SPH Modeling of Wave Transformation over a Coral Reef with Seawall
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 145, Issue 1
Abstract
Wave transformations over a coral reef with a steep front slope were comparatively studied using both laboratory tests and smoothed particle hydrodynamic (SPH) modeling. In the numerical model, nonreflective generation and absorption of waves were realized by adding a source term and a velocity attenuation term into the governing momentum equation. The physical and numerical models were carefully designed so that the nonphysical rise of the mean water level over the reef was avoided. Experimental and numerical results on the free surface elevations and the spatial distributions of wave height and wave setup over the reef with and without a vertical seawall were compared and good agreements were obtained. The cross-spectral transfer of wave energy from the peak frequency to the lower and higher frequencies, the vertical distributions of wave-induced current over the reef, and the effects of the seawall position on the maximum wave setup and wave run-up are discussed.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The improved SPH code used in this paper was developed from the open source parallel SPHysics code. The authors are appreciative to all the developers and contributors of the open source code. This work was supported by the Ng Teng Fong Charitable Foundation through Tsinghua University Education Foundation (TUEF), the National Natural Science Foundation of China under Grant 51679032, and the Open Foundation of the State Key Laboratory of Coastal and Offshore Engineering at Dalian University of Technology under Grant LP1721.
References
Altomare, C., A. J. C. Crespo, B. D. Rogers, J. M. Dominguez, X. Gironella, and M. Gómez-Gesteira. 2014. “Numerical modelling of armour block sea breakwater with smoothed particle hydrodynamics.” Comput. Struct. 130 (Jan): 34–45. https://doi.org/10.1016/j.compstruc.2013.10.011.
Bouscasse, B., A. Colagrossi, S. Marrone, and M. Antuono. 2013. “Nonlinear water wave interaction with floating bodies in SPH.” J. Fluids Struct. 42 (Oct): 112–129. https://doi.org/10.1016/j.jfluidstructs.2013.05.010.
Crespo, A. J. C., C. Altomare, J. M. Domínguez, J. González-Cao, and M. Gómez-Gesteira. 2017. “Towards simulating floating offshore oscillating water column converters with smoothed particle hydrodynamics.” Coastal Eng. 126 (Aug): 11–26. https://doi.org/10.1016/j.coastaleng.2017.05.001.
Crespo, A. J. C., J. M. Domínguez, B. D. Rogers, M. Gómez-Gesteira, S. Longshaw, R. Canelas, R. Vacondio, A. Barreiro, and O. García-Feal. 2015. “DualSPHysics: Open-source parallel CFD solver based on smoothed particle hydrodynamics (SPH).” Comput. Phys. Commun. 187 (Feb): 204–216. https://doi.org/10.1016/j.cpc.2014.10.004.
Crespo, A. J. C., M. Gómez-Gesteira, and R. A. Dalrymple. 2007. “Boundary conditions generated by dynamic particles in SPH methods.” Comput. Mater. Continua 5 (3): 173–184.
Dalrymple, R. A., and B. D. Rogers. 2006. “Numerical modeling of water waves with the SPH method.” Coastal Eng. 53 (2–3): 141–147. https://doi.org/10.1016/j.coastaleng.2005.10.004.
Franklin, G., I. Mariño-Tapia, and A. Torres-Freyermuth. 2013. “Effects of reef roughness on wave setup and surf zone currents.” J. Coastal Res. 2 (Special Issue 65—International Coastal Symposium): 2005–2010. https://doi.org/10.2112/SI65-339.1.
Gong, K., S. Shao, H. Liu, B. Wang, and S. K. Tan. 2016. “Two-phase SPH simulation of fluid–structure interactions.” J. Fluids Struct. 65 (Aug): 155–179. https://doi.org/10.1016/j.jfluidstructs.2016.05.012.
Gourlay, M. R. 1994. “Wave transformation on a coral reef.” Coastal Eng. 23 (1–2): 17–42. https://doi.org/10.1016/0378-3839(94)90013-2.
Gourlay, M. R. 1996a. “Wave set-up on coral reefs. 1. Set-up and wave-generated flow on an idealised two dimensional horizontal reef.” Coastal Eng. 27 (3–4): 161–193. https://doi.org/10.1016/0378-3839(96)00008-7.
Gourlay, M. R. 1996b. “Wave set-up on coral reefs. 2. Set-up on reefs with various profiles.” Coastal Eng. 28 (1–4): 17–55. https://doi.org/10.1016/0378-3839(96)00009-9.
