Numerical Investigation and Parametric Optimization of Novel Dual-Pontoon Breakwater with Arc-Shaped Plate

Abstract

To enhance the hydrodynamic stability of offshore floating photovoltaic (OFPV) platforms under complex sea conditions, this study proposes a novel arc-plate dual-pontoon floating breakwater. A combined methodology of experimental investigation and numerical simulation was integrated to systematically study its hydrodynamic responses and attenuation performance. A two-dimensional numerical wave flume was established in FLOW-3D, and the results were validated against experimental data. The results reveal that the wave energy reduction is primarily achieved through the wave reflection in front of the pontoons and turbulence-induced dissipation guided by the arc plate. The effects of key structural parameters (pontoon draft depth, arc plate span, and the relative freeboard height) were studied to optimize its performance. The results show that both the increasing draft depth and arc plate span can significantly improve the attenuation under long-period waves. Additionally, higher relative freeboard heights help to reduce both the transmission coefficient and horizontal wave force, with the optimal value identified as 0.7. The findings suggest theoretical insights and possible indications for the design of the floating breakwater system in offshore renewable energy applications.

1. Introduction

With the continuous expansion of marine resource development and coastal infrastructure construction, breakwater structures have found increasing application in offshore platforms, ports, and artificial islands. Although traditional rigid breakwaters demonstrate excellent wave reflection performance, their high construction costs, engineering complexity, and significant disturbance to the seabed constrain their application in soft seabed, deep waters, and ecologically sensitive regions [1]. To address the limitations, floating breakwaters (FBs) have emerged as a major research focus in coastal engineering due to their flexible deployment, reusability, and environmental friendliness [2]. Among various configurations, pontoon-type floating breakwaters are widely adopted for their structural simplicity and clearly characterized hydrodynamic behavior. Sannasiraj et al. [3] systematically investigated the motion characteristics and mooring force variations of pontoon structures under different wave conditions through experimental tests, providing a foundational reference for the response analysis of floating breakwaters.

In recent years, studies have increasingly focused on optimizing structural layouts and understanding and mitigating wave transmission mechanisms. Using the Smoothed Particle Hydrodynamics (SPH) method, Chen et al. [4] conducted a comparative analysis of the hydrodynamic performance of single-pontoon and double-pontoon configurations, revealing the superior wave attenuation performance of the latter. Subsequently, Chen et al. [5] examined the influence of pontoon spacing on wave response and confirmed the significant influence of layout parameters on transmission coefficients. Masoudi and Marshall established a diffraction model for multi-pontoon rectangular configurations and explored how deployment schemes influence wave propagation paths [6]. With artificial islands as their engineering background, Zang et al. [7] proposed an optimized arrangement strategy for annular pontoon arrays to enhance wave shielding around reef structures. Zhao et al. [8] incorporated porous media theory into the analysis of submerged breakwaters and demonstrated that pore structure characteristics have a notable influence on solitary wave transmission and energy dissipation mechanisms.

To improve the wave energy dissipation efficiency of floating breakwaters, researchers have introduced innovative frontal components. Li et al. [9] compared the wave attenuation performance of flat and arc-shaped leading-edge structures under various wave conditions and found that the arc-shaped configuration exhibits superior performance under intermediate- and long-period waves. Wu et al. [10] proposed a composite system integrating perforated plates, arc panels, and horizontal slabs, and demonstrated its effectiveness in suppressing wave transmission through SPH-based numerical simulations. Experimental tests conducted by He et al. [11] further showed that the flexible curtain-like components significantly enhance wave energy dissipation and result in an improved wave height distribution in the lee of the breakwater.

Meanwhile, multifunctional floating breakwater structures have garnered growing research interest. Sun et al. [12] conducted a comprehensive review on the integration of breakwaters with energy systems and highlighted that multifunctional and platform-based designs are expected to become prevailing design paradigms. Wang et al. [13] proposed a floating structure integrated with a wave energy converter (WEC), which simultaneously enables wave attenuation and power generation, and demonstrated its energy capture efficiency through numerical simulations. Ding [14] systematically evaluated the response variation in WEC-integrated floating breakwaters under different wave frequencies, elucidating the structural integration advantages. Wang et al. [15] developed a tank-type floating breakwater for aquaculture applications, which integrates wave attenuation and water storage functions, thereby enabling integrated optimization of engineering utility.

Research on the structural stability of floating breakwaters has achieved remarkable development. Panda et al. [16] proposed an H-shaped pile-restrained system that effectively suppresses lateral drift of the floating breakwater, consequently improving platform stability, as shown in Figure 1. Vishwakarma and Karmakar [17] employed frequency-domain simulations to evaluate various hybrid breakwater configurations and characterized the dynamic response behavior under complex wave environments. Li et al. [9] further identified that mooring stiffness and structural aspect ratios have a substantial impact on wave transmission and motion responses. Wang et al. proposed a composite layout strategy combining airbag systems with submerged breakwaters [18], enabling multi-level wave energy dissipation. Elsheikh et al. demonstrated that the porosity and spatial arrangement of permeable structures directly influence the energy attenuation process [19], offering design-oriented insights for material selection and deployment schemes. With optimized wave flume tests, Yang et al. showed that floating photovoltaic systems equipped with floating breakwaters exhibit improved hydrodynamic stability under both head-on and oblique wave incidence [20], with notable reductions in heave, pitch, and roll responses. Based on numerical simulations under oblique wave conditions, Zou et al. [21] demonstrated that the deployment angle governs wave reflection performance, indicating that appropriate orientation of breakwaters can enhance stability under oblique wave attack.

In the context of modeling techniques, Tabatabaei Malazi et al. [22] analyzed the interaction between solitary waves and floating breakwaters using a nonlinear framework, elucidating the behavior of breakwaters in response to variations in wave envelope characteristics. Zhou et al. [23] developed a partial reflection boundary model applicable for predicting the transmission coefficients of floating breakwaters, while Zhou and Zhang [24] proposed an analytical diffraction solution for asymmetrically arranged breakwaters. Wu et al. [25] investigated the energy dissipation mechanism of jet-type structures using a body force model, providing a theoretical basis for the design of unconventional floating breakwaters. Wang et al. [26] established a two-dimensional wave propagation model for optimizing the parameters of rectangular floating breakwater configurations. Experimental work by Young and Testik [27] revealed the effects of curvature in submerged breakwaters on wave reflection coefficients. Chen et al. [28] performed numerical simulations on box-type floating structures and found better energy dissipation adaptability under long-period wave conditions. Loukili et al. [29] pointed out that current theoretical models of floating breakwaters lack comprehensive consideration of nonlinear wave–structure coupling effects, which restricts both predictive accuracy and practical applicability.

