Development of An Integrated Numerical Model for Simulating Wave Interaction with Permeable Submerged Breakwaters Using Extended Navier–Stokes Equations

Abstract

An integrated two-dimensional vertical (2DV) model was developed to investigate wave interactions with permeable submerged breakwaters. The integrated model is capable of predicting the flow field in both surface water and porous media on the basis of the extended volume-averaged Reynolds-averaged Navier–Stokes equations (VARANS). The impact of porous medium was considered by the inclusion of the additional terms of drag and inertia forces into conventional Navier–Stokes equations. Finite volume method (FVM) in an arbitrary Lagrangian–Eulerian (ALE) formulation was adopted for discretization of the governing equations. Projection method was utilized to solve the unsteady incompressible extended Navier–Stokes equations. The time-dependent volume and surface porosities were calculated at each time step using the fraction of a grid open to water and the total porosity of porous medium. The numerical model was first verified against analytical solutions of small amplitude progressive Stokes wave and solitary wave propagation in the absence of a bottom-mounted barrier. Comparisons showed pleasing agreements between the numerical predictions and analytical solutions. The model was then further validated by comparing the numerical model results with the experimental measurements of wave propagation over a permeable submerged breakwater reported in the literature. Good agreements were obtained for the free surface elevations at various spatial and temporal scales, velocity fields around and inside the obstacle, as well as the velocity profiles.

Numerical model for interactions between shallow water wave and continuous submerged porous structures

“…The numerical model based on the N-S equations is recommended in simulating the interaction between waves and structures. This method has been applied to the simulation of wave propagation deformation and wave-induced currents near shores [16,17] or structures such as breakwaters [18,19]. However, the use of numerical models based on the N-S equations to solve the problem of the interaction between cnoidal waves and structures has rarely been studied.…”

Theoretical Analysis of a Vertical Cylindrical Floater in Front of an Orthogonal Breakwater

“…Permeable breakwaters also consist of perforated and slotted structures. These porous protection structures are usually bottom seated, operating as permeable breakwaters increasing wave reflection as their porosity decreases [33,34]. As far as WEC-permeable breakwater systems are concerned, the Wave Star [35] can be considered as a WEC-pile breakwater.…”

Propagation of Solitary Waves over a Submerged Slotted Barrier

“…In recent years, submerged-type structures have been extensively considered as alternative choices [3,4] to enhance water exchange and retain natural coastal landscape for a recreational purpose. On the other hand, coastal structures may have permeable parts, which leads to attenuate additional wave energy through viscous dissipation within the porous media [5,6]. A typical permeable structure mostly consisted of rubble-mounted elements.…”