Gourlay, M. R., and G. Colleter. 2005. “Wave-generated flow on coral reefs—An analysis for two-dimensional horizontal reef-tops with steep faces.” Coastal Eng. 52 (4): 353–387. https://doi.org/10.1016/j.coastaleng.2004.11.007.
Hearn, C. J. 1999. “Wave-breaking hydrodynamics within coral reef systems and the effect of changing relative sea level.” J. Geophys. Res. C Oceans 104 (C12): 30007–30019. https://doi.org/10.1029/1999JC900262.
Khayyer, A., H. Gotoh, and S. D. Shao. 2008. “Corrected incompressible SPH method for accurate water-surface tracking in breaking waves.” Coastal Eng. 55 (3): 236–250. https://doi.org/10.1016/j.coastaleng.2007.10.001.
Marrone, S., M. Antuono, A. Colagrossi, G. Colicchio, D. Le Touzé, and G. Graziani. 2011. “δ-SPH model for simulating violent impact flows.” Comput. Methods Appl. Mech. Eng. 200 (13–16): 1526–1542. https://doi.org/10.1016/j.cma.2010.12.016.
Marrone, S., B. Bouscasse, A. Colagrossi, and M. Antuono. 2012. “Study of ship wave breaking patterns using 3D parallel SPH simulations.” Comput. Fluids 69 (Oct): 54–66. https://doi.org/10.1016/j.compfluid.2012.08.008.
Massel, S. R., and M. R. Gourlay. 2000. “On the modelling of wave breaking and set-up on coral reefs.” Coastal Eng. 39 (1): 1–27. https://doi.org/10.1016/S0378-3839(99)00052-6.
Monaghan, J. J. 1994. “Simulating free surface flows with SPH.” J. Comput. Phys. 110 (2): 399–406. https://doi.org/10.1006/jcph.1994.1034.
Monaghan, J., and A. Kos. 1999. “Solitary waves on a Cretan beach.” J. Waterway, Port, Coastal, Ocean Eng. 125 (3): 145–155. https://doi.org/10.1061/(ASCE)0733-950X(1999)125:3(145).
Nwogu, O. 1993. “Alternative form of Boussinesq equations for nearshore wave propagation.” J. Waterway, Port, Coastal, Ocean Eng. 119 (6): 618–638. https://doi.org/10.1061/(ASCE)0733-950X(1993)119:6(618).
Nwogu, O., and Z. Demirbilek. 2010. “Infragravity wave motions and runup over shallow fringing reefs.” J. Wateray, Port, Coastal, Ocean Eng. 136 (6): 295–305. https://doi.org/10.1061/(ASCE)WW.1943-5460.0000050.
Péquignet, A. C. N., J. M. Becker, M. A. Merrifield, and J. Aucan. 2009. “Forcing of resonant modes on a fringing reef during tropical storm Man-Yi.” Geophys. Res. Lett. 36 (3): L03607. https://doi.org/10.1029/2008GL036259.
Ren, B., M. He, Y. Li, and P. Dong. 2017. “Application of smoothed particle hydrodynamics for modeling the wave-moored floating breakwater interaction.” Appl. Ocean Res. 67 (Sep): 277–290. https://doi.org/10.1016/j.apor.2017.07.011.
Ren, B., H. Wen, P. Dong, and Y. Wang. 2014. “Numerical simulation of wave interaction with porous structures using an improved smoothed particle hydrodynamic method.” Coastal Eng. 88 (Jun): 88–100. https://doi.org/10.1016/j.coastaleng.2014.02.006.
Ren, B., H. Wen, P. Dong, and Y. Wang. 2016. “Improved SPH simulation of wave motions and turbulent flows through porous media.” Coastal Eng. 107 (Jan): 14–27. https://doi.org/10.1016/j.coastaleng.2015.10.004.
Roberts, H. H., S. P. Murray, and J. N. Suhayda. 1975. “Physical process in a fringing reef system.” J. Mar. Res. 33 (2): 233–260.
Roeber, V., and J. D. Bricker. 2015. “Destructive tsunami-like wave generated by surf beat over a coral reef during typhoon haiyan.” Nat. Commun. 6 (Aug): 7854. https://doi.org/10.1038/ncomms8854.
Roeber, V., and K. F. Cheung. 2012. “Boussinesq-type model for energetic breaking waves in fringing reef environments.” Coastal Eng. 70 (Dec): 1–20. https://doi.org/10.1016/j.coastaleng.2012.06.001.