In parallel with the development of floating breakwaters, various studies have explored structural systems combining wave attenuation and energy interaction mechanisms. Dai et al. [2] provided a comprehensive review of floating breakwater typologies and associated hydrodynamic behaviors, forming the basis for understanding multifunctional coastal structures. In addition, performance improvements in oscillating water column (OWC) devices have been achieved through advanced turbine configurations such as twin-turbine systems [30], as well as CFD-based optimization methods tailored for bidirectional flow environments [31]. These works highlight the potential of coupling structural design with energy efficiency considerations under complex wave conditions.

In summary, substantial progress has been made in the structural optimization, response control, and multifunctional integration of floating breakwaters. Remarkably, configurations combining dual pontoons with auxiliary energy-dissipating components demonstrate strong application prospects for offshore environments. In this paper, the present study proposes a novel floating breakwater configuration composed of dual pontoons and arc-shaped dissipative wings. A comprehensive numerical simulation based on computational fluid dynamics (CFD) is conducted to analyze the hydrodynamic behavior and wave attenuation mechanisms of the structure. Furthermore, the sensitivity analysis of geometric parameters is performed to optimize the structural configuration, with the aim of providing theoretical support and practical guidance for future offshore engineering implementation and structural design.

Although arc-shaped plates and dual-pontoon configurations have been individually examined in previous studies, existing designs still face several practical limitations when applied to offshore floating photovoltaic (OFPV) platforms. Most traditional floating breakwaters emphasize either wave reflection or partial energy dissipation, but often fail to balance both mechanisms effectively. In addition, many structures adopt bulky or complex geometries, which hinder modular deployment, increase maintenance difficulty, and reduce compatibility with the limited buoyancy and structural tolerance of OFPV systems. The integrated arc-plate dual-pontoon breakwater proposed in this study addresses these limitations by forming a compact, modular structure that merges frontal wave blocking from the dual pontoons with turbulence-induced energy dissipation generated by the central arc-shaped plate. This dual-function configuration improves the balance between reflection and dissipation, while maintaining structural simplicity and adaptability. While previous works have examined arc-shaped plates and dual pontoons separately, studies that systematically explore their integrated hydrodynamic behavior, especially for OFPV applications, remain scarce. This work aims to contribute to this underexplored area.

2. Materials and Methods

Wave-induced loads represent critical factors influencing the safe operation of box-type offshore floating photovoltaic (FPV) platforms. The loads primarily affect the system in two primary ways. First, the wave excitation may induce significant motion responses in heave, surge, and pitch degrees of freedom. The responses not only undermine structural stability and durability, but also directly reduce the energy conversion efficiency of the photovoltaic power generation system. Second, wave overtopping and wave slamming on the platform surface can produce transient localized impact loads, exposing photovoltaic equipment to immersion or impulsive forces, potentially leading to severe damage to the structural components and power modules. Therefore, platform motion responses and overtopping-related phenomena have emerged as critical technical bottlenecks hindering the deployment of box-type FPV systems in deep-sea environments.

To address the challenges posed by excessive motion responses and frequent overtopping experienced by box-type offshore FPV platforms, two primary engineering strategies have been developed. Initially, floating breakwaters are deployed around the platform to interfere with incident wave propagation and dissipate wave energy, thereby reducing wave-induced excitation and minimizing overall motion responses. The second strategy introduces anti-overtopping structures around the box-type units to block overtopping pathways and reduce the frequency and intensity of local impact loads. Although each approach serves a distinct function, multiple strategies are employed in combination under realistic sea conditions to ensure comprehensive platform stability and operational safety.

In continuation of previous research, this study proposes a novel dual-pontoon floating breakwater integrated with arc-shaped plates, aiming to simultaneously reduce incident wave energy and mitigate overtopping effects. The structure combines pontoons with arc plates to establish a wave reflection and dissipation region, and the arc geometry, together with its deployment orientation, serves to obstruct wave climbing, offering enhanced wave protection and structural resilience under complex sea conditions.

Specifically, this study develops a numerical wave flume model of the proposed floating breakwater and assesses model accuracy by comparing simulated surface elevations and transmission coefficients with results from the experimental tests. Second, under vertical guide pile mooring conditions, systematic numerical simulations are conducted to evaluate the structure’s wave attenuation and overtopping suppression performance under various sea states. Finally, the sensitivity of key structural parameters (pontoon spacing, arc plate dimensions, and deployment angle) to hydrodynamic performance is investigated, and an optimized scheme is proposed accordingly. The findings aim to offer both theoretical insights and practical guidance for the safe deployment of box-type offshore FPV platforms in complex marine environments.

2.1. Breakwater Configuration

Based on the design principles for wave protection structures and inspired by the concept of traditional dual-pontoon floating breakwaters, this study proposes an arc-plate dual-pontoon breakwater configuration. A schematic of the proposed structure is shown in Figure 2.

As illustrated in Figure 2, the structure consists of four main components: two cylindrical pontoons, a cross-beam, mooring rings, and an arc-shaped plate. The cylindrical dual pontoons are designed to enhance stability by increasing the moment of inertia and restoring moment with minimal additional material, thereby improving the hydrodynamic performance of the system. The added arc plate serves as an anti-overtopping element that effectively suppresses wave overtopping. Its curved cross-sectional geometry mitigates wave impact loads by dispersing slamming forces. Structural holes are incorporated into the arc plate to provide secure mooring points for the protected array of box-type floating units. The cross-beam links the two pontoons by passing through the diameters, forming an arcuate triangular system with the arc plate to reinforce overall structural integrity. Mooring rings located at the bottom ends of the pontoon function can be applied as flexible connectors between adjacent breakwater modules and anchoring guides for vertical piles.

Key structural parameters of the arc-plate dual-pontoon breakwater include pontoon diameter (D_AP), overall breakwater width (W_AP), freeboard height (H_AP), draft depth (d_AP), pontoon length (l_AP), and structural self-weight (G_A), as illustrated in Figure 3.

The non-dimensional expressions of the parameters are defined and expressed as follows: relative draft d_AP/L(d_AP/L_s), relative freeboard height H_AP/H (H_AP/H_S, the ratio of arc plate height to incident wave height), relative width W_AP/L(W_AP/L_s), and relative diameter D_AP/W_AP. Based on scaling calculations, the experimental model was fabricated at a geometric scale of 1:14, in accordance with Froude scaling laws, and treated as a rigid-body model. Both subsequent experimental tests and numerical simulations were performed using this scaled configuration.

