Review of Coupled Dynamic Modeling Methods for Floating Offshore Wind Turbines

Abstract

Floating offshore wind turbines (FOWTs) are subjected to multiple environmental loads that induce complex coupled dynamic responses. The development of coupled dynamic methods is therefore essential for FOWT analysis and design and has long attracted significant research attention. This paper presents a comprehensive review of the recent advances in coupled dynamic modeling methods and associated numerical tools for FOWTs. First, the fundamental dynamic components are introduced, including aerodynamics, hydrodynamics, elastodynamics, mooring dynamics, and servodynamics. Next, coupled modeling approaches, such as fully coupled, semi-coupled, and frequency-domain methods, are reviewed and compared in terms of their applicability. The paper then outlines the software tools developed based on these methodologies, along with major international code comparison and validation campaigns. Finally, emerging trends in FOWT coupled dynamics are briefly discussed, including integrated marine energy systems, advanced wake modeling, and the incorporation of artificial intelligence techniques in prediction. This paper systematically synthesizes current knowledge on coupled dynamic methods for FOWTs, providing a foundation for future research while also serving as a practical reference for advancing this area of study.

1. Introduction

Climate change and environmental pollution caused by fossil fuels are becoming increasingly severe, driving a global shift toward green and low-carbon energy. Offshore wind power, characterized by abundant resources, high annual utilization hours, and proximity to major electricity demand centers, stands at the forefront of renewable energy development [1,2]. By the end of 2023, global cumulative offshore wind capacity reached 75.2 GW, with a 24% increase compared to 2022. Projections suggest an annual compound growth rate of 15–25% over the next decade, potentially bringing cumulative capacity to 486 GW by 2033 [3]. Early offshore wind farms were typically located in shallow waters within 30 m depth, relying mainly on fixed foundations such as monopiles and jacket structures. However, as development moves into waters deeper than 50 m and continues toward even greater depths, the foundation and installation costs of bottom-fixed wind turbines will rise sharply. In contrast, floating wind technology can overcome limitations imposed by water depth and seabed conditions, offering more economical and flexible installation, as well as greater potential for design optimization. It is thus regarded as a key pathway for the sustainable advancement of offshore wind energy [4,5,6,7,8].

A floating offshore wind turbine (FOWT) typically consists of a wind turbine, tower, floating platform, mooring system, and dynamic cable [9]. The wind turbine captures wind energy and converts it into electricity, involving drivetrain components and electrical equipment [10]. The tower supports the turbine and serves as a critical load-transfer structure between the nacelle and the platform [11]. The mooring system generally includes winches, fairleads, mooring lines, anchors, and buoyancy or ballast elements, and is primarily responsible for station-keeping of the FOWT [12]. Electrical power is transmitted to shore via subsea cables. To accommodate platform motion, these cables are generally suspended using buoyancy units that shape the cable into a sine shape, allowing it to move within a limited range and providing mechanical buffering [13]. Floating platforms take various types, but all achieve hydrostatic equilibrium at a specific draft. This principle, known as hydrostatic stability, enables classification into the following three main types [14]: buoyancy stabilized (e.g., semi-submersible and barge), ballast stabilized (e.g., spar), and mooring stabilized (e.g., tension leg platform), as shown in Figure 1.

After years of development, FOWTs have progressed from laboratory studies to real-world deployment, with several small-scale demonstration farms now in operation. Selected projects are summarized in

Table 1. Statistics of floating wind power prototype projects.

Types	Projects’ Name	Development Company	Country	Site	Time
Ballast stabilized	Hywind [15]	Equinor	Norway	Southwest coast	2009
	SeaTwirl [16]	SeaTwirl Engineering	Sweden	Lysekil	2011
	Advanced Spar [17]	Japan Marine United	Japan	Fukushima	2013
	Windcrete [18]	U.P. Catalunya	Spain	-	2016
	Hywind Tampen [19]	Equinor	Norway	North Sea	2022
Mooring stabilized	Blue H TLP [20]	Blue H Technologies	The Netherlands	Adriatic Sea	2008
	PelaStar [21]	Glosten Associates	USA	-	2013
	Gicon-SOF [22]	GICON	Germany	-	2015
	Provence Grand Large (PGL) [23]	SBM Offshore	France	Mediterranean Sea	2023
Buoyancy stabilized	WindFloat [24]	Principle Power	Portugal	Aguçadoura coast	2020
	Compact Semi-Sub [25]	Mitusui Engineering	Japan	Fukushima	2013
	Floatgen [26]	BW Ideol	France	Le Croisic	2015
	V-Shape Semi-Sub [27]	Mitsubishi Heavy Industries	Japan	Fukushima	2015
	Three Gorges Lead [28]	Three Gorges	China	Yangjiang	2021
	FuYao [29]	CSSC Haizhuang	China	Wailuo	2022
	Guanlan [30]	CNOOC	China	Wenchang	2023
	OceanX [31]	Mingyang Smart Energy	China	Yangjiang	2024

[15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31]. Currently, the levelized cost of FOWT prototypes remains higher than grid parity prices in most countries, presenting a significant economic challenge. However, costs are expected to decline substantially through technological advances such as larger turbines, standardized floating foundation designs, optimized mooring systems, and scaled-up installation processes, etc. Many governments have incorporated FOWTs into their national energy strategies and established specific capacity targets alongside supportive policies [32,33]. The National Renewable Energy Laboratory (NREL) forecasts that global FOWTs’ capacity could reach 16.5 GW by 2030, with Europe, Asia, and North America emerging as key markets [34].

During operation, FOWTs are subjected to complex environmental loads from wind, waves, and currents, as shown in Figure 2. They inherently couple aerodynamics, hydrodynamics, structural dynamics, kinematics, and control systems [35,36,37]. Compared with conventional oil and gas platforms, FOWTs are far more sensitive to wind loading. In many cases, wind even acts as the dominant load. Under gusts, turbulence, and tower shadow effects, the aerodynamic loads exhibit strong nonlinear behavior, often interacting closely with the turbine controllers [38,39,40]. To date, the full complexity of these coupled dynamic responses remains incompletely understood. Consequently, characterizing the coupled dynamics, developing accurate modeling approaches, and building reliable numerical tools have long been central research priorities in the field of FOWTs [41,42,43].

This paper presents a review of modeling methods for FOWTs, aiming to synthesize advances in coupled dynamics modeling methods over recent years and to highlight promising directions for future research. Section 2 outlines the theoretical models for each physical domain, including aerodynamics, hydrodynamics, structural dynamics, mooring dynamics, and control systems. Section 3 summarizes major numerical simulation approaches, such as fully coupled methods, decoupled methods, and frequency-domain techniques. Section 4 describes representative software tools for modeling FOWTs and discusses their key features. Section 5 identifies emerging trends and future research opportunities in modeling methods of FOWTs.

2. Dynamic Methodologies

Fully coupled simulation of an FOWT requires dynamic models from multiple physical domains—namely aerodynamics, hydrodynamics, structural dynamics, mooring dynamics, and servo dynamics, along with their interactions. Over years of research, various computational approaches have been developed for these dynamic models. The choice of method and coupling strategy directly affects the efficiency and accuracy of FOWT numerical simulations. This section, therefore, summarizes the development status for each of these physical domain models.

2.1. Aerodynamics

The core objective of FOWTs is the efficient harnessing of wind energy. However, they often operate in non-uniform inflow wind fields, including gusts, wind shear, and even platform motion induced by wave and current actions. Unsteady aerodynamic states of FOWTs under operation are shown in Figure 3. Accurate prediction of aerodynamic loads is therefore essential but challenging. To address this, researchers have carried out extensive studies on aerodynamic characteristics and developed several aerodynamic load calculation methods. The main approaches include Blade Element Momentum (BEM) theory, vortex methods, and Computational Fluid Dynamics (CFD).

