Accurate Solutions to Water Wave Scattering by Vertical Thin Porous Barriers

Li, Aijun; Liu, Yong; Li, Huajun

doi:10.1155/2015/985731

Cited by 14 publications

(4 citation statements)

References 32 publications

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“…In Equation (10), φ consent to either φ m or φ m+1 , for the waterside of the barrier, and L w is the vertical intervals of the wall.…”

Section: Methodology 21 the Mathematical Modelmentioning

confidence: 99%

“…Das et al [7] studied the impact of multiple impermeable thin barriers on the scattering of water waves. To further dissipate wave energy, the issues of permeable structures that are thin barriers have been studied [8][9][10][11]. By solving integral equations, Macaskill [12] considered waves scattered by a single permeable barrier at a finite water depth.…”

Section: Introductionmentioning

confidence: 99%

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Bragg Resonance of Water Waves by Multiple Permeable Thin Barriers over Periodic Breakwaters

Tran¹,

Lin

Tsai

2023

Water

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In this study, the Bragg resonance of water waves scattered by multiple permeable thin barriers over a series of periodic breakwaters was solved by employing the eigenfunction matching method (EMM). The geometrical configuration was divided into multiple shelves separated by steps, on which thin permeable barriers were implemented. The solution was approximated using eigenfunctions with unknown coefficients that were considered as the amplitudes of the water waves for each shelf. The conservations of mass and momentum were then applied to form a system of linear equations, which was sequentially solved by a sparse-matrix solver. The proposed method degenerates to traditional EMM formulations if thin barriers, the permeability of the barrier, or bottom undulations are not considered. The validity of the suggested method was examined based on the results in the literature. Bragg resonances by bottom-standing, surface-piecing, and fully submerged permeable barriers over a series of periodic trapezoidal or half-cosine breakwaters were studied. In addition, the breakwater amplitudes, permeable parameters of the barriers, and incident angles of water wave scattering by different types of periodic breakwaters were discussed.

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“…In Equation (10), φ consent to either φ m or φ m+1 , for the waterside of the barrier, and L w is the vertical intervals of the wall.…”

Section: Methodology 21 the Mathematical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bragg Resonance of Water Waves by Multiple Permeable Thin Barriers over Periodic Breakwaters

Tran¹,

Lin

Tsai

2023

Water

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“…The water wave scattering by vertical thin porous barriers has been solved by Li et al [15] considering a surface piercing barrier and a submerged bottomstanding barrier using a multi-term Galerkin method. In recent times, Meng et al [24] presented a hybrid element-free Galerkin (HEFG) method for solving three dimensional wave propagation problem.…”

Section: Introductionmentioning

confidence: 99%

Use of Galerkin Technique to the Rolling of a Plate in Deep Water

Ray

Mandal

2021

Mathematical Modelling and Analysis

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The classical problems of surface water waves produced by small oscillations of a thin vertical plate partially immersed as well as submerged in deep water are reinvestigated here. Each problem is reduced to an integral equation involving horizontal component of velocity across the vertical line outside the plate. The integral equations are solved numerically using Galerkin approximation in terms of simple polynomials multiplied by an appropriate weight function whose form is dictated by the behaviour of the fluid velocity near the edge(s) of the plate. Fairly accurate numerical estimates for the amplitude of the radiated wave at infinity due to rolling and also for swaying of the pate in each case are obtained and these are depicted graphically against the wave number for various cases.

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“…Earlier, Evans and Morris (1972), Evans and Fernyhough (1995), Porter and Evans (1995) used Galerkin approximation technique followed by Havelock's (1929) expansion of water wave potential to obtain numerical estimates for the reflection coefficient for oblique incidence of the wave train on a single vertical barrier in deep as well as finite depth water. Water wave scattering by vertical porous barriers was studied by Li et al (2015) considering both surface piercing barrier and submerged bottom-standing barrier using a multi-term Galerkin method. Meng et al (2018) considered a hybrid element-free Galerkin method for solving three-dimensional wave propagation problems.…”

Section: Introductionmentioning

confidence: 99%

Wave propagation over a rectangular trench in the presence of a partially immersed barrier

Ray

Mandal

2021

Fluid Dyn. Res.

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The problem of water wave propagation over a rectangular submarine trench in the presence of a thin vertical partially immersed barrier for its three different positions are investigated here assuming linear theory. For each position of the barrier, the problem is reduced to solving three weakly singular integral equations of first kind involving horizontal component of velocity above the two edges of the trench and below the barrier. The integral equations are solved employing Galerkin approximation in terms of simple polynomials multiplied by appropriate weight functions whose forms are dictated by the edge conditions at the corners of the trench and at the submerged end of the barrier. The numerical estimates for reflection and transmission coefficients are depicted graphically against the wave number for different lengths and positions of the barrier.

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Accurate Solutions to Water Wave Scattering by Vertical Thin Porous Barriers

Cited by 14 publications

References 32 publications

Bragg Resonance of Water Waves by Multiple Permeable Thin Barriers over Periodic Breakwaters

Bragg Resonance of Water Waves by Multiple Permeable Thin Barriers over Periodic Breakwaters

Use of Galerkin Technique to the Rolling of a Plate in Deep Water

Wave propagation over a rectangular trench in the presence of a partially immersed barrier

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