The structural parameters were determined as follows: The pontoon length l_AP was selected to approximately match the width of the wave flume, enabling two-dimensional sectional wave testing. The overall width of the breakwater was set as W_AP = 450 mm and the pontoon diameter as D_AP = 100 mm. The values were selected to ensure that the relative wavelength, a key factor influencing wave attenuation performance, remains within a controllable and comparable range, as well as the structural stability. The height of the arc plate above the water surface was set as H_AP = 115 mm to provide sufficient freeboard to resist overtopping under a 50-year event. Given the 1:14 scale, the corresponding full-scale maximum wave height would be approximately 22.82 cm. Thus, selecting half of the maximum wave height as the relative freeboard height results in an approximate relative wave height of H_AP/H = 0.5. The draft depth d_AP = 50 mm is in line with common practice for traditional dual-pontoon breakwaters, where the draft typically equals the pontoon radius.

It should be noted that the parameter applications fall within the reasonable design ranges, without implying an optimal configuration. Further refinement and optimization will be conducted through numerical simulations to achieve improved wave attenuation effectiveness.

2.2. Experimental Setup

The experimental tests were conducted in the large irregular wave flume facility at the State Key Laboratory of Hydraulic Engineering Simulation, Tianjin University. The flume measures 90 m in length, 2 m in width, and 2 m in height, with a maximum effective water depth of 1.5 m. A combination of artificial rubble slope and porous wave absorber was installed at the downstream end of the flume to dissipate residual wave energy and suppress end-boundary reflections, as illustrated in Figure 4.

Wave surface elevations were measured using the TKS-7 wave gauge system developed by the China Waterborne Transport Research Institute. The data acquisition system was equipped with an internal analog-to-digital converter capable of collecting data from up to 64 channels at a sampling interval of 0.02 s. Prior to testing, the system was calibrated, achieving a linearity of over 0.999. BG-type wave sensors were employed with a measurement range of 40 cm and resolution of 0.2 mm. The data acquisition system and wave sensors are shown in Figure 5.

The breakwater model was fabricated using polypropylene, a material with a density less than 1 g/cm³. To meet similarity requirements for draft and the moment of inertia, an internal ballast was added to the pontoons. The model was moored using vertical guide piles: steel guide tubes were mounted at both ends of the pontoons with side-wall openings to accommodate mooring components. Linear bearings were installed inside the front-facing tubes to permit free heave motion and constrain surge, sway, and yaw motions. The model setup is illustrated in Figure 6.

A custom-designed steel frame was used to provide vertical guide pile mooring. The frame was suspended from an overhead crossbeam via three-component force sensors and remained off the flume bottom to avoid influencing horizontal force measurements. It was reinforced with inclined struts and cross braces to ensure sufficient stiffness and to prevent excessive deformation under wave loading, which could otherwise affect force transmission and dynamic behavior. The two vertical columns of the frame served as guide piles and were inserted into linear guide rails attached to the front pontoons of the arc-plate dual-pontoon breakwater, enabling vertical motion while constraining horizontal displacement. The crossbeam was positioned 50 cm above the water surface to prevent obstruction of the model’s free dynamic response. The overall experimental configuration is presented in Figure 7.

During the tests, incident waves interacting with the model inevitably generated reflected waves. Since the measured surface elevation represents a superposition of incident and reflected wave components, decomposition analysis was necessary to evaluate wave attenuation performance. Although the downstream wave absorber helped reduce reflections, it did not eliminate them entirely. Therefore, three wave gauges were placed both upstream and downstream of the model to measure wave elevations along the propagation direction and to facilitate decomposition analysis using the three-point method.

Wave gauges were labeled W1 through W6. The spacing between W1–W3 was 0.32 m and 0.42 m, respectively, while the spacing between W4–W6 was 0.45 m and 0.50 m. The breakwater model was centered between W3 and W4 in all test cases, with a distance of 3 m between the model and each of the gauges. The layout of the entire experimental setup is shown in Figure 8.

2.3. Numerical Modeling Approach

2.3.1. Governing Equations of Wave Motion

In the numerical simulation of wave–breakwater interactions, the fluid domain is generally assumed to be an incompressible and viscous medium. Accordingly, the fundamental governing equations consist of the mass continuity Equation (1) and the Navier–Stokes Equations (2)–(4).

(1) Mass continuity equation

$${\displaystyle \frac{\partial }{\partial x}}(u{A}_x)+{\displaystyle \frac{\partial }{\partial y}}(v{A}_y)+{\displaystyle \frac{\partial }{\partial z}}(w{A}_z)=0$$

(1)

In the equation, u, v, and w represent the velocity components in the x, y, and z directions, respectively, while A_x, A_y, and A_z denote the area fraction (or flux area ratio) in the corresponding directions.

(2) Navier–Stokes equations

$${\displaystyle \frac{\partial u}{\partial t}}+{\displaystyle \frac{1}{V_F}}\left(u{A}_x{\displaystyle \frac{\partial u}{\partial x}}+v{A}_y{\displaystyle \frac{\partial u}{\partial y}}+w{A}_z{\displaystyle \frac{\partial u}{\partial z}}\right)=-{\displaystyle \frac{1}{\rho }}{\displaystyle \frac{\partial P}{\partial x}}+G_x+f_x$$

(2)

$${\displaystyle \frac{\partial v}{\partial t}}+{\displaystyle \frac{1}{V_F}}\left(u{A}_x{\displaystyle \frac{\partial v}{\partial x}}+v{A}_y{\displaystyle \frac{\partial v}{\partial y}}+w{A}_z{\displaystyle \frac{\partial v}{\partial z}}\right)=-{\displaystyle \frac{1}{\rho }}{\displaystyle \frac{\partial P}{\partial y}}+G_y+f_y$$

(3)

$${\displaystyle \frac{\partial w}{\partial t}}+{\displaystyle \frac{1}{V_F}}\left(u{A}_x{\displaystyle \frac{\partial w}{\partial x}}+v{A}_y{\displaystyle \frac{\partial w}{\partial y}}+w{A}_z{\displaystyle \frac{\partial w}{\partial z}}\right)=-{\displaystyle \frac{1}{\rho }}{\displaystyle \frac{\partial P}{\partial z}}+G_z+f_z$$

(4)

In the above equation, p denotes the hydrodynamic pressure, and G_x, G_y, and G_z represent the gravitational acceleration components in the x, y, and z directions, respectively. The terms f_x, f_y, and f_z refer to the viscous acceleration components in each corresponding direction, which are defined as Equations (5)–(7):

$$\rho V_F{f}_x=wsx-\left[{\displaystyle \frac{\partial }{\partial x}}\left(A_x{\tau }_{xx}\right)+{\displaystyle \frac{\partial }{\partial y}}\left(A_y{\tau }_{xy}\right)+{\displaystyle \frac{\partial }{\partial z}}\left(A_z{\tau }_{xz}\right)\right]$$

