A second-order solution of waves passing porous structures

Lee, Jaw Fang; Lan, Yuan–Jyh

doi:10.1016/0029-8018(95)00024-0

Cited by 10 publications

(19 citation statements)

References 6 publications

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“…The results of this study closely correlate with those of Lee and Lan [6], with the only discrepancy found in the linear reflection coefficient. Next, the proposed numerical model's accuracy is confirmed by reanalyzing the linear problem by the method of matched eigenfunction expansion, as used by Lee and Lan [6]. The analytical solutions, plotted in Figure 2, closely correlate with the BEM solutions.…”

Section: Numerical Results and Discussionsupporting

confidence: 91%

“…). This figure also compares numerical results in this study with points taken from analytical results of Lee and Lan [6]. The results of this study closely correlate with those of Lee and Lan [6], with the only discrepancy found in the linear reflection coefficient.…”

Section: Numerical Results and Discussionsupporting

confidence: 89%

“…Therefore, the proposed numerical model's accuracy is verified. Reasons for the discrepancy between this study and Lee and Lan [6] still remain unknown. This study also considers two different wave steepnesses, H/L = 0.01 and 0.02, and two different porous structural properties (Table I).…”

Section: Numerical Results and Discussioncontrasting

confidence: 60%

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Numerical solution for the second-order wave interaction with porous structures

Hsu

1999

Int. J. Numer. Meth. Fluids

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This study mathematically formulates the fluid field of a water-wave interaction with a porous structure as a two-dimensional, non-linear boundary value problem (bvp) in terms of a generalized velocity potential. The non-linear bvp is reformulated into an infinite set of linear bvps of ascending order by Stokes perturbation technique, with wave steepness as the perturbation parameter. Only the first-and second-order linear bvps are retained in this study. Each linear bvp is transformed into a boundary integral equation. In addition, the boundary element method (BEM) with linear elements is developed and applied to solve the first-and second-order integral equations. The first-and second-order wave profiles, reflection and transmission coefficients, and the amplitude ratio of the second-order components are computed as well. The numerical results correlate well with previous analytical and experimental results. Numerical results demonstrate that the second-order component can be neglected for a deep water-wave and may become significant for an intermediate depth wave.

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Section: Numerical Results and Discussionsupporting

confidence: 91%

Section: Numerical Results and Discussionsupporting

confidence: 89%

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Numerical solution for the second-order wave interaction with porous structures

Hsu

1999

Int. J. Numer. Meth. Fluids

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“…This can also be found in [27] for wave motion over a submerged bottom-standing rectangular porous bar. Moreover, it can be found in [28] for wave motion over a series of submerged bottom-standing rectangular poro-elastic bars.…”

Section: Analytical Solutionsmentioning

confidence: 69%

An alternative analytical solution for water-wave motion over a submerged horizontal porous plate

Liu

2010

J Eng Math

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This study gives an alternative analytical solution for water-wave motion over an offshore submerged horizontal porous-plate breakwater in the context of linear potential theory. The matched-eigenfunction-expansions method is used to obtain the solution. The solution consists of a symmetric part and an antisymmetric part. The symmetric part is also the solution of wave reflection by a vertical solid wall with a submerged horizontal porous plate attached to it. In comparison with previous analytical solutions with respect to finite submerged horizontal porous plates, no complex water-wave dispersion relations are included in the present solution. Thus, the present solution is easier for numerical implementation. Numerical examples show that the convergence of the present solution is satisfactory. The results of the present solution also agree well with previous results by different analytical approaches, as well as previous numerical results by different boundary-element methods. The present solution can be easily extended to the case of multi-layer submerged horizontal porous plates, which may be more significant in practice for meeting different tide levels.

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“…Using a velocity potential decomposition method (constructing artificial velocity potentials), Lee and Liu (1995) developed an analytical solution for wave motion over a submerged porous rectangular bar. No complex dispersion relations were needed in their solution.…”

Section: Introductionmentioning

confidence: 99%

Wave reflection and transmission by porous breakwaters: A new analytical solution

Liu

2013

Coastal Engineering

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A second-order solution of waves passing porous structures

Cited by 10 publications

References 6 publications

Numerical solution for the second-order wave interaction with porous structures

Numerical solution for the second-order wave interaction with porous structures

An alternative analytical solution for water-wave motion over a submerged horizontal porous plate

Wave reflection and transmission by porous breakwaters: A new analytical solution

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