Document Type : Article

**Authors**

Department of Civil Engineering, Faculty of Engineering, Shahid Bahonar University of Kerman, Kerman, P.O. Box 76169-133, Iran

**Abstract**

In this paper, the Incompressible Smoothed Particle Hydrodynamics (ISPH) method is presented to simulate flood waves in uneven beds. The SPH method is a mesh free particle modeling approach that is capable of tracking the large deformation of free surfaces in an easy and accurate manner. Wave breaking is one of the phenomena that its free surface is complicated. Therefore, ISPH method is robust tool for the modeling of this kind of free surface. The basic equations are the incompressible mass conservation and Navier–Stokes equations that are solved using a two-step fractional method. In the first step, these equations are solved to compute velocity components by omitting the pressure term and in the absence of incompressible condition. In the second step, the continuity constraint is satisfied and the Poisson equation is solved to calculate pressure terms. In the present model, a new technique is applied to allocate density of the particles for the calculations. By employing this technique, ISPH method is stabled. The validation by comparison with laboratory data is conducted for bumpy channel with various boundary conditions. The numerical results showed good agreement with available experimental data. Also relative error is calculated for two numerical cases.

**Keywords**

**Main Subjects**

References:

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22. Dalrymple, R.A. and Rogers, B.D. "Numerical modeling of water waves with the SPH method", Coastal Engineering Journal, 53, pp. 141-147 (2006).

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25. Koshizuka, S. and Oka, Y. "Moving-particle semiimplicit method for fragmentation of incompressible fluid", Nuclear Science and Engineering, 123, pp. 421- 434 (1996).

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28. Koshizuka, S., Oka, Y., and Tamako, H. "A particle method for calculating splashing of incompressible viscous fluid", Int. Conf. Math. Comput., 2, pp. 1514- 1521 (1995).

2. Stoker, J.J., Water Waves. Pure and Applied Mathematics 4, Interscience Publishers, New York (1957).

3. Xia, J., Lin, B., Falconer, R.A., and Wang, G. "Modelling dam-break flows over mobile beds using a 2D coupled approach", Adv. Water Resour., 33(2), pp. 171-183 (2010).

4. Shakibaeinia, A. and Jin, Y.C. "A mesh-free particle model for simulation of mobile-bed dam break", Adv. Water Resour., 34(6), 794-807 (2011).

5. Harlow, F. and Welch, J. "Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface", The Physics of Fluids, 8(12), pp. 2182-2189 (1965).

6. Hirt, C.W. and Nichols, B.D. "Volume of fluid (VOF) method for the dynamics of free boundaries", Journal of Computational Physics, 39, pp. 201-225 (1981).

7. Khanpour, M., Zarrati, A.R., and Kolahdoozan, M. "Numerical simulation of the flow under sluice gates by SPH model", Sharif University of Technology, Scientia Iranica, Transactions A: Civil Engineering, 21(5), pp. 1503-1514 (2014).

8. Shao, S.E. and Lo, E. "Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface", Advances in Water Resources, 26, pp. 787-800 (2003).

9. Fang, J., Parriaux, A., Rentschler, M., and Ancey, Ch. "Improved SPH method for simulating free surface flows of viscous fluids", Applied Numerical Mathematics, 59, pp. 251-271 (2009).

10. Wang, B.L. and Liu, H. "Application of SPH method on free surface flows on GPU", Journal of Hydrodynamics, 22(5), pp. 912-914 (2010).

11. Lee, E.S., Xu, C., Moulinec, R., Violeau, D., Laurence, D., and Stansby, P. "Comparisons of weakly compressible and truly incompressible algorithms for the SPH mesh free particle method", Journal of Computational Physics, 227, pp. 8417-8436 (2008).

12. Khayyer, A. and Gotoh, H. "On particle-based simulation of a dam break over a wet bed", J. Hydraul. 595 Res., 48(2), pp. 238-49 (2010).

13. Ozbulut, M., Yildiz, M., and Goren, O. "A numerical investigation into the correction algorithms for SPH method in modeling violent free surface flows", Journal of Mechanical Sciences, 79, pp. 56-65 (2014).

14. Monaghan, J.J. "Simulating free surface flows with SPH", Journal of Computational Physics, 110, pp. 399-406 (1994).

15. Morris, J.P., Fox, P.J., and Zhu, Y. "Modeling low Reynolds number incompressible flows using SPH", Journal of Computational Physics, 136, pp. 214-226 (1997).

16. Chorin, A.J. "Numerical solution of the Navier-Stokes equations", Mathematics of Computation, 22, pp. 745- 762 (1968).

17. Cummins, S.J. and Rudman, M." An SPH projection method", Journal of Computational Physics, 152, pp. 584-607 (1999).

18. Shao, S. and Gotoh, H. "Simulating coupled motion of progressive wave and floating curtain wall by SPH-LES model", Coastal Engineering Journal, 46, pp. 171-202 (2004).

19. Hu, X.Y. and Adams, N.A. "An incompressible multi-phase SPH method", Journal of Computational Physics, 227, pp. 264-278 (2007).

20. Xenakis, A.M., Lind, S.J., Stansby, P.K., and Rogers, B.D. "An incompressible SPH scheme with improved pressure predictions for free-surface generalized Newtonian flows", Journal of Non-Newtonian Fluid Mechanics, 218, pp. 1-15 (2015).

21. Nomeritae, Daly, E., Grimaldi, S., and Hong Bui, Ha. "Explicite incompressible SPH algorithm for freesurface modeling: A comparison with weakly compressible schemes", Advances in Water Resources, 97, pp. 156-167 (2016).

22. Dalrymple, R.A. and Rogers, B.D. "Numerical modeling of water waves with the SPH method", Coastal Engineering Journal, 53, pp. 141-147 (2006).

23. Monaghan, J.J. "Smoothed particle hydrodynamics", Annu RevAstron Astrophys, 30, pp. 543-57 (1992).

24. Shao, S. "Incompressible SPH flow model for wave interactions with porous media", Coastal Engineering Journal, 57, pp. 304-316 (2010).

25. Koshizuka, S. and Oka, Y. "Moving-particle semiimplicit method for fragmentation of incompressible fluid", Nuclear Science and Engineering, 123, pp. 421- 434 (1996).

26. Ozmen-Cagatay, H., Kocaman, S., and Guzel, H. "Investigation of dam-break flood waves in a dry channel with a hump", Journal of Hydro-environment Research, pp. 1-12 (2014).

27. Soarez Frazao, S., de Bueger, C., Dourson, V., and Zech, Y. "Dam-break wave over a triangular bottom sill", International Conference on Fluvial Hydraulics, pp. 437-442 (2002).

28. Koshizuka, S., Oka, Y., and Tamako, H. "A particle method for calculating splashing of incompressible viscous fluid", Int. Conf. Math. Comput., 2, pp. 1514- 1521 (1995).

Transactions on Civil Engineering (A)

March and April 2019Pages 667-677