Blade Element Momentum (BEM) theory [45] has become the mainstream approach for modeling rotor aerodynamics of FOWTs due to its computational efficiency and acceptable accuracy for engineering applications. The method combines momentum theory and blade element theory into a two-dimensional, quasi-steady formulation, enabling rapid estimation of aerodynamic performance under various operating conditions. In BEM, the blade is divided into multiple independent radial elements, each analyzed as a two-dimensional airfoil. The local lift, drag, and torque are calculated based on the local inflow angle and relative wind speed. Simultaneously, momentum theory is applied to relate the axial and angular induction factors to the thrust and torque exerted by the rotor on the passing airflow. However, BEM relies on several idealized assumptions that limit its applicability. Various corrections have been proposed to improve its accuracy, such as tip/hub loss corrections [46], Glauert correction for high induction factors [47], yaw/tilted wake correction [48], dynamic stall models [49], and dynamic inflow models [50]. Despite these improvements, BEM still struggles under highly unsteady or strongly coupled conditions—particularly when FOWTs undergo large-amplitude motions. For instance, Matha et al. [51] showed that BEM may fail to accurately capture rotor loads during large six-degree-of-freedom platform motions. Sebastian and Lackner [52,53] identified vortex ring state (VRS) conditions when the platform moves downwind, causing wake reflux perpendicular to the rotor plane—a phenomenon that violates BEM’s momentum conservation assumption (see Figure 3). Similarly, Tran et al. [54] compared BEM with the Computational Fluid Dynamics (CFD) method under platform pitching and found that BEM is adequate for small motions but inaccurate under large pitching amplitudes, indicating its limitations in strongly coupled scenarios.

A recent and promising development is the unified momentum model proposed by Liew and Heck [55]. In contrast to conventional BEM models that rely on empirical corrections, this model is founded upon the conservation of mass, momentum, and energy to simulate wake gradients. It employs an Euler solution and a lifting line model for lateral wake flow. The unified momentum model is capable of predicting rotor yaw and high-thrust movements without the necessity for empirical corrections mentioned previously. Although this model considers only uniform flow as the sole inflow, it provides a foundation for future research on turbulent inflows.

Figure 3. Unsteady aerodynamic states of FOWTs under operation [52].

Figure 3. Unsteady aerodynamic states of FOWTs under operation [52].

The vortex method is another important aerodynamic modeling approach that simulates fluid flow by tracking vorticity within a Lagrangian framework. It is well-suited for potential flow over thin surfaces but limited in handling geometrically complex configurations. Among its variants, the Free Vortex Method (FVM) effectively captures unsteady aerodynamics and wake behavior using three-dimensional vortex filaments [56].

In applications to FOWTs, the FVM effectively captures complex flow phenomena such as vortex ring states and dynamic stall during platform motions, providing more accurate predictions of thrust fluctuations than BEM theory. It also allows for detailed analysis of wake–rotor interactions and aeroelastic coupling, although high-fidelity fluid–structure interaction simulations remain computationally intensive. For instance, Sebastian and Lackner [57] developed and validated the Wake Induced Dynamics Simulator (WInDS), an FVM-based code designed to predict the aerodynamic loading and wake evolution of FOWTs. Separately, Rodríguez and Jaworski [58] extended an FVM solver into an aeroelastic framework capable of modeling the rotor–wake interactions specific to FOWT rotors. Their work demonstrated its superior accuracy in capturing the aeroelastic response under wave-induced motions compared to the BEM and the Generalized Dynamic Wake (GDW) methods [59].

Despite its advantages, the FVM faces challenges related to numerical stability during large platform motions and its typically weak coupling with structural dynamics, which often limits its application in high-fidelity fluid–structure interaction (FSI) simulations. Current research is increasingly focused on hybrid approaches, i.e., coupling FVM with actuator line models (ALM) or reduced-order CFD, to better balance predictive accuracy with computational cost. For instance, Shaler et al. [60] evaluated an FVW model for wind farm–wake interactions, demonstrating its effectiveness in capturing the impact on wake structure, rotor power, and structural response, with predictions showing an average error of less than 13% against experimental data. In a separate study, Perez-Becker et al. [61] compared the BEM theory and the Lifting-Line Free Vortex Wake (LLFVW) method for design load calculations. Their findings indicate that the LLFVW method provides more accurate load predictions, potentially reducing fatigue and extreme load estimates. In contrast, the conventional BEM method may overestimate aerodynamic loads under complex conditions, leading to overly conservative design specifications and increased component costs.

Computational Fluid Dynamics (CFD) is currently the most accurate approach for simulating aerodynamic loads on FOWTs. By numerically solving the Navier–Stokes equations under appropriate boundary conditions, CFD resolves the flow field around the turbine, providing detailed pressure and velocity distributions. With the increasing availability of high-performance computing resources, CFD has become an essential tool for FOWT aerodynamic analysis, particularly for high-fidelity wake prediction [62,63,64]. Common CFD approaches for FOWTs include Unsteady Reynolds-Averaged Navier–Stokes (URANS) and Large Eddy Simulation (LES). The k-ω SST turbulence model is frequently adopted to handle the high-Reynolds-number flow (up to ~10⁷) in the rotor region. For instance, Feng et al. [65] used URANS with the SST k-ω model to study the unsteady aerodynamics of an FOWT under blade pitch motion. Wu and Nguyen [66] developed a CFD model using RANS in OpenFOAM to analyze rotor–platform coupling effects and validated it against NREL’s FAST software. Xu et al. [67] applied LES to investigate FOWT wake dynamics under a complex atmospheric boundary layer. Despite its high accuracy, LES is computationally intensive, prompting the development of hybrid RANS-LES methods [68,69], which use RANS near blade surfaces and LES in separated wake regions to balance accuracy and cost.

A major challenge in high-fidelity CFD is the need for body-fitted grids to resolve blade geometry and boundary layers, along with rotating domains and overset grids, leading to high computational expense. To address this, simplified actuator-based models, such as the Actuator Disk Model (ADM) [70,71], Actuator Line Model (ALM) [72], and Actuator Surface Model (ASM) [73], have been developed. These models represent rotor effects via body forces in the Navier–Stokes equations, avoiding explicit blade geometry resolution and significantly reducing computational cost. Among these, ADM treats the rotor as a permeable disk and is suited for large-scale wake and wind farm analysis. ALM discretizes blades into rotating line elements that apply local airfoil-based forces, capturing tip vortices and unsteady wake structures with greater fidelity, making it a popular choice for FOWT simulations. However, actuator models rely heavily on pre-tabulated airfoil data, which may be unavailable during early design stages, limiting their practical applicability in some cases.

In practice, the selection of an aerodynamic method entails a trade-off between computational cost and accuracy, as summarized in

Table 2. Comparison of aerodynamic analysis methods for FOWTs.

Method	Basic Principle	Applicable Scenario	Advantages	Limitations
BEM	Combines blade element theory with momentum theory	Routine design and loads assessment	High computational efficiency; suitable for optimization	Relies on empirical corrections; struggles with highly unsteady conditions during large platform motions
FVM	Vortex filaments in a Lagrangian framework	Unsteady aerodynamic analysis, aeroelastic response under wave-induced motions	Good balance of accuracy and cost; effectively captures unsteady aerodynamic loads	Numeric instability during large platform motions; modeling viscosity and geometries can be limited
CFD	Numerical solution of the N-S equations	High-fidelity research, benchmark validation	Detailed pressure/velocity fields; highest physical fidelity; suitable for large platform motions conditions	High computational expense; high grid resolution for boundary layers

. BEM theory remains the standard for routine aerodynamic loads calculation due to its computational efficiency. FVM offers a balanced alternative, delivering improved accuracy for the unsteady flow conditions typical of FOWTs. CFD is reserved for high-fidelity research and validation tasks where resolving the full flow physics is essential, despite its substantial computational cost.

2.2. Hydrodynamics

Hydrodynamic analysis of FOWTs primarily focuses on wave load calculations. The main computational approaches encompass potential flow theory, Morison’s equation, and Computational Fluid Dynamics (CFD). Each method has its specific scope of application, and they are often used in a complementary or hybrid manner to balance computational accuracy with efficiency.

