Semi-implicit non-hydrostatic model for 2D nonlinear wave interaction with a floating/suspended structure. (English) Zbl 1408.76060
Summary: A non-hydrostatic model is developed to simulate two-dimensional (2D) nonlinear wave interaction with a fixed floating/suspended structure. The immersed boundary method is incorporated in the model to address arbitrary body surfaces. The model employs a semi-implicit, fractional step algorithm to solve the Reynolds-averaged Navier-Stokes (RANS) equations based on a grid system, which is built from a horizontal rectangular grid by adding dozens of horizontal layers. The horizontal layers are distributed following a general boundary-fitted vertical coordinate system. This grid system may overcome the lack of flexibility of other boundary-fitted coordinate systems (e.g., the \(\sigma\)-coordinate system). The model is validated by using three test cases, namely, a solitary wave interacting with a floating rectangular obstacle, a solitary wave incident on a suspended horizontal plate and a solitary wave incident on a coastal-bridge deck with girders. Numerical results of the free surface elevation and wave force exerted on each structure are compared with the results of other models or experimental data. Generally, good agreements are obtained, demonstrating the proposed model’s capability to resolve nonlinear wave interactions with floating/suspended structures. The velocity fields around the structures are also presented and discussed.
MSC:
| 76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
Keywords:
non-hydrostatic model; wave-structure interaction; floating structure; suspended horizontal plate; coastal bridgeReferences:
| [1] | Zhao, M.; Cheng, L.; Teng, B., Numerical simulation of solitary wave scattering by a circular cylinder array, Ocean Eng., 34, 489-499, (2007) |
| [2] | Zhong, Z.; Wang, K., Modeling fully nonlinear shallow-water waves and their interactions with cylindrical structures, Comput. & Fluids, 38, 1018-1025, (2009) · Zbl 1159.76024 |
| [3] | Wang, C.; Wu, G., Interactions between fully nonlinear water waves and cylinder arrays in a wave tank, Ocean Eng., 37, 400-417, (2010) |
| [4] | Zhou, B.; Ning, D.; Teng, B.; Bai, W., Numerical investigation of wave radiation by a vertical cylinder using a fully nonlinear HOBEM, Ocean Eng., 70, 1-13, (2013) |
| [5] | Ai, C.; Jin, S., Non-hydrostatic finite volume model for non-linear waves interacting with structures, Comput. & Fluids, 39, 2090-2100, (2010) · Zbl 1245.76062 |
| [6] | Choi, D. Y.; Yuan, H., A horizontally curvilinear non-hydrostatic model for simulating nonlinear wave motion in curved boundaries, Int. J. Numer. Meth. Fluids., 69, 1923-1938, (2012) |
| [7] | Ai, C.; Ding, W.; Jin, S., A hybrid-grid 3D model for regular waves interacting with cylinders, J.Hydraul. Res., 55, 129-134, (2017) |
| [8] | Lin, P.; Cheng, L.; Liu, D., A two-phase flow model for wave-structure interaction using a virtual boundary force method, Comput. & Fluids, 129, 101-110, (2016) · Zbl 1390.76059 |
| [9] | Xie, Z.; Lu, L.; Stoesser, T.; Lin, J.; Pavlidis, D.; Salinas, P.; Pain, C. C.; Matar, O., Numerical simulation of three-dimensional breaking waves and its interaction with a vertical circular cylinder, J. Hydrodyn., 29, 800-804, (2017) |
| [10] | Yan, S.; Ma, Q., Numerical simulation of fully nonlinear interaction between steep waves and 2D floating bodies using the QALE-FEM method, J.Comput. Phys., 221, 666-692, (2007) · Zbl 1216.76038 |
| [11] | Ma, Q.; Yan, S., QALE FEM for numerical modelling of non linear interaction between 3D moored floating bodies and steep waves, Int.J. Numer. Methods Eng., 78, 713-756, (2009) · Zbl 1183.76811 |
| [12] | Liu, C.; Huang, Z.; Tan, S. K., Nonlinear scattering of non-breaking waves by a submerged horizontal plate: experiments and simulations, Ocean Eng., 36, 1332-1345, (2009) |
| [13] | Bai, W.; Eatock Taylor, R., Fully nonlinear simulation of wave interaction with fixed and floating flared structures, Ocean Eng., 36, 223-236, (2009) |
| [14] | Bai, W.; Hannan, M. A.; Ang, K. K., Numerical simulation of fully nonlinear wave interaction with submerged structures: fixed or subjected to constrained motion, J. Fluids Struct., 49, 534-553, (2014) |
| [15] | Hayatdavoodi, M.; Ertekin, R. C., Wave forces on a submerged horizontal plate-part I: theory and modelling, J. Fluids Struct., 54, 566-579, (2015) |
| [16] | Hayatdavoodi, M.; Ertekin, R. C., Wave forces on a submerged horizontal plate-part II: solitary and cnoidal waves, J. Fluids Struct., 54, 580-596, (2015) |
| [17] | Xiao, H.; Huang, W.; Chen, Q., Effects of submersion depth on wave uplift force acting on biloxi bay bridge decks during hurricane katrina, Comput. & Fluids, 39, 1390-1400, (2010) · Zbl 1242.76048 |
