Meshless Method with Domain Decomposition for Submerged Porous Breakwaters in Waves

Abstract

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.