Potential flow theory, based on the assumption of an inviscid and irrotational fluid, computes the velocity potential by solving Laplace’s equation with appropriate boundary conditions. The resulting pressure distribution and total hydrodynamic loads on a floating body are obtained numerically using the boundary element method. For large-scale floating structures ($D/\lambda >0.2$), i.e., FOWT platforms, the ratio of characteristic body length (D) to incident wavelength ($\lambda$) is often used as a criterion. In such cases, the inertial wave forces dominate, and viscous effects may be neglected. Therefore, potential flow methods provide sufficient engineering accuracy with high computational efficiency, making them widely adopted in practice [74]. Many industry-standard tools based on this theory include WADAM [75], WASIM [76], and AQWA [77]. Potential flow methods are generally categorized into frequency-domain and time-domain formulations. The frequency-domain approach relies on linear wave theory and assumes small platform motions. The total velocity potential is expressed as a linear superposition of incident, diffraction, and radiation potentials. Boundary conditions are applied on the undisturbed free surface and the initial wetted hull surface. This method is efficient and suitable for small-amplitude waves and motions. Hydrodynamic forces are obtained by integrating pressure from Bernoulli’s equation over the hull surface. The Cummins equation [78] is then used to transform the frequency-domain results into the time domain, a process often referred to as the indirect time-domain method. To account for wave drift force and second-order wave load, a quadratic transfer function (QTF) matrix (a frequency-domain function used to characterize the second-order wave loads on floating structures) must be computed for nonlinear time-domain correction in the frequency-domain approach. Jonkman [79] implemented this method in the HydroDyn module of the FAST code, using frequency-domain hydrodynamic coefficients from WAMIT and converting them into time-domain hydrodynamic loads. Owing to its efficiency, this method remains the dominant approach for FOWT hydrodynamic modeling.

In contrast, time-domain potential flow methods solve the velocity potential directly at each time step using the instantaneous body surface and nonlinear free-surface boundary conditions. This eliminates the need for precomputed QTFs and allows real-time updates of the wetted surface and hydrostatic restoring stiffness. To improve accuracy, various levels of nonlinearity are incorporated, leading to weakly or strongly nonlinear formulations. The weakly nonlinear approaches, such as the Froude–Krylov nonlinear method, update the instantaneous wetted surface when computing Froude–Krylov and hydrostatic restoring forces, while retaining linear assumptions for radiation and diffraction forces. The strongly nonlinear approach, such as the Body-Exact method, solves the full nonlinear diffraction and radiation problems on the exact instantaneous free surface. Zeng et al. [80] emphasize that nonlinear hydrodynamic effects arising from complex wave–structure interactions significantly influence FOWT dynamic behavior. Although time-domain potential flow has long been used in ship hydrodynamics [81,82], its application to coupled FOWT response analysis remains limited. Chen et al. [83,84] addressed this gap by coupling FAST with the time-domain potential flow solver WASIM through an in-house dynamic-link library subroutine, developing an integrated FOWT simulation tool named F2W. The F2W tool with updated wetted surface better represents nonlinear hydrostatic and hydrodynamic effects in FOWT simulations.

For slender structural elements (D/L < 0.2), such as bracing members in a floating platform of an FOWT, the semi-empirical Morison’s equation is widely used in engineering practice to estimate hydrodynamic loads or to provide viscous corrections in potential flow methods [85,86]. The Morison equation decomposes wave forces into inertial and drag components as follows:

$$F\left(t\right)={\displaystyle \frac{\rho \pi D^2}{4}}{\displaystyle \frac{dU\left(t\right)}{dt}}{C}_M+{\displaystyle \frac{\rho D}{2}}{C}_{D}U\left(t\right)\left|U\left(t\right)\right|$$

(1)

where $D$ is the member diameter, $\rho$ is the water density, $U\left(t\right)$ is the water particle velocity, $C_M$ is the inertia coefficient, and $C_D$ is the drag coefficient.

The primary advantage of Morison’s equation lies in its computational efficiency, making it suitable for load estimation on slender members in waves and uniform currents. However, its accuracy is highly dependent on the selection of empirical coefficients C_M and C_D, which are typically determined through experiments and may have limited applicability to complex structural geometries. For instance, Song and Lim [87] applied Morison’s equation to compute wave loads on a TLP-type FOWT. It should be noted, however, that the standalone application of Morison’s equation is generally restricted to structures composed predominantly of slender members. In most practical applications for FOWTs, the potential flow theory serves as the primary method for hydrodynamic analysis. The Morison equation is often incorporated in a complementary role, specifically through its drag term (C_D), to account for viscous damping effects on slender elements. A recognized limitation of this approach is that the drag coefficient C_D is Reynolds-number dependent. The conventional use of a constant C_D value fails to accurately capture the nonlinear viscous hydrodynamic variations induced by platform motions. Consequently, ongoing research, such as that within the OC7 project, is exploring methods to dynamically adjust this coefficient for improved fidelity [88].

In addition to the aforementioned Morison’s equation, viscous drag tuning for FOWTs can also be refined by incorporating an additional viscous damping matrix. These damping matrices are 6 × 6 matrices corresponding to the platform’s six degrees of freedom and typically include both a linear damping matrix and a quadratic damping matrix that depend on the platform’s motion velocities. The specific values within these matrices are usually determined through high-fidelity numerical simulations or experimental methods.

With advances in computational power, Computational Fluid Dynamics (CFD) has become increasingly used in hydrodynamic analysis of FOWTs [89,90,91]. By numerically solving the Navier–Stokes equations, CFD avoids assumptions of inviscid or irrotational flow and directly resolves flow details, enabling accurate prediction of pressure distributions and flow characteristics around platforms. CFD approaches are broadly classified by their resolution of flow scales into direct numerical simulation (DNS), large eddy simulation (LES), and Reynolds-averaged Navier–Stokes (RANS). Compared with potential flow methods, CFD can capture complex viscous effects such as vortex-induced vibrations and turbulence, making it suitable for nonlinear problems and geometrically irregular structures. Cheng et al. [92] developed a fully coupled aero-hydrodynamic FOWT model in OpenFOAM, combining an unsteady actuator line model (UALM) with a two-phase CFD solver, and demonstrated strong wave–structure interactions. Tran and Kim [93] simulated a semi-submersible FOWT using CFD with a moving overset grid to handle large-amplitude motions and the volume-of-fluid (VOF) method to resolve free-surface dynamics. Despite its fidelity, CFD remains computationally prohibitive for most industrial FOWT design workflows, which typically involve numerous simulation cases each requiring durations exceeding 3600 s—far beyond practical limits when computational efficiency is critical.

The three hydrodynamic modeling approaches are summarized and compared in

Table 3. Comparison of hydrodynamic analysis methods for FOWTs.

Method	Basic Principle	Applicable Scenario	Advantages	Limitations
Potential Flow Theory	Solves the Laplace equation with boundary conditions	Large-scale structures; preliminary design stage (D/L > 0.2)	High computational efficiency; suitable for optimization	Neglects fluid viscosity; requires correction for viscous effects
Morison’s Equation	Semi-empirical formula (inertia force + drag force)	Slender/small-scale members (D/L < 0.2)	Simple formulation; high computational efficiency	Relies on empirical coefficients; not suitable for large-scale structures
CFD Method	Numerical solution of the N-S equations	Complex flows; detailed analysis	High accuracy; captures complex flow phenomena	High computational cost; time-consuming

. Potential flow methods offer a favorable balance between computational efficiency and accuracy for FOWT analysis but neglect viscous effects. The Morison equation is limited to slender members and relies on empirical or experimentally derived coefficients, often used in conjunction with potential flow models. CFD captures complex viscous flows but incurs a high computational cost. As a matter of fact, the choice of method therefore depends on the specific modeling demand and available computational resources.

2.3. Elastodynamics

The main components of an FOWT and their associated degrees of freedom (DOFs) are illustrated in Figure 4. The system DOFs typically include the platform’s six rigid-body motions, tower deformation, nacelle yaw, shaft rotation, rotor rotation, and blade pitch motion, blades deformation, etc. Elastodynamics modeling must accurately represent the constitutive behavior of these components and their interactions. Based on the considered degrees of freedom, modeling approaches have evolved from simplified single rigid-body models to multi-body rigid systems, rigid–flexible coupled models, and hydroelastic models, progressively enhancing fidelity. These advances deepen understanding of FOWTs’ dynamic behavior and associated control strategies. With the rapid trend toward larger-capacity turbines, high-fidelity elastodynamics analysis has become essential for optimal design.

The single rigid-body model treats the entire FOWT as an undeformable body, considering only rigid-body motions and neglecting elastic deformation and internal relative motion. Dynamics are solved using Newton–Euler equations. Widely used in offshore oil and gas applications, this approach offers simplicity and computational efficiency, making it suitable for preliminary design comparisons. However, it cannot capture nacelle yaw, rotor rotation, blade or tower flexibility, or their coupling effects in an FOWT. To address this, Chen et al. [94] proposed a correction accounting for gyroscopic coupling between rotor rotation and platform motion in the single rigid-body model. On the contrary, multibody rigid models decompose the FOWT into discrete rigid components, such as the platform, tower, nacelle, drivetrain/generator shaft, hub, and blades—connected by kinematic constraints. Dynamics are typically formulated via Lagrange’s equations [95] or Kane’s method [96], enabling representation of relative motion and coupling, including gyroscopic effects and control actions. Yet, this approach still cannot predict flexible responses like blade flapwise motion or tower vibration, nor provide stress distributions, limiting its use in detailed design.

