The present paper aims at getting the porous effect parameter G of a thin permeable wall. The reflection and transmission coefficients of a thin vertical porous wall with different porous shapes an...

Porous effect parameter of thin permeable plates

This short communication presents the Singular Boundary Method (SBM) to solve the obliquely incident water wave passing through the submerged breakwater. The SBM is a recent boundary-type collocation method with the merits of being meshless, integration-free, mathematically simple, easy-to-program, well suited for unbounded domain problems. The accuracy and efficiency of the SBM is first verified in several benchmark examples in comparison with the boundary element method. Then the effects of the position, size and geometry of the breakwater on water wave propagation are investigated through numerical experiments, and some new observations are concluded.

Numerical investigation on the obliquely incident water wave passing through the submerged breakwater by singular boundary method

This study develops a full solution for water wave reflection by a partially perforated caisson breakwater with a rubble mound foundation using multi-domain BEM (boundary element method). Regular and irregular waves are both considered. A quadratic pressure drop condition on caisson perforated wall is adopted, and direct iterative calculations are performed. Due to the use of quadratic pressure drop condition, the effect of wave height on the energy dissipation by the perforated wall is well considered. This study also develops an iterative analytical solution for wave reflection by a partially perforated caisson breakwater on flat bottom using matched eigenfunction expansion method. The reflection coefficients calculated by the multi-domain BEM solution and the analytical solution are in excellent agreement. The present calculated results also agree reasonably well with experimental data from different literatures. Suitable values of discharge coefficient and blockage coefficient in the quadratic pressure drop condition are recommended for perforated caissons. The effects of the wave steepness, the blockage coefficient of perforated wall and the relative wave chamber width on the reflection coefficient are clarified. The present BEM solution is simple and reliable. It may be used for predicting the reflection coefficients of perforated caisson breakwaters in preliminary engineering design.

Iterative multi-domain BEM solution for water wave reflection by perforated caisson breakwaters

https://msvlab.hre.ntou.edu.tw/oe2011-Liu.pdf

Wave interaction with a wave absorbing double curtain-wall breakwater

Dual boundary integral equation (BIE) was developed for problems containing degenerate boundaries in 1988 by Hong and Chen [Journal of Engineering Mechanics-ASCE, 114, 6, 1988] and was termed the dual boundary element method (BEM) in 1992 by Portela et al. [International Journal for Numerical Methods in Engineering, 33, 6, 1992]. After near 30 years, the dual BIE/BEM for the problem containing a zero-thickness barrier was revisited mathematically to study the rank deficiency from the viewpoint of the updating term and the updating document of singular value decomposition (SVD) [Journal of Mechanics, 31, 5, 2015]. In this paper, we revisit the dual BEM from the physical point of view. Although there is no zero-thickness barrier in the real world, it is always required to simulate a finite-thickness degenerate boundary to be zero-thickness in comparison with sea, air or earth scale. For example, a sheet pile, a screen, a crack problem, a thin airfoil and a breakwater were modeled by the geometry of zero-thickness. The role of the dual BEM is evident since Lafe et al. [Journal of the Hydraulics Division-ASCE, 106, 6, 1980] used the conventional BEM to model the finite-thickness pile wall to geometrically approximate zero-thickness barrier but numerically yielding divergent solution. On the contrary, we physically model the finite-thickness breakwater as a zero-thickness barrier. The breakwater is employed as an illustrative case to demonstrate that the dual BEM simulated by a zero-thickness barrier can yield more acceptable results to match the experiment data in comparison with those of the finite thickness using the conventional BEM. Finally, a single horizontal plate and two dual horizontal plates in vertical direction and in horizontal direction are three illustrative cases to tell you why the dual BEM is necessary not only in mathematics but also in physics.

Why dual boundary element method is necessary

In this paper, the dual integral formulation is derived for solving the scattering problem of normal incident wave passing a thin vertical and inclined barrier with rigid boundary condition which is descending from the water surface to a depth. Absorbing and porous boundary conditions are both considered. The breakwater thickness is assumed to be zero since it is negligible in comparison with the water depth and the wavelength of the incident wave. Although the multidomain boundary element method (BEM) can solve boundary value problems with degenerate boundaries by dividing the interesting domain into two subdomains, the hypersingular formulation provides the key to solve the problem more efficiently in a single domain. To demonstrate the effects of the breakwater with rigid, absorbing, and porous boundary conditions for the energy dissipation by the barrier, the transmission and reflection coefficients of the scattering problem are determined by the developed dual BEM program. In addition, the results are obtained for the cases of wave scattering by the barrier with zero thickness in constant water depth and are compared with the analytical solutions, the multidomain BEM solution, and the experimental data.

Sheng-Yih Lin

Papers

Dual Boundary Element Analysis of Normal Incident Wave Passing a Thin Submerged Breakwater with Rigid, Absorbing, and Permeable Boundaries