# A comparison of MCOL and CEL approach for ship-FOWT collision assessment

Palaniswamy Chandrasekaran Abhemanyu, Ye Pyae Sone Oo, Hervé Le Sourne, Patrick Kaeding, Thomas Lindemann

► To cite this version:

Palaniswamy Chandrasekaran Abhemanyu, Ye Pyae Sone Oo, Hervé Le Sourne, Patrick Kaeding, Thomas Lindemann. A comparison of MCOL and CEL approach for ship-FOWT collision assessment. 10th International Conference on Marine Structures (MARSTRUCT 2025), May 2025, Lisbon, Portugal. pp.235-243, 10.1201/9781003642411-29 . hal-05507302

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# A comparison of MCOL and CEL approach for ship-FOWT collision assessment

P.C. Abhemanyu

ICAM School of Engineering, Nantes, France

Universität Rostock, Rostock, Germany

Y. Pyae Sone Oo & H. Le Sourne

ICAM School of Engineering, Nantes, France

Ecole Centrale de Nantes, Nantes University, CNRS, Nantes, France

P. Kaeding & T. Lindemann

Universität Rostock, Rostock, Germany

**ABSTRACT:** Collisions between ships and Floating Offshore Wind Turbines (FOWTs) pose a challenge to the offshore wind industry. Thus, this study aims to develop a framework for numerical simulations of the collision using the Coupled Eulerian Lagrangian (CEL) approach in LS-DYNA. The parameters governing the Fluid-Structure Interaction (FSI) modelled using the CEL approach are calibrated by confronting the results obtained from Boundary Element Method (BEM) solvers. The collision between an Offshore Supply Vessel (OSV) and the NREL 5MW reference wind turbine mounted on the OC3 HYWIND spar platform is simulated. The research compares results from semi-coupled simulations using MCOL solver and fully-coupled simulations based on the CEL approach. The strengths and limitations of both methods in capturing complex FSI phenomena during the collision event are discussed. The complications associated with setting up the correct FSI coupling using the CEL approach are presented while the validated results are critically examined.

## 1 INTRODUCTION

The global push for decarbonisation and fossil fuel independence has led to a significant expansion of offshore wind farms in recent years. As the demand for clean energy grows, Floating Offshore Wind Turbines (FOWT) have emerged as a promising solution for harnessing wind power in deeper waters. However, this rapid growth in offshore installations has also increased the risk of ship collisions with these structures, presenting a critical challenge for the offshore wind industry. Some accidents (Buitendijk 2022; Buljan 2023; Safety4Sea 2020) over the recent years have highlighted that the potential for ship-FOWT collisions is a serious concern requiring thorough investigation and mitigation strategies. These incidents can result in severe consequences, including structural damage, environmental pollution, and potential loss of life.

Ship collisions are characterised by complex physical interactions involving transfer of energy and momentum between the structures and the surrounding environment. In addition to the dynamic effects of rigid body motions, nonlinear effects due to geometry, material and contact are also present (Storheim & Amdahl, 2017). Furthermore, the fluid-structure

interaction effects due to surrounding water also have a dynamic and nonlinear nature (Samuelides & Frieze, 1989; Song et al., 2016).

With recent advancements in computational capabilities, the Coupled Eulerian Lagrangian (CEL) approach seems a promising solution to model the complex Fluid-Structure Interaction (FSI) effects during ship collisions (Gagnon & Wang, 2012; Song et al., 2016; Ye et al., 2023).

Gagnon and Wang (2012), performed numerical simulation of a collision between a tanker and a bergy bit. A parametric study was conducted and a fluid element size of 2m was chosen. The sway motion of the bergy bit due to the bow wave is used as an index to validate the fluid-structure interaction. This strategy has been used by Gagnon and Derradji-Aouat (2006) to compare the results obtained from LS-DYNA ALE (Arbitrary Lagrangian Eulerian) simulations to the experimental data obtained from the tank test.