Furthermore, rigid–flexible coupled multibody models are now the mainstream for FOWT dynamics. In this model, blades and towers are modeled as flexible bodies, while other components remain rigid, i.e., platforms, balancing accuracy, and efficiency in simulations. Flexible members are commonly represented as beam elements. Early studies used Euler–Bernoulli beams [97,98], which are efficient but neglect shear deformation and large-displacement coupling. Chen et al. [99] enhanced this formulation by including axial–transverse strain coupling, enabling capture of dynamic stiffening due to blade rotation. Other researchers [100,101,102] adopted geometrically exact beam models for higher accuracy in large-deformation scenarios, albeit at greater computational cost. Flexible bodies are discretized mainly via modal superposition or finite element methods. Modal superposition reduces degrees of freedom using natural modes, favoring efficiency. Finite element discretization offers higher accuracy at the expense of computational load. The absolute nodal coordinate formulation (ANCF) has emerged as a promising technique for modeling variable-section blades and towers, particularly effective for large deformations [103]. Chen et al. [104] developed a rigid–flexible coupled model to investigate interactions between platform motion and structural deformation. As turbine ratings and platform sizes increase, elastic deformation of the platform and its coupling with hydrodynamics become significant, affecting natural frequencies, strength, and fatigue life. Treating the platform as rigid may introduce non-negligible errors [105,106,107]. Karimirad and Moan [108] modeled a spar-type FOWT using beam elements and Morison’s equation to estimate internal platform loads, though Morison’s approach lacks accuracy in hydrodynamic loading. Luan et al. [109,110] employed a multibody time-domain finite element model coupled with potential flow theory for a semi-submersible platform, redistributing frequency-domain hydrodynamic data onto the structural model to compute internal forces. Hydroelastic analysis of FOWTs is gaining attention [111], and tools like OpenFAST now incorporate capabilities to account for platform hydroelasticity [112].

Chen et al. [113] implemented and compared single rigid-body, multibody rigid, and rigid–flexible coupled models, evaluating their accuracy and efficiency. They further proposed a hybrid dynamics framework that selects modeling fidelity based on design stage requirements. A summary of these methods, their applicability, and numerical characteristics is provided in

Table 4. Comparison of elastodynamic modeling approaches for FOWTs (number of stars represents the level).

Models	Computational Efficiency	Computational Accuracy	Primary Advantages	Applicable Scenarios
Single Rigid Body Model	★★★★	★	Simple modeling, high computational efficiency	Conceptual design, preliminary screening
Multi-Rigid Body Model	★★★	★★	Considers component coupling, high efficiency	Scheme optimization
Rigid–Flexible Coupling Model	★★	★★★	Balances accuracy and efficiency; mainstream method	Detailed design, control optimization
Hydroelastic Model	★	★★★★	Accurate fluid–structure interaction, wet-modal analysis	Hydroelastic response, FSI analysis

.

2.4. Mooring Dynamics

The mooring system provides the connections between the floating platform and anchoring foundations embedded in the seabed and is used for station-keeping of FOWTs. For buoyancy-stabilized platforms, it mainly restricts horizontal offset [114], whereas for tension-leg platforms, it critically constrains both floating equilibrium and vertical motion [115]. Mooring dynamics are governed by highly nonlinear equations that account for geometric and material nonlinearities, fluid–structure interaction, and seabed–mooring contact. FOWT mooring models are broadly classified into quasi-static and dynamic types. Quasi-static models represent each mooring line as a single chain and neglect the inertia and damping. Dynamic models discretize the mooring line—typically using lumped-mass or finite element approaches—and formulate equations of motion via Lagrangian mechanics. These link tension, strain, and external forces at discrete nodes for numerical solution. Masciola et al. [116] compared quasi-static and dynamic mooring simulations for an FOWT. They found that mooring dynamics have little effect on platform motions but significantly influence ultimate line tension and fatigue predictions.

The catenary equation is a quasi-static, approximate formulation for mooring line modeling. It assumes that inertial and damping forces are negligible compared to restoring forces. Therefore, it calculates a single mooring chain in static equilibrium under self-weight and tension, neglecting bending stiffness. The resulting shape can be described by a differential equation whose analytical solution takes the form of a hyperbolic cosine function, which is widely used in FOWT studies [117]. Chen et al. [118] derived the catenary equations for FOWTs’ mooring lines and formulated two distinct nonlinear systems depending on whether a seabed-laid segment exists, enabling tailored initial guesses in Newton–Raphson iterations to improve convergence. Masciola et al. [119] extended the formulation to multiple lines converging at a common point, better representing crowfoot mooring configurations such as those used in the Hywind FOWT. In summary, the catenary method is highly efficient in preliminary mooring design, allowing rapid assessment of line shape and stiffness under varying water depth, chain weight, and pretension. However, its quasi-static assumption prevents accurate representation of dynamic loading induced by wave impacts, mooring–seabed interaction, and material nonlinearity. As a consequence, the mooring dynamic tension mismatch issue may lead to an underestimation of extreme loads or fatigue damage under rapidly varying FOWT operating conditions.

The lumped-mass method discretizes a mooring line into a series of point masses connected by equivalent springs. Contact between the lines and the seabed is modeled using a Coulomb friction element model, and hydrodynamic drift force is incorporated through drag coefficients. By solving the equations of motion at each node, this approach captures the dynamic response of the mooring line under combined wind, wave, and current loads. It does not account for torsional stiffness but remains a widely used dynamic modeling technique for FOWT mooring systems. Hall and Goupee [120] developed such a lumped-mass model, omitting bending and torsional stiffness to enhance computational speed, and validated it against scale-model test data of FOWTs.

The finite element method offers a more accurate numerical framework for mooring dynamics, capable of resolving continuous deformation and stress distribution along the line. The mooring cable is discretized into small elements, each governed by shape functions and material constitutive laws. Dynamic equations are formulated using virtual work or Jourdain’s principle, enabling computation of displacements, stresses, and strains. This approach accounts for axial, bending, and torsional stiffness of mooring lines, allowing detailed analysis of stress concentrations—critical for strength verification and fatigue life prediction in complex three-dimensional scenarios. Li et al. [121] employed a 3D finite element model of FOWT mooring chains, incorporating realistic geometry, nonlinear material behavior, and inter-chain contact, to study time-varying mooring stress under wave loading.

Table 5. Comparison of mooring lines modeling methods for FOWTs.

Methods	Basic Concept	Advantages	Limitations	Applications
Catenary Equation	Based on catenary theory, ignoring inertial and damping effects	High computational efficiency, simple formulation	Unable to capture dynamic effects	Conceptual design, initial screening
Lumped Mass Method	Discrete mass-spring model considering nonlinear effects	Accounts for dynamic mooring effects	Cannot consider torsional stiffness	Detailed design, extreme condition, and fatigue analysis
Finite Element Method	Continuum mechanics approach accurately describing deformations and stresses	Highest theoretical accuracy, detailed stress distribution analysis	High computational cost, poor convergence	Refined strength assessment, local stress analysis

summarizes the advantages, limitations, and typical applications of these three common mooring modeling approaches for FOWTs. In general, the catenary equation offers significant computational speed for preliminary design, but dynamic models, such as lumped-mass and finite element methods, are recommended for fatigue assessment and extreme condition analysis.

The anchor is a critical component of the mooring system, and its type and performance directly affect the overall reliability of the system [122]. Based on working principles and structural features, commonly used anchors in offshore engineering include gravity anchors [123], drag embedment anchors [124], suction anchors [125], screw anchors [126], and pile anchors, etc. In numerical modeling, anchors are typically represented either as fixed or spring-like boundary constraints or through nonlinear anchor–soil interaction models [127].