| [18] | Lo, H.-Y.; Liu, P. L.-F., Solitary waves incident on a submerged horizontal plate, J. Waterway, Port, Coastal, Ocean Eng., 140, 04014009, (2014) |
| [19] | Hayatdavoodi, M.; Seiffert, B.; Ertekin, R. C., Experiments and computations of solitary-wave forces on a coastal-bridge deck. part II: deck with girders, Coastal Eng., 88, 210-228, (2014) |
| [20] | Seiffert, B.; Hayatdavoodi, M.; Ertekin, R. C., Experiments and computations of solitary-wave forces on a coastal-bridge deck. part I: flat plate, Coastal Eng., 88, 194-209, (2014) |
| [21] | Hayatdavoodi, M.; Seiffert, B.; Ertekin, R. C., Experiments and calculations of cnoidal wave loads on a flat plate in shallow-water, J. Ocean Eng. Mar. Energy., 1, 77-99, (2015) |
| [22] | Seiffert, B. R.; Ertekin, R. C.; Robertson, I. N., Wave loads on a coastal bridge deck and the role of entrapped air, Appl. Ocean Res., 53, 91-106, (2015) |
| [23] | Seiffert, B. R.; Hayatdavoodi, M.; Ertekin, R. C., Experiments and calculations of cnoidal wave loads on a coastal-bridge deck with girders, Eur. J. Mech. B Fluids., 52, 191-205, (2015) |
| [24] | Hu, Z. Z.; Greaves, D.; Raby, A., Numerical wave tank study of extreme waves and wave-structure interaction using openfoam, Ocean Eng., 126, 329-342, (2016) |
| [25] | Sarfaraz, M.; Pak, A., SPH numerical simulation of tsunami wave forces impinged on bridge superstructures, Coastal Eng., 121, 145-157, (2017) |
| [26] | Ai, C.; Jin, S.; Lv, B., A new fully nonhydrostatic 3D free surface flow model for water wave motions, Int.J. Numer. Meth. Fluids., 66, 1354-1370, (2011) · Zbl 1419.76075 |
| [27] | Zijlema, M.; Stelling, G.; Smit, P., SWASH: an operational public domain code for simulating wave fields and rapidly varied flows in coastal waters, Coastal Eng., 58, 992-1012, (2011) |
| [28] | Ai, C.; Jin, S., A multi-layer non-hydrostatic model for wave breaking and run-up, Coastal Eng., 62, 1-8, (2012) |
| [29] | Ma, G.; Shi, F.; Kirby, J. T., Shock-capturing non-hydrostatic model for fully dispersive surface wave processes, Ocean Model., 43, 22-35, (2012) |
| [30] | Ai, C.; Ding, W.; Jin, S., A general boundary-fitted 3D non-hydrostatic model for nonlinear focusing wave groups, Ocean Eng., 89, 134-145, (2014) |
| [31] | Matsumura, Y.; Hasumi, H., A non-hydrostatic Ocean model with a scalable multigrid Poisson solver, Ocean Model., 24, 15-28, (2008) |
| [32] | Lai, Z.; Chen, C.; Cowles, G. W.; Beardsley, R. C., A nonhydrostatic version of FVCOM: 1. validation experiments, J. Geophys. Res., 115, (2010) |
| [33] | Vitousek, S.; Fringer, O. B.; nonhydrostatic, A., Isopycnal-coordinate Ocean model for internal waves, Ocean Model., 83, 118-144, (2014) |
| [34] | Ai, C.; Ding, W., A 3D unstructured non-hydrostatic Ocean model for internal waves, Ocean Dyn., 66, 1253-1270, (2016) |
| [35] | Lin, P., A multiple-layer \(\sigma\)-coordinate model for simulation of wave-structure interaction, Comput. & Fluids, 35, 147-167, (2006) · Zbl 1160.76323 |
| [36] | Kang, A.; Lin, P.; Lee, Y. J.; Zhu, B., Numerical simulation of wave interaction with vertical circular cylinders of different submergences using immersed boundary method, Comput. & Fluids, 106, 41-53, (2015) · Zbl 1390.76581 |
| [37] | Ma, G.; Farahani, A. A.; Kirby, J. T.; Shi, F., Modeling wave-structure interactions by an immersed boundary method in a \(\sigma\)-coordinate model, Ocean Eng., 125, 238-247, (2016) |
| [38] | Rijnsdorp, D. P.; Zijlema, M., Simulating waves and their interactions with a restrained ship using a non-hydrostatic wave-flow model, Coastal Eng., 114, 119-136, (2016) |
| [39] | Smagorinsky, J., General circulation experiments with the primitive equations: I. the basic experiment, Mon. Weather Rev., 91, 99-164, (1963) |
| [40] | Zijlema, M.; Stelling, G. S., Further experiences with computing non-hydrostatic free-surface flows involving water waves, Int. J. Numer. Meth. Fluids., 48, 169-197, (2005) · Zbl 1064.76075 |
| [41] | Fadlun, E.; Verzicco, R.; Orlandi, P.; Mohd-Yusof, J., Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations, J. Comput. Phys., 161, 35-60, (2000) · Zbl 0972.76073 |
| [42] | Baker, A. H.; Jessup, E. R.; Manteuffel, T., A technique for accelerating the convergence of restarted GMRES, SIAM J. Matrix Anal., 26, 962-984, (2005) · Zbl 1086.65025 |
| [43] | Hsu, T.-J.; Sakakiyama, T.; Liu, P. L.-F., A numerical model for wave motions and turbulence flows in front of a composite breakwater, Coastal Eng., 46, 25-50, (2002) |
| [44] | Losada, I. J.; Lara, J. L.; Guanche, R.; Gonzalez-Ondina, J. M., Numerical analysis of wave overtopping of rubble mound breakwaters, Coastal Eng., 55, 47-62, (2008) |
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