(5)

$$\rho V_F{f}_y=wsy-\left[{\displaystyle \frac{\partial }{\partial x}}\left(A_x{\tau }_{xy}\right)+{\displaystyle \frac{\partial }{\partial y}}\left(A_y{\tau }_{yy}\right)+{\displaystyle \frac{\partial }{\partial z}}\left(A_z{\tau }_{yz}\right)\right]$$

(6)

$$\rho V_F{f}_z=wsy-\left[{\displaystyle \frac{\partial }{\partial x}}\left(A_x{\tau }_{xz}\right)+{\displaystyle \frac{\partial }{\partial y}}\left(A_y{\tau }_{xz}\right)+{\displaystyle \frac{\partial }{\partial z}}\left(A_z{\tau }_{zz}\right)\right]$$

(7)

τ_ij represents the shear stress in the fluid, where the first subscript i denotes the normal direction of the acting surface, and the second subscript j indicates the direction of the applied stress. μ is the dynamic viscosity of the fluid. The shear stress τ_ij is defined as Equations (8)–(13):

$${\tau }_{xx}=-2\mu \left[{\displaystyle \frac{\partial u}{\partial x}}-{\displaystyle \frac{1}{3}}\left({\displaystyle \frac{\partial u}{\partial x}}+{\displaystyle \frac{\partial v}{\partial y}}+{\displaystyle \frac{\partial w}{\partial z}}\right)\right]$$

(8)

$${\tau }_{\mathrm{yy}}=-2\mu \left[{\displaystyle \frac{\partial u}{\partial y}}-{\displaystyle \frac{1}{3}}\left({\displaystyle \frac{\partial u}{\partial x}}+{\displaystyle \frac{\partial v}{\partial y}}+{\displaystyle \frac{\partial w}{\partial z}}\right)\right]$$

(9)

$${\tau }_{\mathrm{zz}}=-2\mu \left[{\displaystyle \frac{\partial u}{\partial z}}-{\displaystyle \frac{1}{3}}\left({\displaystyle \frac{\partial u}{\partial x}}+{\displaystyle \frac{\partial v}{\partial y}}+{\displaystyle \frac{\partial w}{\partial z}}\right)\right]$$

(10)

$${\tau }_{xy}={\tau }_{yx}=-\mu \left({\displaystyle \frac{\partial v}{\partial x}}+{\displaystyle \frac{\partial u}{\partial y}}\right)$$

(11)

$${\tau }_{xz}={\tau }_{zx}=-\mu \left({\displaystyle \frac{\partial v}{\partial z}}+{\displaystyle \frac{\partial w}{\partial x}}\right)$$

(12)

$${\tau }_{yz}={\tau }_{zy}=-\mu \left({\displaystyle \frac{\partial v}{\partial z}}+{\displaystyle \frac{\partial w}{\partial y}}\right)$$

(13)

2.3.2. Turbulence Model

Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) require considerable computational resources, which make these impractical for routine engineering applications. Therefore, turbulence models are typically employed to approximate turbulence-induced energy dissipation in viscous flows. In FLOW-3D, six turbulence models are available: the Prandtl mixing-length model, the one-equation model, the standard two-equation k–ε model, the Renormalization Group (RNG k–ε) model, the two-equation k–ε model, and LES.

The RNG k–ε model is widely recognized as being effective for simulating turbulence due to its incorporation of Renormalization Group (RNG) theory, which employs statistical techniques to derive turbulent transport equations. Compared to the standard k–ε model, the RNG k–ε model provides improved accuracy in predicting vortex structures and turbulent viscosity. It also exhibits lower numerical dissipation and enhanced performance in shear-dominated and rotational flows. The features make it suitable for a wide range of flow conditions, particularly the high-intensity shear turbulence and flows with strong strain or swirl. Although more advanced models such as Large Eddy Simulation (LES) can offer higher fidelity in capturing complex flow phenomena, they are computationally expensive and often impractical for parametric studies or large-scale simulations. Therefore, the RNG k–ε model was adopted in the present numerical study as a reasonable compromise between computational efficiency and accuracy, and it has been widely used in similar hydrodynamic applications.

The mathematical formulation of the RNG k–ε model in FLOW-3D is derived by modifying the coefficients in the standard k–ε model equations. Since the two models share a similar mathematical structure, the governing equations are introduced here based on the standard k–ε model to facilitate direct comparison. This model consists of a transport equation for the turbulent kinetic energy (k) and an equation for its dissipation rate (ε). The transport equation for k is expressed as Equation (14):

$${\displaystyle \frac{\partial k_T}{\partial t}}+{\displaystyle \frac{1}{V_F}}\left(u{A}_x{\displaystyle \frac{\partial k_T}{\partial x}}+v{A}_y{\displaystyle \frac{\partial k_T}{\partial y}}+w{A}_z{\displaystyle \frac{\partial k_T}{\partial z}}\right)=P_T+G_T+Dif{f}_{k_T}-{\epsilon }_T$$

(14)

The source terms in the k–ε turbulence model include turbulent kinetic energy production, buoyancy effects, dissipation, and diffusion. The components are defined and interpreted as follows:

P_T: Turbulent kinetic energy production term;

G_T: Buoyancy production term;

Diff_kT: Diffusion term for turbulent kinetic energy;

ε_T: Turbulent dissipation term.

The production term P_T is expressed as Equation (15):

$$P_T=CSPRO\left({\displaystyle \frac{u}{\rho V_F}}\right)\left[\begin{array}{l}2A_x{\left({\displaystyle \frac{\mathit{\partial }u}{\mathit{\partial }x}}\right)}^2+2A_y\left({\displaystyle \frac{\partial v}{\partial y}}\right)+2A_z{\left({\displaystyle \frac{\partial w}{\partial z}}\right)}^2+\\ \left({\displaystyle \frac{\partial v}{\partial x}}+{\displaystyle \frac{\partial u}{\partial y}}\right)\left(A_x{\displaystyle \frac{\partial v}{\partial x}}+A_y{\displaystyle \frac{\partial u}{\partial y}}\right)+\\ \left({\displaystyle \frac{\partial u}{\partial z}}+{\displaystyle \frac{\partial w}{\partial x}}\right)\left(A_z{\displaystyle \frac{\partial u}{\partial z}}+A_x{\displaystyle \frac{\partial w}{\partial x}}\right)+\\ \left({\displaystyle \frac{\partial v}{\partial z}}+{\displaystyle \frac{\partial w}{\partial y}}\right)\left(A_z{\displaystyle \frac{\partial v}{\partial z}}+A_y{\displaystyle \frac{\partial w}{\partial y}}\right)\end{array}\right]$$

(15)

In the equation, CSPRO denotes the turbulence model constant, commonly set to 1.0.