2.5. Servodynamics

The wind turbine control system aims to optimize wind energy capture while ensuring system safety. Common controllers include nacelle yawing control, generator speed regulation, and blade pitch control. These are typically organized into three hierarchical levels [128]: supervisory control, operational control, and subsystem control. Supervisory control manages turbine startup and safe shutdown. Operational control maximizes energy capture below rated wind speed and limits power output above it, maintaining power quality and structural safety. Subsystem control acts as the execution layer, directly driving mechanisms such as the blades’ pitch system (adjusting blade angles) and yaw system (orienting the nacelle to the wind). It receives commands from higher-level controllers and executes them precisely.

Inflow wind speed is the primary input for turbine control. Classical control strategies partition the operation into distinct wind speed regions, as illustrated in Figure 5.

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Region 1: Wind speed is below cut-in; the turbine remains shut down as power generation is infeasible.

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Region 2: Wind speed lies between cut-in and rated values. The objective is to maximize energy capture, typically by adjusting generator speed to track the optimal tip-speed ratio, with pitch angle held fixed at an optimal setting.

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Region 3: Wind speed exceeds rated. Control shifts to power regulation, maintaining output at rated capacity by increasing pitch angle to shed excess aerodynamic load.

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Transition zone between Regions 2 and 3: The controller smoothly switches strategies to ensure a seamless shift from power maximization to power limitation without abrupt changes.

This control logic has been widely adopted in FOWT designs, including reference models such as the NREL 5 MW reference wind turbine [129], DTU 10 MW reference wind turbine [130], and IEA 15 MW reference wind turbine [131]. Overall, in regions 1 and 4, the wind turbine is in a shutdown state, during which aerodynamic loads primarily come from the aerodynamic drag force on the tower and the static rotor. Although the wind speed in region 4 is higher, the impact of extreme wind speeds can be mitigated by blades pitching under the controller operations, unless there are abnormal aerodynamic loads due to issues like pitch system failures. Rones 2 and 3 are power generation phases for the wind turbine, where aerodynamic loads are mainly composed of aerodynamic thrust and torque from the rotating rotor, with maximum aerodynamic thrust being reached at rated conditions.

In addition, FOWTs exhibit complex six-degree-of-freedom motion responses under marine environmental loads, particularly pitch motion along with tower vibrations. These motions significantly reduce wind energy capture efficiency and can even induce structural fatigue. Consequently, research into motion and vibration mitigation controllers for FOWTs has gained increasing attention [132], broadly categorized into passive, semi-active, and active control strategies.

A widely adopted vibration suppression method is the tuned mass damper (TMD), consisting of a mass, spring, and damper tuned to the natural frequency of the wind turbine structure. When the turbine vibrates, the TMD generates an opposing vibration to absorb vibration energy and reduce vibration amplitude [133]. By strategically placing TMDs in locations such as the nacelle or platform, local vibration amplitudes can be minimized. Passive control strategies optimize TMD parameters like mass ratio, damping ratio, and tuning frequency based on known natural frequencies of the structure [134]. However, these strategies are limited to mitigating vibrations at specific frequencies and cannot address complex excitations. Active tuned mass dampers (ATMDs) use external actuators (e.g., servo motors and hydraulic actuators) to apply forces actively, adjusting the damper’s response dynamically [135,136,137]. While active control enhances adaptability to varying conditions, it increases maintenance and operational costs due to reliance on external power sources during operation. Semi-active control can combine the stability of passive systems with the adaptability of active systems by adjusting parameters such as damping coefficients, TMD stroke, and mass inertia effects based on sensor feedback [138,139,140].

In addition to conventional TMDs, other anti-motion devices have been developed for FOWTs, including tuned liquid column dampers (TLCDs) and gyroscopic stabilizers. TLCDs utilize fluid dynamics to mitigate structural vibrations. Coudurier et al. [141] demonstrated enhanced pitch suppression using a coupled FOWT-TLCD model under wave conditions. Xue et al. [142] further improved pitch motion suppression by integrating a TLCD into a semi-submersible FOWT. Gyroscopic stabilizers, originally used for ship stabilization, have also been applied to FOWTs due to their effectiveness even at low or zero speeds. They generate counteracting moments against the platform’s rotational movements through the gyroscope’s angular momentum. Manmathakrishnan and Pannerselvam [143] conducted scaled model tests on a barge-type FOWT with gyrostabilizers, proving significant reductions in pitch motions under wave action. Wang et al. [144] derived the dynamics equations for passive gyrostabilizers and systematically studied their design and environmental sensitivity in suppressing pitch motion of a semi-submersible FOWT.

Future FOWT control systems may trend towards model-free controllers, suggesting potential integration with artificial intelligence algorithms. Additionally, addressing the high cost associated with anti-motion control systems remains a critical area of research, aiming to develop cost-effective and highly adaptable anti-motion controllers for practical applications.

3. Coupled Modeling Method

A FOWT is inherently a multiphysics coupled mechanical system. Numerical simulation must account for the aerodynamics, hydrodynamics, structural dynamics, mooring dynamics, control systems, and their interactions. Based on differences in modeling approaches and coupling strategies, simulation methods are broadly classified into frequency-domain and time-domain frameworks. Time-domain methods can be further categorized by their coupling fidelity [145], as illustrated in Figure 6. Among them, fluid–structure interaction based on the CFD–FEM method offers the highest theoretical accuracy. However, its computational cost is generally prohibitive for industrial design workflows and is typically reserved for detailed design stages where local structural stresses or viscous hydrodynamic effects must be resolved. Currently, the dominant approach combines potential flow theory for hydrodynamics and Blade Element Momentum theory for aerodynamics within an aero-servo-hydro-elastic framework. This method delivers sufficient accuracy for engineering purposes at a reasonable computational cost. In early design phases, even simpler models or frequency-domain methods are sometimes adopted to further improve efficiency. In practice, accuracy and computational efficiency in FOWT simulation are often conflicting objectives. Designers must therefore select modeling strategies flexibly according to specific design goals.

3.1. Time-Domain Method

3.1.1. Fully Coupled Method

Fully coupled simulation in the time-domain is the prevailing approach in current FOWT modeling. It captures the complex interactions among aerodynamics, hydrodynamics, mooring dynamics, structural dynamics, and servo-dynamics by numerically integrating the system’s nonlinear equations of motion to produce high-fidelity time histories of dynamic response. A typical computational workflow is illustrated in Figure 7. At each time step, physical field data are computed and exchanged across subsystems. In aerodynamics, ambient wind velocities at the blades and tower are combined with structural motion to determine relative inflow. Rotor aerodynamic loads are typically computed using BEM theory or, more accurately, via free-vortex methods. Tower aerodynamic loads are often estimated with simplified drag formulations. For hydrodynamics, the platform response is usually modeled using potential flow theory. A common practice is to first compute frequency-domain hydrodynamic coefficients about the mean waterline, then convert them into the time-domain via Cummins’ equation. Second-order wave forces and wave drift force are often calculated using QTF matrices [146,147]. Structural flexibility is commonly represented using Euler–Bernoulli beam theory for blades and towers, though geometrically exact or Timoshenko beam models are also employed. Structural discretization typically relies on modal superposition or finite element methods. Because the solution proceeds in the time domain, controller dynamics are naturally incorporated into the simulation loop. With all loads and state variables assembled at the current time step, the system dynamic equation, i.e., Kane’s equations, is used to solve generalized accelerations of an FOWT. Time integration then updates positions and velocities, and the process repeats until the simulation reaches its prescribed end time or condition.

3.1.2. Semi-Coupled Method

During early design stages, when turbine configurations are not yet finalized and numerous parameters require optimization, high-fidelity modeling is often impractical. Simplified time-domain coupled models are therefore more suitable. Aerodynamic loads can be approximated using a wind resistance disk model, employing empirical drag formulas, interpolated aerodynamic coefficients, or precomputed load time histories. Mooring systems are typically represented by equivalent linear stiffness matrices or load–displacement lookup tables. In practice, turbine–tower and floater–mooring designs are often handled by separate teams. Load transfer between subsystems is achieved by reducing the turbine–tower unit to equivalent tower-base loads, which are applied at the tower–platform interface for iterative platform analysis. This approach is commonly referred to as the semi-coupled method, as illustrated in Figure 8.

