M. Asai and Y. Sonoda, Modelling of surface tension force for free surface flows in ISPH method. Int..J.Numer. Method H., 23 (2013) 3.
A. M. Aly, M. Asai and Y. Sonoda, Simulation of free falling rigid body into water by a stabilized incompressible SPH method, Ocean Sys. Eng., 1(3) (2011) 207–222.
H. Gotoh, S. Shao and T. Memita, SPH-LES model for numerical investigation of wave interaction with partially immersed breakwater, Coast. Eng. J. JSCE, 46(1) (2001) 39–63.
M. Tanaka and T. Masunaga, Stabilization and smoothing of pressure in MPS method by Quasi-Compressibility, J. Comput. Phys., 229 (2010) 4279–4290.
D. Violeau and R. Issa, Numerical modelling of complex turbulent free-surface flows with the SPH method: an overview, Int. J. Numer. Meth. Fluids, 53 (2007) 277–304.
S. Shao and H. Gotoh, Turbulence particle models for tracking free surfaces, J. Hydraul. Res., IAHR, 43(3) (2005) 276–289.
G. R. Liu and M. B. Liu, Smoothed Particle Hydrodynamic, a mesh free particle method, World scientific Publishing Co. Pte. Ltd. (2003).
S. Koshizuka and Y. Oka, Moving-particle semi-implicit method for fragmentation of incompressible fluid, Nuc. Sci. Eng., 123(3) (1996) 421–434.
H. Gotoh and T. Sakai, Key issues in the particle method for computation of wave breaking, Coast Eng., 53 (2006) 171–179.
S. Shao, Incompressible SPH simulation of water entry of a free-falling object, Int. J. Numer. Meth. Fluids, 59 (2009) 91–115.
T. H. Lee, Z. Q. Zhou and Y. S. Cao, Numerical simulations of hydraulic jumps in water sloshing and water impacting, J Fluid Eng, 124 (2002) 215–226.
Liu Xin, Xu Haihua, Shao Songdong and Lin Pengzhi, An improved incompressible SPH model for simulation of wave-structure interaction, Comput. & Fluids, 71 (2013) 113–123.
G. Colicchio, M. Greco, M. Miozzi and C. Lugni, Experimental and numerical investigation of the water-entry and water-exit of a circular cylinder, Int. Workshop on Water Waves and Floating Bodies, 24 (2009) Russia.
J. S. Park, S. H. Oh, S. H. Kwon and J. Y. Chung, A study on slamming impact pressure, Korea Ocean Eng., 23(1) (2009) 67–73 (In Korean).
J. P. Morris, P. J. Fox and Y. Zhu, Modeling low reynolds number incompressible flows using SPH, J. Comput. Phys., 136 (1997) 214–226.
Recommended by Associate Editor Gihun Son
A. M. Aly received his Ph.D. in Civil Engineering from Kyushu University, Japan in 2012. Currently, he is an Assistant Professor of the Department of Mathematics at South Valley University, Egypt. His research interests include computational fluid dynamics and heat transfer.
S.-W. Lee received his Ph.D. in Mechanical Engineering from the University of Illinois at Chicago in 2005. Currently, he is an Associate Professor of the School of Mechanical Engineering at the University of Ulsan. His research interests include cardiovascular mechanics and computational fluid dynamics.
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Aly, A.M., Lee, SW. Numerical simulations of impact flows with incompressible smoothed particle hydrodynamics. J Mech Sci Technol 28, 2179–2188 (2014). https://doi.org/10.1007/s12206-014-0120-8
- Incompressible SPH
- Free surface flow
- Dam-break flow
- Inclined plane
- Water entry
- Circular cylinder