The G_T is expressed as Equation (16)

$$G_T=-CRHO\left({\displaystyle \frac{\mu }{{\rho }^3}}\right)\left({\displaystyle \frac{\partial \rho }{\partial x}}{\displaystyle \frac{\partial p}{\partial x}}+{\displaystyle \frac{\partial \rho }{\partial y}}{\displaystyle \frac{\partial p}{\partial y}}+{\displaystyle \frac{\partial \rho }{\partial z}}{\displaystyle \frac{\partial p}{\partial z}}\right)$$

(16)

where CRHO is the buoyancy influence coefficient, with a default value of 0.0. For stratified or density-driven flows, a typical value is 2.5.

The diffusion term for turbulent kinetic energy is given by Equation (17)

$$Dif{f}_{k_T}={\displaystyle \frac{1}{V_F}}\left[{\displaystyle \frac{\partial }{\partial x}}\left({\upsilon }_k{A}_x{\displaystyle \frac{\partial k_T}{\partial x}}\right)+{\displaystyle \frac{\partial }{\partial y}}\left({\upsilon }_k{A}_y{\displaystyle \frac{\partial k_T}{\partial y}}\right)+{\displaystyle \frac{\partial }{\partial z}}\left({\upsilon }_k{A}_z{\displaystyle \frac{\partial k_T}{\partial z}}\right)\right]$$

(17)

where υ_k is the diffusion coefficient for turbulent kinetic energy and calculated in FLOW-3D using the turbulent viscosity and a user-defined model parameter RMTKE. The standard k–ε model uses RMTKE = 1.0, while the RNG k–ε model typically adopts RMTKE = 1.39.

The transport equation for the turbulent dissipation rate ε is formulated as Equation (18)

$${\displaystyle \frac{\partial {\epsilon }_T}{\partial t}}+{\displaystyle \frac{1}{V_F}}\left(u_x{A}_x{\displaystyle \frac{\partial {\epsilon }_T}{\partial x}}+v{A}_y{\displaystyle \frac{\partial {\epsilon }_T}{\partial y}}+w{A}_z{\displaystyle \frac{\partial {\epsilon }_T}{\partial z}}\right)={\displaystyle \frac{CDIS1\cdot {\epsilon }_T}{k_T}}\left(P_T+CDIS3\cdot G_T\right)+Dif{f}_{\epsilon }-CDIS2{\displaystyle \frac{{\epsilon }_T^2}{k_T}}$$

(18)

where CDIS1, CDIS2, and CDIS3 are empirical constants. In the standard k–ε model, the values are CDIS1 = 1.44, CDIS2 = 1.92, and CDIS3 = 0.2. In the RNG k–ε model, CDIS1 is typically 1.42, while CDIS2 is dynamically determined based on turbulent shear production and often expressed in terms of k_T and P_T.

The diffusion term for ε is expressed as Equation (19)

$$Dif{f}_{\epsilon }={\displaystyle \frac{1}{V_F}}\left[{\displaystyle \frac{\partial }{\partial x}}\left({\upsilon }_{\epsilon }{A}_x{\displaystyle \frac{\partial {\epsilon }_T}{\partial x}}\right)+{\displaystyle \frac{\partial }{\partial y}}\left({\upsilon }_{\epsilon }{A}_y{\displaystyle \frac{\partial {\epsilon }_T}{\partial y}}\right)+{\displaystyle \frac{\partial }{\partial z}}\left({\upsilon }_{\epsilon }{A}_z{\displaystyle \frac{\partial {\epsilon }_T}{\partial z}}\right)\right]$$

(19)

where υ_ε denotes the diffusion coefficient for the dissipation rate.

The turbulent eddy viscosity υ_T in both turbulence models is computed as Equation (20):

$${\upsilon }_T=CNU{\displaystyle \frac{k_T^2}{{\epsilon }_T}}$$

(20)

The model coefficient CNU is assigned a value of 0.09 in the standard k–ε model and 0.085 in the RNG k–ε model.

During the computation of υ_T, near-zero values of ε_T may occur due to numerical limitations. Although k_T should also approach zero in such cases, numerical instability may lead to unrealistically large values of υ_T. To mitigate this, a lower bound is imposed on ε_T and given by Equation (21)

$${\epsilon }_{T,\min }=CN{U}^{{\displaystyle \raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}}{\displaystyle \frac{k_T^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}{TLEN}}$$

(21)

where TLEN is the maximum turbulence length scale and used to constrain excessive dissipation. It can be either user-defined or set to a default value in FLOW-3D, and is typically taken as 7% of the minimum domain dimension.

2.3.3. Volume-of-Fluid (VOF) Free Surface Tracking Method

Numerical approaches for tracking free surfaces generally fall into three categories: Lagrangian, Eulerian, and Euler–Lagrange methods. The Volume-of-Fluid (VOF) method, a Eulerian approach, simulates free surface evolution by tracking the fluid interface’s position and shape. It is particularly well-suited for handling complex interfacial behaviors such as multiple fluid interfaces, overturning, and wave breaking.

In the VOF method, the fluid domain is discretized into finite computational cells. Each cell assigns a scalar volume fraction FFF, representing the proportion of fluid within the cell. The interface position is determined by the discontinuity in F. Specifically, F = 1 indicates a fully fluid-filled cell, F = 0 indicates an empty cell, and 0 < F < 1 denotes a partially filled interface cell. Such interface cells are typically adjacent to empty cells and represent the location of the free surface or internal gas–liquid interfaces.

The volume fraction F satisfies the following transport equation, Equation 22:

$${\displaystyle \frac{\partial F}{\partial t}}+{\displaystyle \frac{\partial uF}{\partial x}}+{\displaystyle \frac{\partial vF}{\partial y}}+{\displaystyle \frac{\partial wF}{\partial z}}=0$$

(22)

As F behaves as a step function, direct discretization can introduce spurious numerical diffusion or oscillations near the interface. To mitigate this, the VOF method in conjunction with the donor–acceptor scheme for improved interface reconstruction was originally proposed.

In FLOW-3D, a proprietary implementation known as TruVOF is adopted. This method employs geometric interface reconstruction and ensures strict mass conservation across interfaces. Additionally, TruVOF incorporates linear interpolation to estimate physical properties near the interface and includes surface tension models accounting for curvature and vorticity-induced shear. Although specific algorithmic details are not publicly disclosed, TruVOF has demonstrated robust performance in capturing complex interfacial dynamics.

Owing to the accuracy and stability, the TruVOF method in FLOW-3D is particularly suitable for simulating free surface evolution in wave–structure interaction problems, such as the wave attenuation performance of floating breakwaters investigated in this study.