Undoubtedly, the aforementioned decoupling approaches introduce some computational error. The choice of method depends on the design stage and the desired balance between efficiency and accuracy. Kim and Boo [150] compared a fully coupled approach with two semi-coupled methods: one precomputed rotor thrust from a bottom-fixed turbine and applied it at the hub; the other approximated aerodynamic loading using an equivalent actuator disk and drag formulation. Both decoupled methods yielded acceptable errors relative to the full coupling method, making them suitable for rapid preliminary design of FOWT foundations and mooring systems. Gao et al. [151] evaluated a fully coupled model against two decoupled variants. In Model A, wind turbine loads were applied as time histories at the tower base; in Model B, loads were transferred at the hub to the platform–tower system. Their study highlighted the importance of tower flexibility, showing that Model B better reproduced fully coupled results. Furthermore, Wang et al. [149] compared fully and semi-coupled methods for a semi-submersible FOWT, focusing on platform motions and mooring tension. The semi-coupled approach produced slightly more aggressive responses, supporting its use in early-stage design.

However, these decoupled or semi-decoupled methods typically neglect the real-time influence of platform motion on aerodynamic loads, often omitting aerodynamic damping—a simplification that can lead to significant errors. To address this issue, Deng et al. [152] constructed aerodynamic damping coefficients across wind speeds and frequencies, combined them with hydrodynamic coefficients, and incorporated the result into decoupled simulations. Comparison with a standard fully coupled method confirmed the effectiveness of this correction.

3.2. Frequency-Domain Method

In early studies, limited by the immaturity of time-domain coupling theory and tools, researchers often adopted frequency-domain methods and software from the offshore oil and gas industry to analyze FOWT dynamics. For example, Lee [153] applied frequency-domain techniques to evaluate the hydrodynamic performance of a tension-leg FOWT, using response amplitude operators (RAOs) to characterize its fundamental dynamic behaviors. In this model, the rotor system was represented as added mass in the platform’s mass matrix, while hydrostatic stiffness and damping were adjusted to account for aerodynamic effects such as aerodynamic damping. However, unlike oil platforms, FOWTs are strongly influenced by aerodynamic loads and active control actions. Neglecting these effects often leads to significant inaccuracies. Consequently, although frequency-domain methods can capture basic dynamic characteristics, they received limited academic attention for FOWTs and were mainly used only in preliminary design stages. Recently, several researchers have revisited the frequency-domain approach by developing models that incorporate aerodynamic loading. Pegalajar-Jurado et al. [154] introduced QuLAF (Quick Load Analysis of Floating Wind Turbines), which uses precomputed aerodynamic loads from FAST and extracts aerodynamic damping from free-decay simulations to enable rapid frequency-domain analysis of four planar degrees of freedom of an FOWT. Notably, QuLAF simplifies blade motion effects by approximating aerodynamic loads with those of a fixed hub, rigid blades, and linear damping terms. Later, Hall et al. [155] developed RAFT (Response Amplitudes of Floating Turbines), a new frequency-domain dynamics model that couples quasi-static mooring reactions and linearized turbine control. Its key innovation lies in accounting for dynamic variations in rotor speed and pitch angle by linearizing the equations of motion, yielding a simplified but more accurate aero-control representation in the frequency-domain. Chen et al. [156] adopted a similar strategy to develop DARwind-FD, a frequency-domain tool for FOWTs. Validation against FAST simulations showed good agreement, demonstrating the renewed potential of frequency-domain methods when enhanced with appropriate aerodynamic and control modeling.

The three coupled modeling methods are summarized in

Table 6. Comparison of coupled modeling methods.

Method	Basic Principle	Accuracy	Efficiency	Scenario
Fully Coupled	Solves loads and dynamics jointly in each time step via time integration.	High; suitable for nonlinear loads and control behavior.	Relatively low, depends on the flow-field solver.	Detailed design stage.
Semi-Coupled	Allows separate solving of loads; uses load time history or simplified models.	Acceptable for engineering (may need iterations).	Fits engineering workflow needs.	Common commercial collaborations
Frequency domain	Based on linear superposition; solves in the frequency-domain.	Captures main characteristics but misses nonlinear behavior.	Fast solution speed.	Preliminary design

. The aero-servo-hydro-elastic fully coupled method is currently the most widely used approach; it can simulate nonlinear time-domain behavior of the FOWT system and offers high computational accuracy, though its efficiency is generally low (depending on the specific aerodynamic and hydrodynamic flow field calculation methods adopted). The semi-coupled method allows loads to be solved separately, making it suitable for collaboration between different design teams; its accuracy often requires improvement through multiple iterative calculations between collaborators. In contrast, the frequency-domain method is based on the principle of linear superposition, making it incapable of capturing nonlinear system behaviors, but it boasts high computational efficiency and is well-suited for preliminary design stages.

4. Development of Numerical Software

Based on the numerical methods and coupling strategies described above, numerous simulation tools for FOWTs have been developed [157]. These can be broadly categorized into frequency-domain tools, such as QuLAF [154] and RAFT [155], and time-domain tools, with the latter being the most numerous and widely used for integrated FOWT analysis. The key distinctions among these software packages are summarized in

Table 7. Comparison of FOWTs simulation codes.

Code Name	Aerodynamics	Structural Dynamics	Hydrodynamics	Mooring Model	Controller Model	References
FAST	(BEM or GDW) + DS + DI	T: Mod/MBS P: Rigid	PF + QD + MD	QS/FE/Dyn	DLL or UD or SM	Jonkman, et al. [148]
FAST + CHARM3D	(BEM or GDW) + DS	T: Mod/MB P: Rigid	PF + ME + MD + NA + IP + IW	FE/Dyn	DLL or UD	Shim and Kim [167]
F2A (FAST + AQWA)	(BEM or GDW) + DS	T: Mod/MB P: Rigid	PF + ME	QS/Dyn	DLL or UD	Yang, et al. [169]
F2W (FAST + WAMIT)	(BEM or GDW) + DS	T: Mod/MB P: Rigid	TF + ME + MD + IP + IW	QS/Dyn	DLL or UD	Chen, et al. [83]
BLADED	(BEM or GDW) + DS	T: Mod/MB P: MB	ME + IP + IW	QS	DLL	Hassan [162]
QBlade	BEM + FVM	T: Mod/MB P: MB	PF + QD + MD	QS/Dyn	DLL	Perez-Becker et al. [166]
SIMA (SIMO/RIFLEX)	BEM + DS + DI	T: FE P: Rigid	PF + ME	FEM	DLL or UD	Chen et al. [158]
OrcaFlex	BEM, GDW, or FDT	T: FE P: Rigid	PF + ME	LM/Dyn	UD	Thomsen et al. [159]
HAWC2	(BEM or GDW) + DS	T: MB/FE P: MB/FE	ME	FE/Dyn	DLL or UD	Larsen and Hansen [163]
3Dfloat	BEM + FDT	T: FE P: FE	ME + (IW)	FE/Dyn	DLL or UD	Nygaard et al. [160]
DeepLinesWT	BEM	T: FE P: FE	PF + ME + (IW)	FE/Dyn	DLL	Papi et al. [165]
SIMPACK + HydroDyn	BEM or GDW	T: Mod/MB P: Rigid	PF + QD	QS	DLL	Matha et al. [168]
SAToe	BEM	T: Mod/MB P: Rigid	PF + ME + MD + NA + QD	QS/Dyn	UD	Chen et al. [164]
Structural Dynamics: • T = Turbine • P = Platform • W = Water • Mod = Modal • MB = Multi-Body • FE = Finite Element •N/A = Not Applicable	Aerodynamics: • BEM = Blade-Element/Momentum • GDW = Generalized Dynamic Wake • DS = Dynamic Stall • FDT = Filtered Dynamic Thrust • FWV = Free-Wake Vortex		Hydrodynamics: • PF = Potential Flow theory • ME = Morison Equation • MD = Mean Drift • NA = Newman’s Approximation • IP = Instantaneous Position • IW = Instantaneous Water Level • QD = Quadratic Drag		Mooring Model: • QS = Quasi-static • Dyn = Dynamic • LM = Lumped Mass • FE = Finite Element

. Some tools originated from marine hydrodynamic software and were later extended with aerodynamic and control modules—for example, SIMA [158], OrcaFlex [159], and 3DFLOAT [160]. Others evolved from simulation platforms originally designed for bottom-fixed offshore wind turbines, enhanced with hydrodynamic and mooring modules, including FAST [161], Bladed [162], and HAWC2 [163]. A third group was developed specifically to address the rigid–flexible coupling characteristics of FOWTs, such as SAToe [164], DeepLinesWT [165], and QBlade [166]. A further category integrates functionalities from multiple existing tools or leverages open-source modules through multi-program coupling to achieve comprehensive FOWT simulations. Examples include CHARM3D + FAST [167], SIMPACK + HydroDyn [168], F2A [169], and F2W [83,84].

