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**Numerical simulation of solitary wave induced flow motion around a permeable submerged breakwater.**
*(English)*
Zbl 1264.76027

Summary: We present a numerical model for the simulation of solitary wave transformation around a permeable submerged breakwater. The wave-structure interaction is obtained by solving the Volume-Averaged Reynolds-Averaged Navier-Stokes governing equations (VARANS) and volume of fluid (VOF) theory. This model is applied to understand the effects of porosity, equivalent mean diameter of porous media, structure height, and structure width on the propagation of a solitary wave in the vicinity of a permeable submerged structure. The results show that solitary wave propagation around a permeable breakwater is essentially different from that around impermeable one. It is also found that the structure porosity has more impact than equivalent mean diameter on the wave transformation and flow structure. After interacting with the higher structure, the wave has smaller wave height behind the structure with a lower travelling speed. When the wave propagates over the breakwater with longer width, the wave travelling speed is obviously reduced with more wave energy dissipated inside porous structure.

### MSC:

76B25 | Solitary waves for incompressible inviscid fluids |

76S05 | Flows in porous media; filtration; seepage |

76M25 | Other numerical methods (fluid mechanics) (MSC2010) |

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\textit{J. Zhang} et al., J. Appl. Math. 2012, Article ID 508754, 14 p. (2012; Zbl 1264.76027)

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### References:

[1] | Y. S. Cho, J. I. Lee, and Y. T. Kim, “Experimental study of strong reflection of regular water waves over submerged breakwaters in tandem,” Ocean Engineering, vol. 31, no. 10, pp. 1325-1335, 2004. |

[2] | H. B. Chen, C. P. Tsai, and J. R. Chiu, “Wave reflection from vertical breakwater with porous structure,” Ocean Engineering, vol. 33, no. 13, pp. 1705-1717, 2006. |

[3] | J. L. Lara, I. J. Losada, and R. Guanche, “Wave interaction with low-mound breakwaters using a RANS model,” Ocean Engineering, vol. 35, no. 13, pp. 1388-1400, 2008. |

[4] | D.-S. Hur, W.-D. Lee, and W.-C. Cho, “Characteristics of wave run-up height on a sandy beach behind dual-submerged breakwaters,” Ocean Engineering, vol. 45, pp. 38-55, 2012. |

[5] | C. J. Huang, H. H. Chang, and H. H. Hwung, “Structural permeability effects on the interaction of a solitary wave and a submerged breakwater,” Coastal Engineering, vol. 49, no. 1-2, pp. 1-24, 2003. |

[6] | C. L. Ting, M. C. Lin, and C. Y. Cheng, “Porosity effects on non-breaking surface waves over permeable submerged breakwaters,” Coastal Engineering, vol. 50, no. 4, pp. 213-224, 2004. |

[7] | L. H. Huang and H. I. Chao, “Reflection and transmission of water wave by porous breakwater,” Journal of Waterway, Port, Coastal, and Ocean Engineering, vol. 118, no. 5, pp. 437-452, 1992. |

[8] | I. J. Losada, M. D. Patterson, and M. A. Losada, “Harmonic generation past a submerged porous step,” Coastal Engineering, vol. 31, no. 1-4, pp. 281-304, 1997. |

[9] | N. Kobayashi, L. E. Meigs, T. Ota, and J. A. Melby, “Irregular breaking wave transmission over submerged porous breakwater,” Journal of Waterway, Port, Coastal and Ocean Engineering, vol. 133, no. 2, pp. 104-116, 2007. |

[10] | I. J. Losada, J. L. Lara, R. Guanche, and J. M. Gonzalez-Ondina, “Numerical analysis of wave overtopping of rubble mound breakwaters,” Coastal Engineering, vol. 55, no. 1, pp. 47-62, 2008. |

[11] | A. S. Koraim, E. M. Heikal, and O. S. Rageh, “Hydrodynamic characteristics of double permeable breakwater under regular waves,” Marine Structures, vol. 24, no. 4, pp. 503-527, 2011. |

[12] | A. Nakayama and F. Kuwahara, “Macroscopic turbulence model for flow in a porous medium,” Journal of Fluids Engineering, Transactions of the ASME, vol. 121, no. 2, pp. 427-433, 1999. |

[13] | P. L.-F. Liu, P. Lin, K. A. Chang, and T. Sakakiyama, “Numerical modeling of wave interaction with porous structures,” Journal of Waterway, Port, Coastal and Ocean Engineering, vol. 125, no. 6, pp. 322-330, 1999. |

[14] | M. H. J. Pedras and M. J. S. de Lemos, “Macroscopic turbulence modeling for incompressible flow through undefromable porous media,” International Journal of Heat and Mass Transfer, vol. 44, no. 6, pp. 1081-1093, 2001. · Zbl 1014.76087 |

[15] | T.-J. Hsu, T. Sakakiyama, and P. L.-F. Liu, “A numerical model for wave motions and turbulence flows in front of a composite breakwater,” Coastal Engineering, vol. 46, no. 1, pp. 25-50, 2002. |

[16] | M. Chandesris, G. Serre, and P. Sagaut, “A macroscopic turbulence model for flow in porous media suited for channel, pipe and rod bundle flows,” International Journal of Heat and Mass Transfer, vol. 49, no. 15-16, pp. 2739-2750, 2006. · Zbl 1189.76298 |

[17] | M. F. Karim, K. Tanimoto, and P. D. Hieu, “Modelling and simulation of wave transformation in porous structures using VOF based two-phase flow model,” Applied Mathematical Modelling, vol. 33, no. 1, pp. 343-360, 2009. · Zbl 1167.76377 |

[18] | F. J. Mendez, I. J. Losada, and M. A. Losada, “Wave-induced mean magnitudes in permeable submerged breakwaters,” Journal of Waterway, Port, Coastal and Ocean Engineering, vol. 127, no. 1, pp. 7-15, 2001. |

[19] | M. R. A. van Gent, “The modelling of wave action on and in coastal structures,” Coastal Engineering, vol. 22, no. 3-4, pp. 311-339, 1994. |

[20] | E. C. Cruz, M. Isobe, and A. Watanabe, “Boussinesq equations for wave transformation on porous beds,” Coastal Engineering, vol. 30, no. 1-2, pp. 125-156, 1997. |

[21] | J. L. Lara, I. J. Losada, M. Maza, and R. Guanche, “Breaking solitary wave evolution over a porous underwater step,” Coastal Engineering, vol. 58, no. 9, pp. 837-850, 2011. |

[22] | P. Lin and P. L.-F. Liu, “Internal wave-maker for Navier-Stokes equations models,” Journal of Waterway, Port, Coastal and Ocean Engineering, vol. 125, no. 4, pp. 207-215, 1999. |

[23] | P. Lin and P. L.-F. Liu, “A numerical study of breaking waves in the surf zone,” Journal of Fluid Mechanics, vol. 359, pp. 239-264, 1998. · Zbl 0916.76009 |

[24] | C. W. Hirt and B. D. Nichols, “Volume of fluid (VOF) method for the dynamics of free boundaries,” Journal of Computational Physics, vol. 39, no. 1, pp. 201-225, 1981. · Zbl 0462.76020 |

[25] | W. J. Rider and D. B. Kothe, “Reconstructing volume tracking,” Journal of Computational Physics, vol. 141, no. 2, pp. 112-152, 1998. · Zbl 0933.76069 |

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