2.3.4. Numerical Solution Method

A structured and staggered grid is employed to discretize the computational domain for solving the governing equations. In FLOW-3D, the equations can be discretized using either the finite difference method (FDM) or the finite volume method (FVM). The finite difference method divides the domain into nodal points and approximates differential operators using Taylor series expansions. In contrast, the finite volume method partitions the domain into discrete control volumes and applies the integral form of conservation laws by evaluating fluxes across volume surfaces.

To solve the resulting algebraic equations, FLOW-3D provides three pressure–velocity coupling algorithms: the Alternating Direction Implicit (ADI) method, the Successive Over-Relaxation (SOR) method, and the Generalized Minimal Residual (GMRES) method. The GMRES algorithm is preferred for its high accuracy, rapid convergence, and computational efficiency in solving the Navier–Stokes equations. Therefore, the GMRES method is employed in this study, combined with fully implicit time discretization to maintain numerical stability.

3. Numerical Model Development and Validation

A numerical model was developed based on the experimental tests of the arc-plate dual-pontoon breakwater moored by vertical guide piles. The model’s accuracy was validated by comparing the simulated free surface elevation and transmission coefficients with the experimental results.

3.1. Numerical Wave Flume

(1)

Geometric Configuration and Breakwater Placement

The numerical wave flume is 45 m long, sufficient to prevent inflow boundary interference under all tested wave conditions. The wave propagates along the x-axis. As the breakwater test is conducted as a sectional test, a two-dimensional (2D) wave flume was adopted to improve computational efficiency, given that the performance difference from 3D models is typically within 10%.

The water depth is set to 0.4 m, consistent with the experimental tests. The vertical domain height is 0.8 m to accommodate wave run-up and splash. The breakwater, with the same cross-sectional dimensions as the experimental model, spans the flume width and is located at one-third of the domain length from the inlet. A 5 m long wave absorption zone is placed at the outlet to minimize boundary reflection. Wave gauges #1 to #6 are placed at the same positions as in the experimental tests. The breakwater is constrained to vertical (z-axis) motion only, simulating the guide pile mooring mechanism.

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Boundary Conditions

• x-direction: The inflow boundary is defined as a wave-generating condition using FLOW-3D’s Wave module. Stokes waves are prescribed by specifying wave parameters such as height, period, and depth. The outlet is treated as an uutflow boundary based on the Sommerfeld radiation condition [32].
• y-direction: Symmetry conditions are applied on sidewalls to represent symmetric flow behavior, reducing computational load.
• z-direction: A pressure boundary is used at the free surface (set to zero), while a symmetry condition is applied at the flume bottom to minimize bottom friction.

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Initial Conditions

The initial pressure distribution is hydrostatic, and all flow velocities are initialized to zero.

(4)

Mesh Configuration

A structured rectangular mesh is applied. Local refinement is used near the wave source, breakwater, and adjacent wave interaction zone, with grid resolutions of 0.005 m in the x- and z-directions and 0.004 m in the y-direction. To maintain solution accuracy, the cell aspect ratio is kept below 5, and the grid size ratio between adjacent cells does not exceed 1.25. The total number of active mesh cells is approximately 260,000. The mesh layout near the breakwater is shown in Figure 9.

3.2. Numerical Model Validation

Considering that the nonlinear wave–structure interactions become more pronounced under larger wave heights and steepness, H = 0.08 m and T = 0.85 s are selected to examine the surface wave profiles near the arc-plate dual-pontoon breakwater. Snapshots of the wave surfaces, both in the presence and absence of the breakwater, are presented in Figure 10.

An examination of the results shows that the numerical wave flume accurately reproduces the target wave profile. The initial wave surface at t = 0 s is nearly identical to that at t = 10 s, indicating minimal energy dissipation over time. Moreover, the presence of the breakwater clearly alters the free surface, with wave overtopping observed at the arc plate and a distinct difference in wave heights upstream and downstream of the structure.

To further assess the validity of the numerical model, a comparison is conducted between the free surface elevations measured in the flume and the corresponding values computed in the numerical flume. As an example, the wave elevation time series at wave gauge #4 is shown in Figure 11.

The results indicate that, for the case without the breakwater, the numerically generated wave profiles (wave height and shape) match well with the values measured in the wave flume. However, after the breakwater is installed, discrepancies appear in both wave height and period. As mentioned above, the differences are primarily attributed to limitations in the experimental setup: the vertical guide piles in the experiment cannot fully constrain the breakwater, leading to elastic deformation under wave loading. This deformation not only restricts the intended heave motion but also induces additional surge due to structural oscillation during the deformation–restoration cycle. This motion superimposes radiated waves into the surrounding fluid, resulting in divergence between the experimental and numerical wave profiles over time.

The comparison between the numerically computed and experimentally measured transmission coefficients and horizontal wave forces acting on the arc-plate dual-pontoon breakwater with a constant wave height of H = 8 cm across various wave periods is shown in Figure 12.

To quantitatively assess the agreement between the experimental and numerical results, the root mean square error (RMSE) and correlation coefficient r were calculated for both transmission coefficients and horizontal wave forces.

The RMSE is defined as Equation (23)

$$RMSE=\sqrt{{\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n{(x_i-y_i)}^2}}$$

(23)

and the Pearson correlation coefficient is given by Equation (24)

$$r={\displaystyle \frac{{\displaystyle {\sum }_{i=1}^n(x_i-\overline{x})(y_i-\overline{y})}}{\sqrt{{\displaystyle {\sum }_{i=1}^n{(x_i-\overline{x})}^2}}\cdot \sqrt{{\displaystyle {\sum }_{i=1}^n{(y_i-\overline{y})}^2}}}}$$

(24)

where x_i and y_i represent the numerical and experimental values, respectively, and n is the number of data points. For transmission coefficients, the RMSE was 0.052 and the correlation coefficient reached 0.990. For horizontal wave forces, the RMSE was 0.085 and the correlation coefficient reached 0.995. These results indicate that the numerical model exhibits excellent agreement with experimental data, exceeding common validation criteria (e.g., RMSE < 0.1 and r > 0.95).

The results show that the transmission coefficients obtained from numerical simulations slightly overestimate the experimental values when the relative wavelength is less than 0.35, but slightly underestimate them when the relative wavelength exceeds 0.35. The maximum deviation noted across all conditions is approximately 10%. This discrepancy is primarily attributed to the finite stiffness of the vertical guide pile system in the experimental model, which constrains the heave motion of the arc-plate dual-pontoon breakwater. In contrast, the numerical model assumes unconstrained heave motion without pile-induced restrictions. This limitation in the experimental setup also results in larger horizontal forces observed in the experimental model under long-period wave conditions compared to those predicted numerically.

Overall, the simulation results are in good agreement with experimental measurements in both transmission coefficients and horizontal wave forces, with consistent trends across all tested wave conditions. The findings validate the accuracy of the numerical wave flume setup and demonstrate the reliability of the simulation methodology for modeling wave–structure interactions.