Song et al., (2016), compared the FSI method and the Constant Added Mass (CAM) method for simulating ice-structure collisions. The FSI in LS-DYNA was validated by comparing the added mass coefficients to the results obtained from the potential flow solver WADAM. The accelerations of the floating
block obtained from FSI simulations were in close agreement with the experimental results during the initial response stage. The study concludes that the FSI method could provide more accurate results, but at a significantly higher computational cost.

Ye et al., (2023) used the ALE method to simulate oblique ship-bridge collisions. The fluid-structure interaction was verified using the same process as Song et al., (2016). The effect of including ambient boundaries has also been studied. Their study concludes that, while the CAM method may be suitable for head-on collision scenarios, the impact duration and impulse for oblique collisions are underestimated by such an approach.

The FSI of ship-ship collision was studied using LS-DYNA ALE by Song et al., (2017). A fluid mesh size of 1m was determined to be appropriate. The results of penetration and loss of initial kinetic energy were discussed. The contact forces obtained from the FSI simulations significantly differed from the CAM simulations for a moving struck ship. However, FSI and CAM methods predicted the energy dissipation in good agreement with each other and analytical formulations for a stationary struck ship. The study also shows that the CPU time for the ALE approach is one order of magnitude higher than that of the CAM approach.

Guo et al., (2022) studied the collision of a ship with a Tension Leg Platform (TLP) wind turbine using LS-DYNA ALE. The hydrodynamic effects of surrounding water for the striking ship were modelled using the CAM method, while the ALE method was used for the TLP. The research article shows that internal energy accounts for more than 80% of the total energy in the system. The authors recommended using the ALE method to analyse hydrodynamic effects during ship-FOWT collisions.

The study reported in ClassNK (2023), showed identical results for the sway velocity of the struck ship using MCOL and S-ALE (Structured-ALE). The difference in energy absorbed by the struck ship between MCOL and S-ALE was only 3%.

The effectiveness and added value of using the CEL approach to model ship-FOWT collisions are still active areas of research. The present work aims to develop a fully-coupled numerical simulation framework using the CEL approach and validate the FSI effects obtained. Finally, a numerical simulation of an OSV colliding with a FOWT is performed using a semi-coupled approach based on the MCOL solver and a fully-coupled CEL approach, and the results are compared.

# 2 METHODOLOGY

## 2.1 LS-DYNA/MCOL coupling

MCOL is a rigid body dynamics solver, used to analyse ship collisions ()Le Sourne et al., 2001, 2003. LS-DYNA/MCOL is a semi-coupled approach in

which the internal mechanics are solved by the Non-Linear Finite Element Analysis (NLFEA) solver of LS-DYNA, and the rigid body motions influenced by fluid-structure interactions are solved using MCOL.

In such a semi-coupled approach, the surrounding water is not explicitly modelled. Instead, parameters governing FSI, such as the hydrodynamic added mass matrix, wave radiation damping matrices and hydrostatic restoring matrix, are computed using external seakeeping codes and given as user-defined inputs to the MCOL solver (Ferry, 2002b, 2002a). The latter calculates the hydrodynamic forces acting on the floating structure, such as water inertial, hydrostatic, wave radiation and drag-damping forces. The NLFEA solver in LS-DYNA computes the contact force, which is an input to MCOL. The kinematic quantities resulting from solving the governing equation of motion, are transferred from MCOL to LS-DYNA for subsequent time steps, and this loop continues until the termination time is reached. This study uses the commercial software package ANSYS AQWA to calculate the hydrostatic and hydrodynamic properties of the striking OSV and the struck FOWT, which are required as inputs to MCOL.

## 2.2 Coupled Eulerian-Lagrangian approach

The Coupled Eulerian-Lagrangian (CEL) is a fullycoupled approach where the surrounding water is explicitly modelled. The floating structures, namely the striking ship and the FOWT, are modelled using the Lagrangian description. The surrounding water is meshed using the multi-material Arbitrary Lagrangian Eulerian (ALE) elements with a single integration point in LS-DYNA. The ALE method is a computational technique that combines the advantages of both Lagrangian and Eulerian methods to model the dynamics of deformable objects and fluid-structure interactions (Donea et al., 2004).

