Simulating wave-structure interactions using a modified WCSPH scheme


Sahand University of Technology


A weakly compressible SPH (WCSPH) scheme has been developed to simulate interaction between waves and rigid bodies. The developed WCSPH scheme is improved by applying a modified equation to calculate the wave-structure interaction, in order to increase its accuracy. The effects of relative fluid/solid particles’ acceleration are considered in the modified equation. To evaluate the efficiency of developed model, the dynamics of structural movements and related pressure fields are investigated for several test cases and the results are compared with the experimental data. It seems that the modified algorithm is able to improve the accuracy of simulated wave-structure interactions.


1- Adami, S., Hu, X. Y. and Adams, N. A., (2012), A generalized wall boundary condition for smoothed particle hydrodynamics, Journal of Computational Physics, Vol. 231, p. 7057–7075. 2- Bouscasse, B., Colagrossi, A., Marrone, S. and Antuono, M., (2013), Nonlinear water wave interaction with floating bodies in SPH, Journal of Fluids and Structures, Vol. 42, p. 112-129. 3- Cao, X. Y., Ming, F. R. and Zhang, A, M., (2014), Sloshing in a rectangular tank based on SPH simulation, Applied Ocean Research, Vol. 47, p. 241-254. 4- Delavari, E. and Gharabaghi, A. R. M., (2014), A modified sponge layer boundary condition for a numerical wave flume based on the SPH scheme, The 11th Int. Conf. on Coasts, Ports and Marine Structures (ICOPMAS 2014), Tehran. 5- Faltinsen, O. M., (1977), Numerical solution of transient nonlinear free-surface motion outside or inside moving bodies, In: Proceedings Second Int. Conf. on Num. Ship Hydrodynamics, UC Berkeley, p. 257–266. 6- Gao, R., Ren, B., Wang, G. and Wang, Y., (2012), Numerical modeling of regular wave slamming on surface of open-piled structures with the corrected SPH method, Applied Ocean Research, Vol. 34, p. 173-186. 7- Ghia, U., Ghia, K. N. and Shin, C. T., (1982), High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method, Journal of Computational Physics, Vol. 48(3), p. 387-411. 8- Gomez-Gesteria, M., Rogers, B.D., Crespo, A.J.C., Dalrymple, R.A., Narayanaswamy, M. and Dominguez, J.M., (2012), SPHysics-Development of a free surface fluid solver-part 1: Theory and formulations, Computers and Geosciences, Vol. 48, p. 289-299. 9- Greenhow, M. and Lin, W-M., (1983), Nonlinear free surface effects: Experiments and theory, Report No. 83-19, Massachusetts Institute of Technology. 10- Hashemi, M. R., Fatehi, R. and Manzari, M. T., (2012), A modified SPH method for simulating motion of rigid bodies in Newtonian fluid flows, International Journal of Non-linear Mechanics, Vol. 47, p. 626-638. 11- Jung, K-H., (2004), Experimental study on rectangular barge in beam sea, Ph.D. Thesis, Texas A&M University. 12- Kajtar, J. B., (2009), Smooth lattice general relatively and SPH simulations swimming linked bodies, Ph.D. Thesis, Monash University. 13- Kajtar, J. and Monaghan, J. J., (2008), SPH simulations of swimming linked bodies, Journal of Computational Physics, 227, p. 8568-8587. 14- Kajtar, J. B. and Monaghan, J. J., (2010), On the dynamics of swimming linked bodies, European Journal of Mechanics B/Fluids, Vol. 29, p. 377-386. 15- Koo, W., (2003), Fully nonlinear wave-body interactions by a 2D potential numerical wave tank, Ph.D. Thesis, Texas A&M University. 16- Liu, M. B., Shao, J. R. and Li, H. Q., (2014), An SPH model for free surface flows with moving rigid objects, International Journal for Numerical Methods in Fluids, Vol. 74, p. 684-697. 