4. Analysis of Wave Attenuation Mechanism

Due to the experimental limitations, it is difficult to achieve ideal vertical guide pile mooring in experimental tests. This constraint partially restricts the heave motion of the arc-plate dual-pontoon structure, complicating the interpretation of the wave attenuation mechanism. Additionally, the flow field around the structure cannot be directly captured in experimental tests, making it challenging to visualize the energy dissipation process. Therefore, this section analyzes the wave attenuation mechanism based on numerical simulation results, focusing on the flow field around the arc-plate dual-pontoon breakwater under representative wave conditions.

Two representative wave periods were selected based on the transmission coefficients observed in previous analyses: T = 1.2 s (corresponding to a higher transmission coefficient) and T = 0.85 s (corresponding to a lower transmission coefficient). Flow field characteristics under the two conditions were analyzed and compared. Figure 13 and Figure 14 illustrate the flow fields around the arc-plate dual-pontoon breakwater at four equally spaced time instances over one wave period for the T = 0.85 s and T = 1.2 s cases, respectively.

For T = 0.85 s (Figure 13), as the wave front reaches the structure, part of the flow is reflected by the front pontoon, while the remainder is diverted upward and downward. The diversion leads to the formation of turbulence zones near the pontoon surfaces. The upward flow overtops the front pontoon and strikes the arc plate, which further redirects the flow upward along its curved surface. During this process, the flow gains gravitational potential energy and gradually decelerates before reversing direction and returning along the arc, impacting the free surface and generating additional turbulence. Simultaneously, the downward-directed flow interacts with the lower wave surface beneath the arc plate, inducing a second turbulent region near the rear pontoon. This combination of wave reflection and localized energy dissipation through turbulence results in effective wave attenuation.

In contrast, for T = 1.2 s (Figure 14), the wave energy is insufficient to reach the arc plate, and interaction is limited to the pontoon surfaces. The near-surface particle velocities are lower, and turbulence formation is weaker and more localized. As a result, wave attenuation occurs primarily via limited reflection from the pontoons, with minimal contribution from the arc plate or turbulence-induced dissipation.

Therefore, the structure exhibits significantly better performance at T = 0.85 s, both in terms of wave reflection and energy dissipation. This finding accounts for the lower transmission coefficient observed in this case, confirming the effectiveness of the arc-plate dual-pontoon design under shorter-period, higher-energy waves.

5. Parametric Study on Structural Influence

As discussed previously, the vertical guide pile system employed in the experimental tests partially restricts the heave motion of the arc-plate dual-pontoon breakwater, limiting the arc plate’s ability to interact with incoming waves. This suggests that the draft depth or arc plate height may not be optimal. Other structural parameters, such as breakwater width and pontoon diameter, may also significantly influence wave attenuation performance. Numerical simulations allow for flexible adjustment of the variables and are therefore employed to examine the effects on wave transmission and hydrodynamic forces.

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Effect of Pontoon Draft Depth

As noted above, when wave energy reaches the arc plate, enhanced reflection and intensified turbulence are observed compared to traditional dual-pontoon breakwaters. Increasing the draft depth may reduce the relative freeboard height H_AP, allowing more incident wave energy to reach and interact with the arc plate, thus improving attenuation performance.

Using the baseline model with a draft of 0.5D_AP, additional models with draft depths of 0.75D_AP and 0.9D_AP were developed. With constant wave height (H = 8 cm), the transmission coefficients and horizontal wave forces were computed. The results are shown in Figure 15.

From Figure 15a, the model with 0.5D_AP draft shows a noticeably different transmission behavior from the deeper-draft models. For T < 0.9 s, it exhibits slightly better attenuation. However, for T > 0.9 s, the transmission coefficient increases rapidly, exceeding those of the deeper-draft models. The difference between the cases of 0.75D_AP and 0.9D_AP is relatively small, though the latter achieves lower transmission coefficients for long-period waves. Both deep-draft models display slower increases in transmission with increasing wave period, indicating improved performance under long waves.

As shown in Figure 15b, the horizontal forces on the 0.75D_AP and 0.9D_AP models follow similar trends and remain relatively constant with respect to wave period. In contrast, the force on the 0.5D_AP model decreases significantly as wave period increases. The 0.9D_AP model experiences approximately 90% of the horizontal force observed in the 0.75D_AP model. For T < 0.9 s, all three models show similar force levels, while for T > 0.9 s, the force on the shallow-draft model drops to nearly one-third of that experienced by the deeper-draft cases.

The results demonstrate that draft depth has a pronounced influence on both wave attenuation and hydrodynamic loading under long-period wave conditions. To further investigate the underlying mechanisms, flow fields for the 0.75D_AP and 0.9D_AP models at T = 1.2 s are analyzed and compared with the 0.5D_AP model.

As shown in Figure 14, the 0.5D_AP model exhibits minimal overtopping and limited interaction with the arc plate at T = 1.2 s. Wave attenuation primarily occurs through reflection at the front pontoon and weak turbulence.

In contrast, Figure 16 indicates that in the 0.75D_AP case, wave overtopping reaches the arc plate. The increased draft heightens the reflective surface area and enables stronger flow deflection. The overtopped water generates additional turbulence as it descends along the arc plate and re-enters the wave field, contributing to greater energy dissipation near the front pontoon and lower transmission.

Compared to the 0.75D_AP model, Figure 17 shows that the 0.9D_AP configuration further enhances the wave–structure interaction. The deeper draft enables a greater proportion of wave energy to reach the arc plate. Overtopped water travels further along the arc and impacts the rear pontoon with higher velocity, generating a larger and more intense turbulence region in the lee of the structure. This leads to even more effective wave energy dissipation.

In summary, although the maximum horizontal force acting on the 0.9D_AP model is approximately 1.2 times that of the 0.5D_AP case, the improved wave attenuation achieved through stronger turbulence and more effective flow redirection makes the deeper-draft configurations, particularly 0.9D_AP, the most effective among the three designs evaluated.

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Effect of Arc Plate Span

The baseline experimental model had a total width of 450 mm. To assess the influence of arc plate span on wave attenuation, two additional models with widths of 350 mm and 550 mm were developed, while all other parameters were held constant. Based on previous analysis, the optimal performance was achieved at a draft depth of 0.9D_AP, which is therefore adopted for all tests in this section. Under identical wave conditions, the transmission coefficients and horizontal wave forces were computed as functions of wave period, as shown in Figure 18.