The new S-ALE solver in LS-DYNA is used in this study. This allows for easier creation of rectilinear meshes to represent the fluid domain. The number of inputs needed to define the FSI coupling has also been reduced. FSI coupling is modelled using the penalty algorithm in the compression direction (Chen, 2016, 2020). With this new keyword \*ALE\_STRUCTURE\_D\_FSI, only the penalty factor PFAC governing the coupling stiffness needs to be correctly defined. The software automatically adjusts the number of coupling points, leakage control parameters and damping.

Nevertheless, there are several limitations to modelling an FSI problem using penalty coupling in the ALE formulation (LS-DYNA Aerospace Working Group, 2022).

* The solver used is not a complete Navier-Stokes solver. Hence, it cannot fully account for the effects of fluid viscosity, such as the boundary layer.

* Turbulence models are not included in the solver. Hence, the effects of vortex generation (e.g. drag effect) cannot be accurately modelled.
<figure><img src="image_2.png" /><figcaption>Figure 1. Finite element model of the FOWT.</figcaption></figure>

* The compressible solver was mainly developed for short-duration simulations with high-velocity gradients and is predominantly applicable for laminar flows.

* The penalty coupling algorithm models fluid-structure interaction using virtual springs that prevent a fluid element (Eulerian) from penetrating a solid/shell element (Lagrangian). Hence, the fluid-structure interaction force is always a function of penetration, whereas in reality, the fluid-structure interaction forces are proportional to accelerations (fluid inertial forces) and velocities (drag and wave radiation forces) (Song et al., 2016).

# 3 NUMERICAL MODELLING

## 3.1 Finite Element modelling

The 5 MW baseline wind turbine from NREL (Jonkman et al., 2009) and OC3 HYWIND Spar (Jonkman, 2010) are used in this study. The turbine tower and the floating spar platform are modelled as simple tubes without internal stiffening elements. The rotor-nacelle-assembly (RNA) is modelled as a rigid body. An arbitrary hull form resembling an Offshore Supply Vessel (OSV) is used for the striking ship. The geometry of the striking ship's bow is modelled according to the dimensions reported by Echeverry Jaramillo, (2021).

Under-integrated Belytschko-Tsay shell elements with five through-thickness integration points are used to model the Lagrangian parts — OSV and FOWT. The stress-strain relationship for steel is modelled as a bilinear curve. The material properties of steel used in this study are shown in Table 1.

Unlike LS-DYNA/MCOL, in CEL simulations, the submerged portion of the FOWT is subjected to

external hydrostatic pressure. Since internal stiffening elements are not included in the finite element model, the thickness of the submerged portion must be sufficient to resist buckling by external pressure. The thickness of the submerged FOWT portion is adjusted to resist buckling and maintain the center of gravity (COG) same as the original model described by (Jonkman, 2010).

A refined mesh of 200 mm is used for the region of the FOWT tower impacted by the ship. A mesh size of 1m is used for the submerged portion of the spar. This maintains a 1:1 ratio between the Lagrangian and ALE parts. Finally, the nodes around the meta-center of the FOWT are grouped as a nodal rigid body (see Figure 1) to apply kinematic boundary conditions.

<table><caption>Table 1. Steel properties used for FE model.</caption><thead><tr><th></th><th></th><th>FOWT Tower</th><th>SPAR</th></tr></thead><tbody><tr><td>Density</td><td>[kg/m³]</td><td>8200</td><td>7800</td></tr><tr><td>Young's Modulus</td><td>[GPa]</td><td>210</td><td>210</td></tr><tr><td>Poisson's Ratio</td><td></td><td>0.33</td><td>0.33</td></tr><tr><td>Yield Stress</td><td>[MPa]</td><td>255</td><td>255</td></tr><tr><td>Tangent Modulus</td><td>[GPa]</td><td>4</td><td>4</td></tr><tr><td>Failure Strain</td><td></td><td>0.2</td><td>-</td></tr></tbody></table>

## 3.2 Fluid Domain modelling

In the ALE approach, the surrounding water and air are modelled as NULL materials using linear polynomial equations of state (EOS). The properties and corresponding coefficients of air and water used for modelling are listed in Table 2. Gravity load must be
considered for the correct representation of buoyancy forces. The intensity of gravity load is increased over 0.5 seconds, to eliminate pressure fluctuations in the fluid.