As shown in Figure 9a, most FOWT hydrodynamic solvers rely primarily on frequency-domain potential flow theory based on the mean waterline and wetted surface. Time-domain hydrodynamic forces are then reconstructed via Cummins’ equation using predefined sea state parameters. However, this approach cannot capture nonlinear variations in hydrostatic and hydrodynamic forces caused by dynamic changes in the platform’s wetted surface. It also fails to provide direct time-domain external pressure distributions on hull panels. Consequently, subsequent structural stress analyses often require additional tools to perform forced-motion simulations that reproduce hydrodynamic pressures [170,171]. To address this limitation, Chen et al. [83,84] developed the F2W tool, which couples the time-domain potential flow solver WASIM with FAST’s aerodynamic and control subroutines via in-house dynamic link libraries. This enables continuous updating of the platform’s waterline and wetted surface at each time step, allowing direct computation of external panel pressures. The resulting structural analysis workflow, shown in Figure 9b, improves both the accuracy and the efficiency of the stress analysis workflow.

To verify the accuracy of numerical simulation tools for FOWTs, researchers commonly employ code-to-code comparisons or code-to-experiment validation. The International Energy Agency (IEA) has sponsored a series of benchmarking initiatives, including the well-known OC3 (Offshore Code Comparison Collaboration) [172], OC4 (Offshore Code Comparison Collaboration Continuation) [173,174], OC5 (Offshore Code Comparison Collaboration Continued with Correlation) [175,176,177], OC6 (OC5 with unCertainty) [178,179,180,181], and the most recent OC7 (Offshore Code Comparison Collaboration 7) [88]. The primary objectives of these projects are summarized in

Table 8. Statistics of OC projects for FOWT numerical tools.

Project	Time	Primary Objectives	Key Technical Focus
OC3	2007–2010	Establish benchmark for coupled simulation tools of FOWTs, focusing on spar-type platforms.	Used Hywind Spar (5 MW turbine) to validate aero-hydro-servo-elastic coupling models.
OC4	2014–2017	Validate semi-submersible platform modeling tools through code-to-code comparisons.	Adopted OC4-DeepCwind semi-sub design (5 MW turbine); compared Morison equation vs. potential flow theory.
OC5	2017–2020	Validate simulation tools against physical test data (1:50 scale model).	Conducted decay/wave tests to separate wave excitation/radiation forces, quantifying viscous drag errors.
OC6	2019–2023 (phased)	Three-way validation: high-fidelity tools (CFD), engineering tools, and experimental data.	Introduced the TetraSpar platform (1:43 scale) and analyzed nonlinear hydrodynamics/wake effects.
OC7	2024–2027 (ongoing)	Improve hydrodynamic load predictions for large-scale FOWTs (10 MW+) and reduce LCOE to €40–60/MWh.	Focuses on viscous drag tuning, structural flexibility, and farm-scale wake modeling.

. Over the years, they have brought together researchers worldwide to systematically compare and validate diverse numerical methods and simulation tools for FOWTs, significantly advancing the development of FOWT numerical modeling techniques.

5. Future Trends and Challenges

The following three key trends are poised to shape the future of FOWT modeling: their integration into broader marine energy systems, the growing challenge of wake effects in large-scale FOWT farms, and the transformative application of artificial intelligence to numerical simulation. This section will examine these developments and their potential impact on FOWTs’ modeling.

5.1. Integrated Marine Energy Systems

In recent years, to reduce costs and improve energy output, some researchers have proposed integrating FOTWs with wave energy converters (FOWT–WECs). The EU FP7 MARINA Platform project introduced several conceptual designs of such hybrid systems [182], including the Spar–Torus Combination (STC, see Figure 10a) [183,184], WaveStar [185], W2Power [186], and SFC (see Figure 10b) [187]. Compared with standalone FOWTs, the submerged WEC components in FOWT–WECs can harvest wave energy to supplement power generation and simultaneously mitigate platform heave and pitch motions, thereby enhancing energy capture efficiency [188,189,190]. However, the more complex structure may increase system failure risk and pose additional challenges for coupled dynamic modeling.

On one hand, the relative motion between the floating platform and WECs introduces multibody constraint conditions and complex hydrodynamic interactions. Lee et al. [191] treated the entire FOWT–WEC system as a single rigid body, neglecting internal relative motion, and then analyzed the performance of multiple heaving WECs mounted on a semi-submersible platform in the frequency domain. Muliawan et al. [192] developed a numerical model of the STC, representing the power take-off (PTO) system as a linear spring–damper and evaluating its dynamic response. Zhang et al. [193] studied the coupling between an FOWT and two types of WECs, modeling each WEC’s PTO as a heave-directional spring–damper system. Zheng et al. [194] examined how PTO control affects the dynamics of a combined wind–wave system, modeling the hydraulic PTO as a Coulomb damping system for greater realism. On the other hand, coupling between aerodynamic and hydrodynamic loads remains a key challenge. Zhou et al. [195] computed hydrodynamic coefficients for a TLP-type FOWT integrated with a WEC using AQWA, while aerodynamic thrust was estimated via a thrust–wind speed fitting function derived from the NREL 5 MW reference turbine data. Ermando Petracca et al. [196] implemented an aerodynamic module based on Blade Element Momentum theory in MATLAB R2022 and coupled it through Simulink with a WEC-Sim model that included mooring lines, point absorbers, and the floating platform to simulate the full coupled system.

Beyond wind–wave integration, researchers have also explored FOWT combinations with tidal energy converters (see Figure 10c) [197,198,199] and floating photovoltaics (see Figure 10d) [200,201]. These integrated marine platforms are becoming increasingly complex in structure. Their numerical modeling must address structural constraints among subsystems, hydroelasticity, and full aero-hydro-structural-servo coupling. Given the limitations of any single software package, coupling multiple specialized tools—often via dynamic link libraries or co-simulation interfaces—has emerged as a key enabling technique in this field.

Figure 10. Integration with renewable energy systems. (a) STC [183], (b) SFC [187], (c) HWNC [197], (d) FOWTs+ solar PV [200].

Figure 10. Integration with renewable energy systems. (a) STC [183], (b) SFC [187], (c) HWNC [197], (d) FOWTs+ solar PV [200].

5.2. Wake Modeling

Compared with fixed-bottom wind farms, FOWT farms exhibit several distinct characteristics. For example, FOWTs’ supporting structures undergo significantly larger motions—horizontal displacements can reach tens of meters, pitch angles may approach 10°, and notable yaw motion is also present. Consequently, the wake field behind FOWTs becomes considerably more complex [202,203,204]. Lee et al. [205] investigated wake evolution under different platform motion modes using the nonlinear vortex lattice method (NVLM). They found that pitch, roll, and yaw motions exert a stronger influence on the wake than the other motions and that platform motions intensify wake breakdown—a behavior markedly different from that of fixed turbines. In general, the wake region is typically divided into a near-wake and a far-wake zone, as shown in Figure 11. The near wake contains multiscale vortex structures, including tip, root, and hub vortices. As these vortices advect downstream, they progressively break down and dissipate into small-scale turbulence in the far wake, where the flow gradually recovers its velocity. Therefore, accurate prediction of wake structure is essential for simulating floating wind farms and forecasting their performance. Primary computational approaches include analytical wake models and Computational Fluid Dynamics (CFD).

In analytical wake modeling, Jensen [206] proposed the well-known Jensen wake model in 1983, based on momentum conservation and assuming an axisymmetric velocity deficit profile. This model was later extended and refined by Katić et al. [207] and is now widely implemented in bottom-fixed wind farm analysis tools such as WAsP [208] and WindPRO [209]. More recent analytical models include the Larsen model [210], the Ishihara wake model [211]—an extension of the BP model that accounts for both velocity deficit and turbulence intensity—and the dynamic wake meandering (DWM) model [212], which captures unsteady wake oscillations behind wind turbines. However, these models were originally developed for bottom-fixed turbines. For FOWTs, platform motions introduce additional complexity into wake dynamics. Adapting conventional models requires corrections for motion-induced turbulence and wake centerline displacement, which has become a focal point of current research. Li and Yang [213] developed a linearized wake model using resolvent analysis of the Linearized Navier–Stokes Equations (LNSE). This approach efficiently predicts coherent turbulent structures driven by harmonic platform motions, with each simulation completing in minutes on a standard personal computer. Wang et al. [214] proposed a novel three-dimensional analytical wake prediction method that integrates realistic inflow disturbances and a physics-based wake expansion formulation tailored for FOWTs. Jonkman et al. [215,216,217] developed FAST.Farm, a numerical tool for simulating floating wind farms, by integrating an enhanced DWM model within the OpenFAST software. This improved model overcomes several limitations inherent in conventional DWM implementations.

