Un-Ryong Rim
ABSTRACT
Recently, Rim [16, 17] suggested an exact Dirichlet-to-Neumann (DtN) artificial boundary condition to study the three-dimensional wave diffraction for horizontally-unlimited water domain of finite-depth. This paper focuses on water wave motion over undulated seabed in front of a vertical wall. Horizontally semi-infinite water domain due to the vertical wall is transferred into a horizontally-infinite water domain by adopting the method of mirror image while the vertical wall is neglected and the imaginary undulated seabed of the original one about the wall is generated. An exact DtN boundary condition is derived on an artificial boundary which is chosen as a circular cylindrical surface so that it can enclose the original undulated seabed and its imaginary one, and it is used as a boundary condition to estimate water wave elevation in the interior subdomain numerically by using boundary integral equation. Upon validation of the present model through comparison with ANSYS AQWA in case of a circular paraboloidal shoal, the effects of incident wave angle and distance from the wall to the shoal with different submergence on wave elevation are considered.
- 2018. ANSYS AQWA, Release 19.2. ANSYS-Inc.Google Scholar
- D. Carevic, G. Loncar, and M. Prsic. 2013. Wave parameters after smooth submerged breakwater. Coast. Engng. 79 (2013), 32–41.Google ScholarCross Ref
- H. K. Chang and J. C. Liou. 2007. Long wave reflection from submerged trapezoidal breakwaters. Ocean Engng. 34 (2007), 185–191.Google ScholarCross Ref
- H. B. Chen, C. P. Tsai, and C. C. Jeng. 2007. Wave transformation between submerged breakwater and seawall. J. Coast. Res. 50 (2007), 1069–1074.Google Scholar
- R. Eatock Taylor, S. M. Hung, and F. P. Chau. 1989. On the distribution of second order pressure on a vertical circular cylinder. Appl. Ocean Res. 11(4) (1989), 183–193.Google Scholar
- R. L. Higdon. 1986. Absorbing boundary conditions for difference approximations to the multi-dimensional wave equation. Math. Comput. 47 (1986), 437–459.Google ScholarDigital Library
- R. L. Higdon. 1987. Numerical absorbing boundary conditions for the wave equation. Math. Comput. 49 (1987), 65–90.Google ScholarCross Ref
- S. S. Hsiao, C. M. Chang, and C. C. Wen. 2009. Solution for wave propagation through a circular cylinder mounted on different topography ripple-bed profile shoals using DRBEM. Engng. Anal. Bound. Elem. 33 (2009), 1246–1257.Google ScholarCross Ref
- H. H. Hsu and Y. C. Wu. 1997. The hydrodynamic coefficients for an oscillating rectangular structure on a free surface with sidewall. Ocean Engng. 24(2) (1997), 177–199.Google Scholar
- D. S. Jeng, C. Schacht, and C. Lemckert. 2005. Experimental study on ocean waves propagating over a submerged breakwater in front of a vertical seawall. Ocean Engng. 32(17) (2005), 2231–2240.Google Scholar
- S. Koley, H. Behera, and T. Sahoo. 2014. Oblique wave trapping by porous structures near a wall. J. Engng. Mech. 141(3) (2014), 04014122.Google Scholar
- Z. P. Liao. 1996. Extrapolation non-reflecting boundary conditions. Wave Motion 24 (1996), 117–138.Google ScholarCross Ref
- H. W. Liu, Q. B. Chen, and J. J. Xie. 2017. Analytical benchmark for linear wave scattering by a submerged circular shoal in the water from shallow to deep. Ocean Engng. 146 (2017), 29–45.Google ScholarCross Ref
- H. W. Liu, P. Lin, and N. J. Shankar. 2004. An analytical solution of the mild-slope equation for waves around a circular island on a paraboloidal shoal. Coast. Engng. 51 (2004), 421–437.Google ScholarCross Ref
- M. G. Reddy and S. Neelamani. 2005. Hydrodynamic studies on vertical seawall defenced by low-crested breakwater. Ocean Engng. 32(5) (2005), 747–764.Google Scholar
- U. R. Rim. [n. d.]. Wave interaction with multiple bodies bottom-mounted on an undulated seabed using an exact. ([n. d.]).Google Scholar
- U. R. Rim. 2021. Wave diffraction by floating bodies in water of finite depth using an exact DtN boundary condition. Ocean Engng. (2021).Google Scholar
- U. R. Rim, G. H. Choe, N. H. Ri, M. H. Jon, W. S. Pae, and U. H. Han. 2023. An exact DtN artificial boundary condition for motion analysis of water wave with undulated seabed. Wave Motion 116 (2023), 103063. https://doi.org/10.1016/j.wavemoti.2022.103063Google ScholarCross Ref
- U. R. Rim, Y. G. Ri, W. C. Do, P. S. Dong, C. W. Kim, and J. S. Kim. [n. d.]. Wave diffraction and radiation by a fully-submerged body in front of a vertical wall by using an exact. ([n. d.]).Google Scholar
- Y. L. Shao and O. M. Faltinsen. 2010. Use of body-fixed coordinate system in analysis of weakly nonlinear wave–body problems. Appl. Ocean Res. 32 (2010), 20–33.Google ScholarCross Ref
- C. P. Tsai, C. H. Yu, H. B. Chen, and H. Y. Chen. 2012. Wave height transformation and set-up between a submerged permeable breakwater and a seawall. China Ocean Engng. 26 (2012), 167–176.Google ScholarCross Ref
- Y. T. Wu and S. C. Hsiao. 2013. Propagation of solitary waves over a submerged permeable breakwater. Coast. Engng. 81 (2013), 1–18.Google ScholarCross Ref
- G. Xu and W. Y. Duan. 2013. Time-domain simulation of wave–structure interaction based on multi-transmitting formula coupled with damping zone method for radiation boundary condition. Appl. Ocean Res. 42 (2013), 136–143.Google ScholarCross Ref
- Z. Yang, L. Yong, and L. Huajun. 2016. Wave Interaction with a Partially Reflecting Vertical Wall Protected by a Submerged Porous Bar. J. Ocean Univ. China 15(4) (2016), 619–626.Google Scholar
- Z. Yang, L. Yong, L. Huajun, and C. Anteng. 2017. Oblique Wave Motion over Multiple Submerged Porous Bars near a Vertical Wall. J. Ocean Univ. China 16(4) (2017), 568–574.Google Scholar
- X. Yu and B. Zhang. 2003. An extended analytic solution for combined refraction and diffraction of long waves over circular shoals. Ocean Engng. 30 (2003), 1253–1267.Google ScholarCross Ref
- Y. H. Zheng, Y. M. Shen, and J. Tang. 2007. Radiation and diffraction of linear water waves by an infinitely long submerged rectangular structure parallel to a vertical wall. Ocean Engng. 34(1) (2007), 69–82.Google Scholar
Index Terms
- Numerical simulation for water wave motion over undulated seabed in front of a vertical wall by using an exact DtN boundary condition
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