<table><caption>Table 2. Coefficients of air and water EOS models.</caption><thead><tr><th></th><th></th><th>Air</th><th>Water</th></tr></thead><tbody><tr><td>Density – ρ</td><td>[kg/m³]</td><td>1.18</td><td>1025</td></tr><tr><td>C0</td><td>[Pa]</td><td>0</td><td>101325</td></tr><tr><td>C1</td><td>[Pa]</td><td>0</td><td>2.25×10⁹</td></tr><tr><td>C2,C3,C6</td><td></td><td>0</td><td>0</td></tr><tr><td>C4,C5</td><td></td><td>0.4</td><td>0</td></tr><tr><td>E0</td><td>[Pa]</td><td>253312.5</td><td>0</td></tr></tbody></table>

## 2.5 FSI validation

Setting proper penalty coupling parameters in the CEL approach is crucial for correctly representing the FSI forces. An over-stiff coupling can cause an abrupt computation halt, while insufficient coupling stiffness leads to fluid leakage through the structure. Initially, the FOWT is placed in the water domain at its floating equilibrium position. All degrees of freedom (DOFs) of the FOWT are constrained for the first 0.8 seconds and later released. Irrespective of the PFAC value, the FOWT did not remain in a floating equilibrium position. For this study, the representation of hydrodynamic added mass of FOWT in surge or sway direction is prioritised over hydrostatic equilibrium. A sensitivity analysis is performed to choose the PFAC value that can correctly represent the added mass of the FOWT. A common strategy used to verify added mass is to apply an oscillating force to the submerged structure, compute the added mass from the equation of dynamic equilibrium shown in (Song et al., 2016; Ye et al., 2023).

$$ (M + M_a)\ddot{x} + C\dot{x} + Kx = F_x \quad (1) $$

where M is the rigid body mass matrix, $M_a$ is the hydrodynamic added mass matrix, C is the damping matrix, K is the hydrostatic restoring matrix, x is the displacement vector and $F_x$ is the resulting force vector.

A similar strategy is used in this study. The Morison's equation (2), which describes FSI forces for an oscillating flow around a cylinder, is used to validate the CEL approach. The FOWT is placed in its floating equilibrium position in the fluid domain. All other DOFs except surge are constrained, and a sinusoidal displacement ($x = A \sin(\omega t)$) is imposed on the FOWT.

$$ F_{\text{ext}} = (M + M_a)\ddot{x} + \frac{1}{2} \cdot \rho A_{\text{proj}} C_D \dot{x} |\dot{x}| \quad (2) $$

The resulting sway force ($F_x$) and kinematic quantities - acceleration ($\ddot{x}$) and velocity ($\dot{x}$) are measured. The added mass in surge ($M_a$) and the drag coefficient

($C_D$) are computed by curve fitting $F_x$, $\ddot{x}$ and $\dot{x}$ to equation (2). The range of usable PFAC values to avoid uncontrolled computation halt, as well as resulting added mass and drag coefficients are highlighted in green in . PFAC values greater than $1 \times 10^{-4}$ lead to an over-stiff coupling and those lesser than $1 \times 10^{-6}$ lead to fluid leakage. It is observed that both $M_a$ and $C_D$ are overestimated using the CEL approach in LS-DYNA.