To achieve more precise wake field details, researchers have employed CFD methods, which solve the three-dimensional Navier–Stokes equations to obtain flow field information. These methods include direct numerical simulation (DNS) [218], large eddy simulation (LES) [219], and Reynolds-averaged Navier–Stokes (RANS) simulations [220]. Due to the high computational cost of directly simulating wind turbines and wind fields, actuator disk/actuator line methods (ADM/ALM) are often used to represent the effects of turbine blades. Mikkelsen [221] combined LES with actuator line modeling (ALM) to conduct numerical analyses of turbine wake fields, demonstrating the accuracy of LES coupled with ALM for wake calculations.

In summary, FOWTs exhibit coupled aerodynamic-motion characteristics, often involving significant pitch and yaw motions, making their wake fields more complex and variable compared to fixed-bottom turbines. While CFD methods can simulate intricate flow phenomena, they struggle to accurately account for blade aeroelastic effects and pitch control actions on FOWT wakes, often facing high computational costs. Meanwhile, conventional analytical wake models fail to fully incorporate the influence of FOWT motions on wake structures, leading to significant prediction errors. Therefore, developing efficient and accurate analytical wake models for FOWTs is crucial. This advancement holds significant practical importance for improving the design and operation of floating offshore wind farms.

Figure 11. Wake structure of an FOWT [214].

Figure 11. Wake structure of an FOWT [214].

5.3. Intelligent Computing and Prediction

Accurate wind power forecasting is critical for grid dispatch, yet full physical simulations of wind farm wakes and power output are computationally expensive. Consequently, many researchers have turned to artificial intelligence for efficient prediction. Common approaches include convolutional neural networks (CNNs), long short-term memory networks (LSTMs), and temporal convolutional networks (TCNs). These models leverage historical data to capture spatial and temporal dependencies in wind speed or power, though their performance depends heavily on the availability of large, high-quality datasets. Wang et al. [222] proposed a deep learning ensemble for probabilistic wind power forecasting. Their method applies a wavelet transform to decompose the signal, then uses a CNN for feature extraction and point prediction, and finally constructs a probability distribution by quantifying data uncertainties. Zhang et al. [223] enhanced forecast accuracy by integrating numerical weather prediction (NWP) wind speed correction with an EMD-LSTM framework. The model decomposes the power time series and predicts each component separately with LSTM, effectively handling volatility. Chen et al. [224] developed a deep spatio-temporal network (DSTN) that exploits multi-location spatio-temporal correlations for multi-step, multi-site wind speed forecasting. Dai et al. [225] introduced a hybrid model combining improved K-means clustering with a weighted DCNN–LSTM–Transformer architecture for 24 h offshore wind power prediction. Zhang et al. [226] proposed a hybrid wind speed forecasting model that couples Variational Mode Decomposition optimized by the White Shark Optimizer (WSO-VMD) with a multi-scale CNN–GRU network. In addition, Wu et al. [227] proposed a rapid wake forecasting method for an FOWT using dynamic mode decomposition (DMD) and bidirectional long short-term memory (BiLSTM).

In addition, short-term prediction of FOWT dynamic responses can provide early input signals for control systems, enhancing operational safety. Yin et al. [228] employed a bidirectional long short-term memory (BiLSTM) network to forecast platform motions induced by irregular waves, achieving reliable predictions up to 10 s ahead with high accuracy even under strong noise. Shi et al. [229] proposed a multi-input LSTM method using platform motion, wave height, and mooring tension as inputs. Compared with a multi-input 1D convolutional neural network (MI1D-CNN), their model delivered accurate short-term forecasts across various sea states. Jiang et al. [230] combined intermediate-scale physical testing and numerical simulation of a semi-submersible FOWT to generate high-fidelity data. They trained and compared machine learning models, including genetic algorithm–back propagation (GA-BP), support vector machine (SVM), and Gaussian process (GP), finding GP most effective, especially for mooring tension prediction. This highlights the potential of GP to link environmental loads with dynamic responses for FOWT monitoring. Ilardi et al. [231] applied kernel methods, neural networks, and ensemble algorithms to rapidly predict hydrodynamic response amplitude operators (RAOs) of FOWTs. Their approach reduced computation time significantly while maintaining accuracy within 3% of CFD results. Wang et al. [232] introduced the Low-frequency Adds Wave-frequency Responses (LAWR) method, using an optimized LSTM to separately predict low- and wave-frequency components of mooring tension before superposition. This strategy improved prediction accuracy by over 30%. Bjørni et al. [233] used artificial neural networks (ANNs) to predict mooring tension for a spar-type FOWT, aiming to replace computationally intensive simulations. Their optimized ANN achieved high accuracy, particularly in mild sea states, showing promise for efficient mooring design. Chen et al. [234] developed an AI-based approach named SADA, which combines a Deep Deterministic Policy Gradient (DDPG) algorithm with the numerical solver. Trained on basin test data, SADA adaptively tunes key model parameters to substantially improve the prediction accuracy of FOWT dynamic responses.

Data-driven artificial intelligence (AI) algorithms are revolutionizing the computation and prediction of dynamic responses in FOWTs, achieving levels of accuracy and efficiency unattainable by traditional methods. Despite this promise, the practical application of these data-driven algorithms in FOWT engineering projects faces significant hurdles. Their inherent black-box nature, which limits interpretability, coupled with a heavy reliance on extensive training datasets and poor transferability to new scenarios, hinders their deployment. Nevertheless, emerging advancements in AI large models and the integration of physics-informed methods are illuminating novel pathways to overcome these barriers, heralding a new phase for AI-driven modeling in floating wind energy.

6. Conclusions

This paper provides a comprehensive review of coupled dynamic theories, modeling approaches, and numerical tools for FOWTs. It also examines emerging trends and key challenges in FOWT coupled dynamics. The synthesis offers a systematic technical reference for FOWT calculation and outlines potential pathways for future development. Key conclusions are summarized as follows:

FOWT simulations require multi-physics modeling. The choice of method typically balances computational efficiency and accuracy. In aerodynamics, BEM remains dominant; CFD is indispensable for high-fidelity wake modeling; and FVM offers a favorable trade-off between accuracy and cost. For hydrodynamics, frequency-domain potential flow theory is still standard, though time-domain potential flow and viscous correction approaches are gaining attention. Structural dynamics primarily rely on rigid–flexible multibody formulations, with fully flexible hydroelastic models emerging as turbine size increases. Mooring dynamics are commonly modeled using dynamic lumped-mass approaches, while quasi-static catenary models persist in early design due to their high efficiency. Control strategies now extend beyond rotor speed and bladed-pitch control to include nacelle vibration and platform motion mitigation.

Coupled FOWT modeling is broadly categorized into time-domain and frequency-domain approaches. Fully coupled time-domain simulation remains the industry standard. However, semi-coupled methods are often adopted in practice due to data or resource constraints. Enhancing the fidelity of semi-coupled approaches presents a persistent engineering challenge. A range of simulation tools has emerged based on different theoretical and coupling frameworks. Most are built on time-domain fully coupled formulations, combining BEM aerodynamics with frequency-domain potential-flow hydrodynamics. The central goal is to improve accuracy without compromising computational efficiency. Emerging tools increasingly integrate FVM aerodynamics, time-domain potential-flow hydrodynamics, and data-driven artificial intelligence techniques, reshaping the landscape of FOWT simulation.

Looking ahead, as FOWTs grow in individual capacity and are deployed at scale, their modeling methods and tools will continue to evolve. This review highlights several emerging directions and associated modeling challenges, including integrated marine energy systems based on FOWTs, floating wind farm wakes, and data-driven simulation powered by artificial intelligence technology.