17- Lo, E. Y. M. and Shao, S., (2002), Simulation of nearshore solitary wave mechanics by an incompressible SPH method, Applied Ocean Research, Vol. 24, p. 275-286. 18- Loverty, S. M., (2004), Experimental hydrodynamics of spherical projectiles impacting on a free surface using high speed imaging techniques, M.Sc. Thesis, Massachusetts Institute of Technology. 19- Monaghan, J. J., (1994), Simulating free surface flows with SPH, Journal of Computational Physics, Vol. 110, p. 399-406. 20- Monaghan, J. J., (2000), SPH without a tensile instability, Journal of Computational Physics, Vol. 159, p. 290-311. 21- Monaghan, J. J. and Kajtar, J. B., (2009), SPH particle boundary forces for arbitrary boundaries, Computer Physics Communications, Vol. 180, p. 1811-1820. 22- Monaghan, J. J. and Lattanzio, J. C., (1985), A refined particle method for astrophysical problems, Astronomy and Astrophysics, Vol. 149, p. 135-143. 23- Morris, J. P. and Fox, P. J., Y. Zhu, (1997), Modeling low Reynolds number incompressible flows using SPH, Journal of Computational Physics, Vol. 136, p. 214–226. 24- Ni, X., Feng, W. B. and Wu, D., (2014), Numerical simulations of wave interactions with vertical wave barriers using the SPH method, International Journal for Numerical Methods in Fluids, DOI:10.1002/fld.3933. 25- Omidvar, P., Stansby, P. K. and Rogers, B. D., (2012), Wave body interaction in 2D using smoothed particle hydrodynamics (SPH) with variable particle mass, International Journal for Numerical Methods in Fluids, Vol. 68, p. 686-705. 26- Omidvar, P., Stansby, P. K. and Rogers, B. D., (2013), SPH for 3D Floating Bodies Using Variable Mass Particle Distribution, International Journal for Numerical Methods in Fluids, Vol. 72 (4), p. 427-452. 27- Ren, B., He, M., Dong, P. and Wen, H., (2015), Nonlinear simulations of wave-induced motions of a freely floating body using WCSPH method, Applied Ocean Research, Vol. 50, p. 1-12. 28- Sun, H. and Faltinsen, O. M., (2006), Water impact of horizontal circular cylinders and cylindrical shells, Applied Ocean Research, Vol. 28, p. 299-311. 29- Sun, P., Ming, F. and Zhang, A., (2015), Numerical simulation of interactions between free surface and rigid body using a robust SPH method, Ocean Engineering, Vol. 98, p. 32-49. 30- Tolba, E. R. A. S., (1998), Behaviour of floating breakwaters under wave action, Ph.D. Thesis, Suez Canal University, Panama. 31- Valizadeh, A. and Monaghan, J. J., (2015), A study of solid wall models for weakly compressible SPH, Journal of Computational Physics, Vol. 300, p. 5-19. 32- Yan, R., Monaghan, J. J., Valizadeh, A. and Xu, F., (2015), The effect of air on solid body impact with water in two dimensions, Journal of Fluids and Structures, Vol. 59, p. 146-164. 33- Yang, S. H., Lee, H. H., Park, T. H., Lee, I. H. and Lee, Y. W., (2007), Experimental and numerical study on the water entry of symmetric wedges and a stern section of modern containership, In: Proceedings of the 10th International Symposium on Practical Design of Ships and other Floating Structures (PRADS 2007), Houston, Texas, USA, p. 518-526. 34- Yettou, E-M., Desrochers, A. and Champoux, Y., (2006), Experimental study on the water impact of a symmetrical wedge, Fluid Dynamics Research, Vol. 38, p. 47-66. 35- Yoon, S. B. and Choi, J. W., (2001), A Note on extension of fully dispersive weakly nonlinear wave equations for rapidly varying topography, Coastal Engineering Journal, Vol. 43(3), p. 143-160.