The overestimation of $M_a$ and $C_D$ is a possible consequence of interface reconstruction (Olovsson, 2006) and handling of FSI forces using the ALE method. The added mass is purely a result of fluid motion and is unaffected by the hydrostatic pressure. Whereas in the ALE method, the user-defined coupling parameter – PFAC is responsible for avoiding fluid penetration into the structure (Olovsson, 2006). Hence, the penalty coupling must simultaneously account for both the inertial pressure of the fluid and the hydrostatic pressure. For the SPAR structure with a draft of 120 m, the variation in hydrostatic pressure along the depth is very high and could lead to a possible error in estimating the added mass effect. Similarly, the uncertainty of using the ALE method for long explicit simulations might also contribute to this error in added mass (LS-DYNA Aerospace Working Group, 2022). Nevertheless, the exact reason for the overestimation of $M_a$ and $C_D$ is still unknown. For the subsequent collision simulations, a PFAC value of $1 \times 10^{-4}$ is chosen.

# 4 CASE STUDIES

## 4.1 Simulation setup

External effects due to wind, waves and mooring lines are ignored for this study. Only a head-on collision scenario is considered. Due to the symmetry of events about the longitudinal vertical plane, the sway, roll and yaw DOFs are constrained for both the OSV and the FOWT. Four simulations are performed for each OSV striking velocity of 2m/s and 5m/s. The boundary conditions used for the different simulations are explained below.

### 4.1.1 LS-DYNA/MCOL

Two LS-DYNA/MCOL simulations are performed for each striking velocity. In both simulations, the OSV is placed close to the FOWT tower there are no initial penetrations. Initial velocities of the OSV are prescribed for each simulation. The OSV is treated as an object with a constant added mass (CAM), including the hydrodynamic added mass to its rigid body mass.

**M:SPAR** - MCOL boundary condition is enabled only for the FOWT. The OSV is constrained in all DOFs except surge.

**M:SPAR+SHIP** - MCOL boundary condition is enabled for the FOWT and the OSV. No additional boundary conditions are imposed on the OSV.

### 4.1.2 CEL simulations (LS-DYNA/S-ALE)

Two CEL simulations are performed for each striking velocity. Only the FOWT is coupled to the surrounding
water using the S-ALE penalty coupling. The striking OSV is always treated as a CAM object and is con- strained in all DOFs except surge. In all CEL simula- tions, gravity load is imposed on the fluid domain and all structural parts, except the OSV. In S:SPAR, the FOWT can translate freely in the heave direction. In S: SPAR (Noheave) an artificial constraint is imposed on the heave DOF of the FOWT. This helps prevent FOWT's sinking and maintains the same point of impact when the OSV collides with the FOWT tower.

ship and FOWT occur over a single contact. In CEL simulations, only a single contact is observed for a ship speed of 2 m/s, whereas for a ship speed of 5 m/s, a second contact is also observed.

### 4.2.2 Penetration

The penetration value reported in this study is the node-to-node distance between two circumferen- tially opposite points in the impacted zone. It is used as a representative measure of the local crush-

<figure><img src="image_3.png" /><figcaption>Figure 2. Variation in added mass and drag coefficient with PFAC.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Figure 3. Time history of contact force in surge (horizontal) direction.</figcaption></figure>

## 4.2 Results

### 4.2.1 Contact force

Figure 3 shows the time evolutions of contact force in the surge direction during the collision for the two striking velocities of 2m/s and 5m/s. Both MCOL and CEL approaches predicted the same forces for the first 0.2 seconds. In all MCOL simulations, the energy and momentum transfer between the striking

ing as well as the global bending of the tower (if applicable).

Figure 4 shows the time history of penetration for different simulations. Both CEL and MCOL approaches show similar time evolutions of penetra- tion. Variations in penetration are observed even when contact forces are zero. This phenomenon is attributed to the global bending and elastic vibrations of the FOWT tower.
<figure><img src="image_5.png" /><figcaption>Figure 4. Time history of penetration in the horizontal direction.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Figure 5. Time evolution of deformation energy of the impacted region.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Figure 6. Contours of Von-Mises stress and Effective plastic strain, 2.5 seconds after impact.</figcaption></figure>

### 4.2.3 Deformation energy

The time evolution of deformation energy is measured only at the impacted region and shown in Figure 5. Both CEL and MCOL simulations predict similar damage to the FOWT tower, with the CEL simulation showing slightly higher deformation

energy (approximately 2 MJ for a striking velocity of 5m/s).