As shown in Figure 18a, the transmission coefficient decreases as the arc plate span increases, while all three models exhibit a consistent upward trend in transmission as the wave period increases. Regarding hydrodynamic loading (Figure 18b), the horizontal wave forces show similar trends across all cases. However, the 350 mm model experiences the highest force, despite have the smallest span. This is attributed to its steeper arc plate slope, which produces stronger wave reflection. In contrast, the 550 mm model, with its shallower slope, generates the lowest force. The 450 mm case lies between the two values. The results indicate that the arc plate slope has a more significant influence on structural loading than the span itself.

To further assess wave attenuation under consistent relative wavelengths, transmission coefficients were plotted against normalized wavelength, as shown in Figure 19.

The transmission curves are nearly parallel and follow similar trends, suggesting that the underlying attenuation mechanism remains consistent across all models. Performance differences arise primarily from variations in wave reflection and energy dissipation along arc plates of different lengths. At shorter wave periods (larger relative wavelengths), narrower-span models show better attenuation. Under longer-period (smaller relative wavelength) conditions, performance differences diminish and become negligible.

In summary, arc-plate dual-pontoon breakwaters with smaller spans offer improved attenuation in shorter-period waves, compact dimensions, and lower construction costs, making them advantageous for deployment. However, the narrower-span configurations experience higher wave forces and slightly reduced performance under long-period wave conditions compared to wider-span configurations.

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Effect of Relative Freeboard Height (H_AP/H)

To investigate the influence of relative freeboard height on wave attenuation, a series of numerical simulations were conducted using a fixed wave period of 1.0 s and varying wave heights. The test model was the arc-plate dual-pontoon breakwater with a draft of 0.9D_AP and a total width of 350 mm. The selected wave heights correspond to typical sea conditions under the considered scale and were chosen to cover a range of relative freeboard values. Detailed wave conditions are listed in

Table 1. Test cases for evaluating the influence of relative freeboard height.

Wave Period	Wave Heights
1 s	8 cm, 10 cm, 12 cm, 14 cm

.

The corresponding transmission coefficients and horizontal wave forces under different relative freeboard heights were computed and are presented in Figure 20.

As shown in the figure, both the transmission coefficient and the horizontal wave force increase with rising wave height, corresponding to a decrease in the relative freeboard height H_AP/H. Moreover, the growth rates also become more pronounced as the relative freeboard decreases. The increasing arc plate height can raise the relative freeboard and improve wave attenuation, but this approach has practical limitations. Excessively tall arc plates may compromise the structural stability of the breakwater and substantially increase fabrication and installation costs. Considering both hydrodynamic performance and structural feasibility, a relative freeboard height of approximately 0.7 is identified as an optimal balance between energy dissipation effectiveness and engineering practicality.

According to the study by Chen et al. [4], the hydrodynamic performances of both single-pontoon (SPFB) and double-pontoon floating breakwaters (DPFB) were systematically evaluated using the Smoothed Particle Hydrodynamics (SPH) method. The simulations were conducted under various wave periods and incident wave heights, with the pontoon height and draft uniformly set to 0.30 m.

Their results revealed that increasing wave height generally leads to higher transmission coefficients, which is consistent with established hydrodynamic theory. Notably, when the wave height H = 0.10 m and the wave period T ≈ 1.6 s, the transmission coefficient K_t of the DPFB reaches approximately 0.90. However, under the same conditions, the SPFB exhibits a comparable performance, indicating that the adoption of a double-pontoon configuration does not always yield a substantial improvement in wave attenuation.

By contrast, the arc-plate double-pontoon breakwater proposed in this study—featuring cylindrical pontoons of 0.10 m diameter and 0.09 m draft—achieves a significantly lower transmission coefficient of 0.73 under a shorter wave height of H = 0.08 m. When normalized by floater draft, this corresponds to a relative wave height H/d = 0.89, which is markedly higher than that of the conventional DPFB case (H/d = 0.33). Given the known trend that higher relative wave heights tend to increase transmission, the superior performance of the proposed design under harsher wave conditions further demonstrates its enhanced dissipative capability. This improvement is attributed to the integration of the arc-shaped plate, which effectively augments turbulence and energy dissipation—a mechanism absent in traditional SPFB and DPFB structures.

6. Conclusions

In this study, the wave attenuation performance of a novel arc-plate dual-pontoon floating breakwater with various wave conditions was numerically and experimentally evaluated. The numerical model is in good agreement with the hydrodynamic responses of the arc-plate dual-pontoon breakwater with 10% deviation in both transmission coefficients and horizontal wave forces compared to experimental tests. The findings confirm that appropriate geometric configurations can significantly enhance hydrodynamic efficiency while maintaining structural stability. The main conclusions are summarized below:

• For short-period waves, the arc plate effectively engages with the incident wave, generating strong turbulence and flow redirection that enhance energy dissipation. In contrast, for longer-period waves, the interaction is limited primarily to the front pontoon, resulting in reduced turbulence and weaker wave attenuation. The results highlight the importance of wave–structure interaction timing in determining attenuation effectiveness.
• The increased draft from 0.5D_AS to 0.9D_AP decreased the transmission coefficient at 1.2 s by 33% (from 0.91 to 0.61), while the corresponding horizontal wave force increased by 178% (from 21.8 N to 60.5 N). This demonstrates that the deeper drafts improve wave attenuation significantly but amplify the structural loading.
• Expanding the arc plate span from 350 mm to 550 mm resulted in a 5.9% decrease in transmission coefficient at 1.2 s (from 0.63 to 0.593). The associated horizontal wave force decreased by 31% (from 72.6 N to 49.9 N). Narrower spans enhance wave blocking due to steeper geometry but lead to higher loading.
• As wave height increased from 8 cm to 14 cm, the transmission coefficient increased by 27% (from 0.58 to 0.735), while the horizontal wave force increased by 95% (from 58.5 N to 114.2 N). This indicates that reduced freeboard significantly impairs attenuation effectiveness and increases hydrodynamic loads. A relative freeboard height around 0.7 offers the best performance balance.
• A draft depth of 0.9D_AP, an arc plate span of 450–550 mm, and a relative freeboard height of approximately 0.7 are recommended to achieve optimal wave attenuation and structural efficiency under typical offshore wave conditions.

In future research, several aspects will be further investigated to improve the engineering applicability of the proposed arc-plate dual-pontoon breakwater. First, real-sea experiments will be conducted to validate the model performance under irregular and multidirectional wave conditions and to capture environmental uncertainties not reflected in controlled wave flumes. Second, structural durability under long-term cyclic loading, including fatigue behavior and material degradation, will be examined to ensure operational stability. Lastly, integration with renewable energy systems will be explored, such as coupling the breakwater with floating photovoltaic arrays or wave energy converters, aiming to develop multifunctional offshore platforms that simultaneously provide wave protection and energy harvesting. These developments are expected to enhance the practical value and sustainability of the proposed system in real marine environments.