Numerical investigation of free surface flood wave and solitary wave using incompressible SPH method

Document Type: Research Paper


Department of Water Engineering, Shahid Bahonar University of Kerman, Kerman, Iran.


Simulation of free surface flow and sudden wave profile are recognized as the most challenging problem in computational hydraulics. Several Eulerian/Lagrangian approaches and models can be implemented for simulating such phenomena in which the smoothed particle hydrodynamics method (SPH) is categorized as a proper candidate. The incompressible SPH (ISPH) method hires a precise incompressible hydrodynamic formulation to calculate the pressure of fluid, and the numerical solution is obtained by using a two-step semi-implicit scheme. This study presents an ISPH method to simulate three free surface problems; (1) a problem of sudden dam-break flood wave on a dry bed with and obstacle in the downstream, (2) a test case of the gradual collapse of the water column on a wet bed and (3) a case of solitary wave propagation problem. The model has been confirmed based on the results of experiments for the dam-break problems (in which was set up by the authors) as well as the collapse of the water column test case and analytical calculations for the solitary wave simulation. The computational results with a mean relative error less than 10%/4% for the wave height/wave front position, demonstrated that the applied ISPH flow model is an appropriate modeling tool in free surface hydrodynamic applications.


  1. A. Shakibaeinia and Y. Jin, MPS-Based Mesh-Free Particle Method for Modeling Open-Channel Flows,  Hydraul. Eng J., 137(2011), pp. 1375–1384.  
  2. A. Colagrossi and M. Landrini, Numerical simulation of interfacial flows by smoothed particle hydrodynamics, Comput. Phys J., 191(2003), pp. 448-475.
  3. A.J.C. Crespo, M. Gómez-Gesteira and R.A. Dalrymple, Modeling dam break behavior over a wet bed by a SPH technique, Waterw. Port Coastal Ocean Eng J., 134(2008), pp. 313–320.
  4. B. Ataie-Ashtiani and G. Shobeyri, Numerical simulation of landslide impulsive waves by incompressible smoothed particle hydrodynamics, Int. J. Numer. Methods Fluids., 56 (2008), pp. 209-232.  
  5. B. Ataie-Ashtiani, G. Shobeyri and L. Farhadi, Modified incompressible SPH method for simulating free surface problems,  Fluid Dyn. Res J., 40(2008),  pp. 637-661.
  6. C. Altomare, A.J.C. Crespo, J.M. Domínguez, M. Gómez-Gesteira, T. Suzuki and T. Verwaest, Applicability of Smoothed Particle Hydrodynamics for estimation of sea wave impact on coastal structures, Coastal Eng J.,  96(2015), pp. 1-12. 
  7. E. Džebo, D. Žagar, M. Krzyk, M. Četina and G. Petkovšek, Different ways of defining wall shear in smoothed particle hydrodynamics simulations of a dam-break wave, Hydraulic Research J., 52(2014), pp. 453-464.
  8. E. Fontaine, M. Landrini and M. Tulin, Breaking: Splashing and ploughing phases, Int. Workshop on Waterwaves and Floating Bodies J., 4(2000),  pp. 34 –38.
  9. E.S. Lee, C. Moulinec, R. Xu, D. Violeau, D. Laurence and P. Stansby, Comparisons of weakly compressible and truly incompressiblealgorithms for the SPH mesh free particle method, Comput. Phys J., 227(2008), pp. 8417–8436. 
  10. I. Janosi M, D. Jan, K.G. Szabo and T. Tel, Turbulent drag reduction in dam-break flows, Exp. Fluids J., 37(2004),  pp. 219–229. 
  11. J.J. Monaghan, SPH without a tensile instability, Comput. Phys J, 159(2000), pp. 290-311.  
  12. J. Monaghan and A. Kos, Solitary waves on a Cretan beach, Waterw. Port Coastal Ocean Eng J., 125(1999), pp. 145-155.   
  13. P. Jonsson, P. Jonsén, P. Andreasson, TS. Lundström, J. Gunnar and I. Hellström, Modelling Dam Break Evolution over a Wet Bed with Smoothed Particle Hydrodynamics: A Parameter Study, Engineering J., 7(2015), pp. 248-260. 
  14. P.K. Stansby, A. Chegini and T.C.D. Barnes, The initial stages of dam-break flow, Fluid Mech J., 374(1998),  pp. 407-424.   
  15. R.A. Dalrymple, O. Knio, Dn.T. Cox, M. Gesteira and S. Zou, Using a Lagrangian particle method for deck overtopping, Proc., Waves J., (2002),  pp. 1082–1091.       
  16. R. Gingold and J.J. Monaghan, Smoothed particle hydrodynamics: theory and application to non-spherical stars,  Mon. Not. R. Astron. Soc J., 181(1977), pp. 375-389.
  17. R. Xu, P. Stansby and D. Laurence, Accuracy and stability in incompressible SPH (ISPH) based on the projection method and a new approach, Comput. Phys J.,  228(2009), pp. 6703-6725.     
  18. S. Lind, R. Xu, P.K. Stansby and B.D. Rogers, Incompressible smoothed particle hydrodynamics for free-surface flows: A generalised diffusion-based algorithm for stability and validations for impulsive flows and propagating waves, Comput. Phys J., 231(2012),  pp. 1499–1523. 
  19. S. Lind, P.K. Stansby and B.D. Rogers and P.M. Lloyd, Numerical predictions of water–air wave slam using incompressible–compressible smoothed particle hydrodynamics,  Appl. Ocean Res J., 49(2015),  pp. 57-71.
  20. S. Shao and E.Y. Lo, Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface,  Adv. Water Resour J.,  26(2003),  pp. 787-800.  
  21. S. Shao, Incompressible SPH flow model for wave interactions with porous media, Coastal Eng J.,  57(2010), pp. 304-316.