This observation is further supported by the stress-strain contours of the damaged tower shown in Figure 6, where CEL simulation shows slightly larger regions of higher effective von Mises stress.
Large masses at the RNA and the bottom of the SPAR affect the tower's global bending after impact. The rigid body motions of the tower and the SPAR and, consequently the global bending also influence the damage by creating zones of local crushing, which are highlighted in red in Figure 6.

## 4.3 Rigid body motions

The time evolutions of the surge displacement and pitch angle of the impacted FOWT are shown in Figure 7 & Figure 8 respectively. The initial metacentre of the FOWT is used as a reference point to measure both the surge displacement and the pitch angle.

In both CEL and MCOL simulations, the displacements are similar for the initial stages of collision. But, after approximately 1 second, a significant deviation is observed between MCOL and CEL, for both pitch angle and surge displacement.

The percentage reduction in surge displacement and pitch angle compared to MCOL at t=4s after impact are shown in Table 3. By imposing artificial constraints on the heave motion, CEL simulations predict slightly higher displacements than simulations without the heave constraint.

<figure><img src="image_8.png" /><figcaption>Figure 7. Surge displacement of FOWT after impact measured at metacentre.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Figure 8. Pitch angle of FOWT after impact, measured about metacentre.</figcaption></figure>

<table><caption>Table 3. Reduction in surge and pitch for CEL simulations.</caption><thead><tr><th></th><th>v<sub>impact</sub> = 5m/s</th><th>v<sub>impact</sub> = 2m/s</th></tr></thead><tbody><tr><td colspan="3"><strong>Surge Displacement</strong></td></tr><tr><td>S:SPAR</td><td>47.9%</td><td>44.7%</td></tr><tr><td>S:SPAR (Noheave)</td><td>42.7%</td><td>40.1%</td></tr><tr><td colspan="3"><strong>Pitch Angle</strong></td></tr><tr><td>S:SPAR</td><td>49.8%</td><td>55.3%</td></tr><tr><td>S:SPAR (Noheave)</td><td>38.7%</td><td>47.3%</td></tr></tbody></table>

The overestimation of FSI forces can reason for the reduction in displacements ($M_a$ and $C_D$) in the CEL approach, as observed in the validation studies. The CEL approach highly overestimates the drag coefficient. During the initial stage of collision, the velocity of the FOWT is negligibly small and hence drag forces are insignificant. However, as the velocity of FOWT increases after collision, the drag forces acting on it also increase, leading to reduced surge displacement in CEL simulations. In the same way, the overestimated water-added mass results in too much inertial pressure

<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /></figure>
exerted by the fluid and, consequently, in an underesti-
mated displacement and pitch of the FOWT.

Additionally, the pitch angle is influenced by the
hydrostatic restoring moment acting on the SPAR. In
LS-DYNA S-ALE, the restoring moment could not be
accurately measured during the validation studies.
However, given that the added mass and drag forces
are overestimated, similar reasoning can be extended to
the hydrostatic restoring moment due to the penalty
coupling.

3.4 Computational efforts

All MCOL simulations were performed using LS-
DYNA version: SMP d R11.0.0, whereas all CEL
simulations were performed using LS-DYNA version:
MPP d R14 with 128 cores. For CEL simulations
using the ALE method, additional simulation time is
required to impose gravity loads while avoiding
abrupt pressure fluctuations in the fluid domain.

Due to differences in the simulation end times and software versions, a direct comparison of the CPU time cannot be made. A more convenient and meaningful way to compare computational efforts is to compare the ratio of CPU time to the total simulation end times for each simulation. The computational efforts measured using CPU time are compared for MCOL and CEL simulations in Table 4. The advection and FSI processes in S-ALE make the highest contribution to the computation costs. Similarly, the inclusion of 8-noded solid elements to represent the surrounding water in CEL simulations also adds to the higher computational cost.

