The Method of Fundamental Solutions for Water-Wave Diffraction by Thin Porous Breakwater

Tsai, Chia-Cheng; Young, D. L.

doi:10.1017/jmech.2011.16

Cited by 14 publications

(3 citation statements)

References 14 publications

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“…Scattering problems involving porous breakwater were studied by many researchers using various sophisticated mathematical techniques. Among them the works of Yu [6], Mclver [7], Evans and Peter [8], Tsai and Young [9] may be mentioned. Recently Gayen and Mandal [10] used second kind hypersingular integral equation formulation to study the problem of wave scattering by a submerged porous plate in ocean with free surface.…”

Section: Introductionmentioning

confidence: 99%

Scattering of water waves by a porous circular arc-shaped barrier submerged in ocean

Mondal¹,

Banerjea²

2016

Int. J. CMEM

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In this paper, we study the problem of scattering of surface water waves by a thin circular arc shaped porous plate submerged in the deep ocean. The problem is formulated in terms of a hypersingular integral equation of the second kind in terms of an unknown function representing the difference of potential function across the curved barrier. The hypersingular integral equation is then solved by a collocation method after expanding the unknown function in terms of Chebyshev polynomials of the second kind. Using the solution of the hyper-singular integral equation, the reflection coefficient, transmission coefficient and energy dissipation coefficient are computed and depicted graphically against the wave number. Known results for the rigid curved barrier are recovered. It is observed that the porosity of the barrier reduces the reflection and transmission of the waves and enhances the dissipation of wave energy. The reflection coefficient and dissipation of wave energy decreases as the length of the porous curved barrier increases. Also the reflection coefficient is almost independent of the inertial force coefficient of the material of the porous barrier. However, the inertial force coefficient of the material of the porous barrier enhances transmission and reduces dissipation of wave energy.

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Section: Introductionmentioning

confidence: 99%

Scattering of water waves by a porous circular arc-shaped barrier submerged in ocean

Mondal¹,

Banerjea²

2016

Int. J. CMEM

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“…In order to avoid the mesh generation and numerical integration, many meshless methods are proposed recently, such as the MFS [3,6,[13][14][15][16], the radial basis function collocation methods [17][18][19], the MCTM [20][21][22][23][24][25], etc. For the current problem, since positions of some boundary points are unknown, it is then nature for us to adopt the boundary-type meshless scheme to solve the problem.…”

Section: Introductionmentioning

confidence: 99%

The Modified Collocation Trefftz Method and Exponentially Convergent Scalar Homotopy Algorithm for the Inverse Boundary Determination Problem for the Biharmonic Equation

Chan

Fan

2013

J. mech.

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In this paper, the modified collocation Trefftz method (MCTM) and the exponentially convergent scalar homotopy algorithm (ECSHA) are adopted to analyze the inverse boundary determination problem governed by the biharmonic equation. The position for part of the boundary with given boundary condition is unknown and the position for the rest of the boundary with overspecified Cauchy boundary conditions is given a priori. Since the spatial position for portion of boundary is not given a priori, it is extremely difficult to solve such a boundary determination problem by any numerical scheme. In order to stably solve the boundary determination problem, the MCTM will be adopted in this study owing to that it can avoid the generation of mesh grid and numerical integration. When this problem is modeled by MCTM, a system of nonlinear algebraic equations will be formed and then be solved by ECSHA. Some numerical examples will be provided to demonstrate the ability and accuracy of the proposed scheme. In addition, the stability of the proposed meshless method will be tested by adding some noise into the prescribed boundary conditions and then to see how does that affect the numerical results.

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“…The first theoretical model on water wave interaction with permeable barriers was presented by Sollitt and Cross [26]. Later several semi-analytical and numerical studies were made on the problem of scattering of water waves by various kinds of permeable barriers (see [4,17,27]). Employing Green's integral theorem to suitable Green's function and potential function, Gayen and Mondal [12] solved the problem of water wave scattering by vertical and inclined permeable plates by reducing it into a second kind hypersingular integral equation.…”

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confidence: 99%

Water Wave Scattering by a Thin Vertical Submerged Permeable Plate

Gayen

Gupta

Chakrabarti

2021

Mathematical Modelling and Analysis

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An alternative approach is proposed here to investigate the problem of scattering of surface water waves by a vertical permeable plate submerged in deep water within the framework of linear water wave theory. Using Havelock’s expansion of water wave potential, the associated boundary value problem is reduced to a second kind hypersingular integral equation of order 2. The unknown function of the hypersingular integral equation is expressed as a product of a suitable weight function and an unknown polynomial. The associated hypersingular integral of order 2 is evaluated by representing it as the derivative of a singular integral of the Cauchy type which is computed by employing an idea explained in Gakhov’s book [7]. The values of the reflection coefficient computed with the help of present method match exactly with the previous results available in the literature. The energy identity is derived using the Havelock’s theorems.

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The Method of Fundamental Solutions for Water-Wave Diffraction by Thin Porous Breakwater

Cited by 14 publications

References 14 publications

Scattering of water waves by a porous circular arc-shaped barrier submerged in ocean

Scattering of water waves by a porous circular arc-shaped barrier submerged in ocean

The Modified Collocation Trefftz Method and Exponentially Convergent Scalar Homotopy Algorithm for the Inverse Boundary Determination Problem for the Biharmonic Equation

Water Wave Scattering by a Thin Vertical Submerged Permeable Plate

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