In the present work, the improved version of the meshless singular boundary method(ISBM) is developed for analyzing the performance of bottom standing submerged permeable breakwaters in regular normally incident waves...In the present work, the improved version of the meshless singular boundary method(ISBM) is developed for analyzing the performance of bottom standing submerged permeable breakwaters in regular normally incident waves and in the proximity of a vertical wall. Both single and dual prismatic breakwaters of rectangular and trapezoidal forms are examined. The physical problem is cast in terms of the Laplace equation governing an irrotational flow and incompressible fluid motion with appropriate mixed type boundary conditions, and solved numerically using the ISBM. To model the permeability of the breakwaters fully absorbing boundary conditions are assumed. Numerical results are presented in terms of hydrodynamic quantities of the reflection coefficients. These are firstly validated against the results of a multi-domain boundary element method(BEM) developed independently for a previous study. The agreement between the results of the two methods is excellent. The coefficients of reflection are then computed and discussed for a variety of structural conditions including the breakwaters height, width, spacing, and absorbing permeability. Effects of the proximity of the vertical plane wall are also investigated. The breakwater's width is found to have only marginal effects compared with its height. Permeability tends to decrease the minimum reflections. These coefficients show periodic variations with the spacing relative to the wavelength. Trapezoidal breakwaters are found to be more cost-effective than the rectangular breakwaters. Dual breakwater systems are confirmed to perform much better than single structures.展开更多
Based on the improved version of the meshless singular boundary method(ISBM)in multi domain(MD),a numerical method is proposed in this paper to study the interaction of submerged permeable breakwaters and regular wave...Based on the improved version of the meshless singular boundary method(ISBM)in multi domain(MD),a numerical method is proposed in this paper to study the interaction of submerged permeable breakwaters and regular waves at normal incidence.To account for fluid flow inside the porous breakwaters,the conventional model of Sollitt and Cross for porous media is adopted.Both single and dual trapezoidal breakwaters are examined.The physical problem is formulated in the context of the linear potential wave theory.The domain decomposition method(DDM)is employed,in which the full computational domain is decomposed into separate domains,that is,the fluid domain and the domains of the breakwaters.Respectively,appropriate mixed type boundary and continuity conditions are applied for each subdomain and at the interfaces between domains.The solution is approximated in each subdomain by the ISBM.The discretized algebraic equations are combined,resulting in an overdetermined full system that is solved using a least-square solution procedure.The numerical results are presented in terms of the hydrodynamic quantities of reflection,transmission,and wave-energy dissipation.The relevance of the results of the present numerical procedure is first validated against data of previous studies,and then selected computations are discussed for various structural conditions.The proposed method is demonstrated to be highly accurate and computationally efficient.展开更多
基金financially supported by the Direction Général des Enseignements et de la Formation Supérieure of Algeria(Grant CNEPRU No.G0301920140029)
文摘In the present work, the improved version of the meshless singular boundary method(ISBM) is developed for analyzing the performance of bottom standing submerged permeable breakwaters in regular normally incident waves and in the proximity of a vertical wall. Both single and dual prismatic breakwaters of rectangular and trapezoidal forms are examined. The physical problem is cast in terms of the Laplace equation governing an irrotational flow and incompressible fluid motion with appropriate mixed type boundary conditions, and solved numerically using the ISBM. To model the permeability of the breakwaters fully absorbing boundary conditions are assumed. Numerical results are presented in terms of hydrodynamic quantities of the reflection coefficients. These are firstly validated against the results of a multi-domain boundary element method(BEM) developed independently for a previous study. The agreement between the results of the two methods is excellent. The coefficients of reflection are then computed and discussed for a variety of structural conditions including the breakwaters height, width, spacing, and absorbing permeability. Effects of the proximity of the vertical plane wall are also investigated. The breakwater's width is found to have only marginal effects compared with its height. Permeability tends to decrease the minimum reflections. These coefficients show periodic variations with the spacing relative to the wavelength. Trapezoidal breakwaters are found to be more cost-effective than the rectangular breakwaters. Dual breakwater systems are confirmed to perform much better than single structures.
基金the Ministry of Higher Edu-cation and Scientific Research of Algeria(grant PRFU number A01L06UN310220200002).
文摘Based on the improved version of the meshless singular boundary method(ISBM)in multi domain(MD),a numerical method is proposed in this paper to study the interaction of submerged permeable breakwaters and regular waves at normal incidence.To account for fluid flow inside the porous breakwaters,the conventional model of Sollitt and Cross for porous media is adopted.Both single and dual trapezoidal breakwaters are examined.The physical problem is formulated in the context of the linear potential wave theory.The domain decomposition method(DDM)is employed,in which the full computational domain is decomposed into separate domains,that is,the fluid domain and the domains of the breakwaters.Respectively,appropriate mixed type boundary and continuity conditions are applied for each subdomain and at the interfaces between domains.The solution is approximated in each subdomain by the ISBM.The discretized algebraic equations are combined,resulting in an overdetermined full system that is solved using a least-square solution procedure.The numerical results are presented in terms of the hydrodynamic quantities of reflection,transmission,and wave-energy dissipation.The relevance of the results of the present numerical procedure is first validated against data of previous studies,and then selected computations are discussed for various structural conditions.The proposed method is demonstrated to be highly accurate and computationally efficient.