Schäffer, H. A., P. A. Madsen, and R. Deigaard. 1993. “A Boussinesq model for waves breaking in shallow water.” Coastal Eng. 20 (3–4): 185–202. https://doi.org/10.1016/0378-3839(93)90001-O.
Seelig, W. N. 1983. “Laboratory study of reef-lagoon system hydraulics.” J. Waterw. Port Coastal Ocean Eng. 109 (4): 380–391. https://doi.org/10.1061/(ASCE)0733-950X(1983)109:4(380).
Shao, S., and H. Gotoh. 2004. “Simulating coupled motion of progressive wave and floating curtain wall by SPH-LES model.” Coastal Eng. J. 46 (2): 171–202. https://doi.org/10.1142/S0578563404001026.
Shao, S., and C. Ji. 2006. “SPH computation of plunging waves using a 2-D sub-particle scale (SPS) turbulence model.” Int. J. Numer. Methods Fluids 51 (8): 913–936. https://doi.org/10.1002/fld.1165.
Shi, Y., S. Li, H. Chen, M. He, and S. Shao. 2018. “Improved SPH simulation of spilled oil contained by flexible floating boom under wave–current coupling condition.” J. Fluids Struct. 76 (Jan): 272–300. https://doi.org/10.1016/j.jfluidstructs.2017.09.014.
Shi, H., X. Yu, and R. A. Dalrymple. 2017. “Development of a two-phase SPH model for sediment laden flows.” Comput. Phys. Commun. 221 (Dec): 259–272. https://doi.org/10.1016/j.cpc.2017.08.024.
Skotner, C., and C. J. Apelt. 1999. “Application of a Boussinesq model for the computation of breaking waves: Part 2: Wave-induced setdown and setup on a submerged coral reef.” Ocean Eng. 26 (10): 927–947. https://doi.org/10.1016/S0029-8018(98)00062-6.
Sun, P., F. Ming, and A. Zhang. 2015. “Numerical simulation of interactions between free surface and rigid body using a robust SPH method.” Ocean Eng. 98 (Apr): 32–49. https://doi.org/10.1016/j.oceaneng.2015.01.019.
Symonds, G., K. P. Black, and I. R. Young. 1995. “Wave-driven flow over shallow reefs.” J. Geophys. Res. C Oceans 100 (C2): 2639–2648. https://doi.org/10.1029/94JC02736.
Taebi, S., R. J. Lowe, C. B. Pattiaratchi, G. N. Ivey, G. Symonds, and R. Brinkman. 2011. “Nearshore circulation in a tropical fringing reef system.” J. Geophys. Res. C Oceans 116 (C2): C02016. https://doi.org/10.1029/2010JC006439.
Valdez-Balderas, D., J. M. Domínguez, B. D. Rogers, and A. J. C. Crespo. 2013. “Towards accelerating smoothed particle hydrodynamics simulations for free-surface flows on multi-GPU clusters.” J. Parallel Distrib. Comput. 73 (11): 1483–1493. https://doi.org/10.1016/j.jpdc.2012.07.010.
Wendland, H. 1995. “Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree.” Adv. Comput. Math. 4 (1): 389–396. https://doi.org/10.1007/BF02123482.
Wen, H., and B. Ren. 2018. “A non-reflective spectral wave maker for SPH modeling of nonlinear wave motion.” Wave Motion 79 (Jun): 112–128. https://doi.org/10.1016/j.wavemoti.2018.03.003.
Wen, H., B. Ren, P. Dong, and Y. Wang. 2016. “A SPH numerical wave basin for modeling wave-structure interactions.” Appl. Ocean Res. 59 (Sep): 366–377. https://doi.org/10.1016/j.apor.2016.06.012.
Wen, H., B. Ren, and X. Yu. 2018. “An improved SPH model for turbulent hydrodynamics of a 2D oscillating water chamber.” Ocean Eng. 150 (Feb): 152–166. https://doi.org/10.1016/j.oceaneng.2017.12.047.
Yao, Y., Z. Huang, S. G. Monismith, and E. Y. Lo. 2012. “1DH Boussinesq modeling of wave transformation over fringing reefs.” Ocean Eng. 47 (Jun): 30–42. https://doi.org/10.1016/j.oceaneng.2012.03.010.
Information & Authors
Information
Published In
Copyright
© 2018 American Society of Civil Engineers.
History
Received: Dec 7, 2017
Accepted: May 25, 2018
Published online: Sep 21, 2018
Published in print: Jan 1, 2019
Discussion open until: Feb 21, 2019
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.