<table><caption>Table 4. Comparison of computational cost.</caption>
  <thead>
    <tr>
      <th></th>
      <th colspan="2">MCOL</th>
      <th colspan="2">CEL</th>
    </tr>
    <tr>
      <th>Sim End Time</th>
      <th>7.5 seconds<br>Time [s]</th>
      <th>Ratio</th>
      <th>10 seconds<br>Time [s]</th>
      <th>Ratio</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <th colspan="5" style="text-align: left;">Element Processing</th>
    </tr>
    <tr>
      <td>Shell</td>
      <td>425.0</td>
      <td>56.7</td>
      <td>35.45</td>
      <td>3.54</td>
    </tr>
    <tr>
      <td>Solid</td>
      <td>-</td>
      <td>-</td>
      <td>934.36</td>
      <td>93.44</td>
    </tr>
    <tr>
      <th colspan="5" style="text-align: left;">Contact Algorithm</th>
    </tr>
    <tr>
      <td></td>
      <td>213.0</td>
      <td>28.4</td>
      <td>335.59</td>
      <td>33.56</td>
    </tr>
    <tr>
      <th colspan="5" style="text-align: left;">S-ALE</th>
    </tr>
    <tr>
      <td>FSI</td>
      <td>-</td>
      <td>-</td>
      <td>2610.6</td>
      <td>261.06</td>
    </tr>
    <tr>
      <td>Advection</td>
      <td>-</td>
      <td>-</td>
      <td>5554.1</td>
      <td>555.41</td>
    </tr>
    <tr>
      <td><strong>Total CPU time</strong></td>
      <td>2493.0</td>
      <td>332.4</td>
      <td>14418</td>
      <td>1441.80</td>
    </tr>
  </tbody>
</table>

4 CONCLUSION

Head-on collision of an OSV with a FOWT is com-
pared using a semi-coupled simulation - LS-DYNA
/MCOL, and a fully-coupled CEL simulation using

LS-DYNA/S-ALE. The nature of FSI forces obtained using LS-DYNA/ALE was validated against results obtained from Boundary Element Method (BEM) solvers. The main results from the study are summarised as follows:

* The FSI forces obtained in LS-DYNA/ALE were overestimated by a large margin compared to BEM solvers.

* The results obtained between LS-DYNA/MCOL and LS-DYNA/S-ALE for the peak contact force and deformation energies agree well.

* Overestimation of FSI forces (added mass and drag coefficient) in LS-DYNA/S-ALE results in underestimation of rigid body motions of the struck FOWT, but the damage to FOWT remains largely unaffected by this.

* CEL simulations incur higher computational costs due to explicit modelling of surrounding water and how fluid-structure interaction is handled using the S-ALE approach.

* CEL simulations using LS-DYNA/S-ALE presented some modelling challenges discussed below.

In addition to the limitations of the ALE formu-
lation and penalty coupling algorithm, modelling
the collision event in the CEL approach presented
several other challenges. The buoyancy forces
could not be correctly modelled in LS-DYNA
/S-ALE. This created a need to impose artificial
constraints on the heave DOF of the FOWT.
Another major drawback of the penalty coupling
algorithm concerns the choice of coupling param-
eters. The existing guidelines for modelling FSI
using LS-DYNA/S-ALE (LS-DYNA Aerospace
Working Group, 2022) focus on preventing fluid
leakage through the fluid-structure interface. This
approach works well for simulating short-duration
events such as slamming (Yu et al., 2019), bird
impacts, etc. However, the efficacy of this approach
in accurately representing FSI forces in ship collis-
sions remains uncertain.

No specific guidelines exist for modelling FSI of
large floating bodies using LS-DYNA/S-ALE. The
appropriate choice of coupling parameters can only
be determined through trial and error, requiring
a significant amount of computation time to set up
a simulation. Every simulation necessitates unique
calibration of the coupling stiffness. Hence, the
results obtained from LS-DYNA/S-ALE cannot be
generalised based on the same coupling parameters.
This restricts the use of CEL simulations performed
with LS-DYNA/S-ALE as a benchmark tool to val-
idate other numerical methods.

Similarly, the lack of a well-defined procedure for
validating the CEL simulations is also a limitation.
Experimental verification of maritime accident scen-
arios can be expensive and time-consuming. Even if
experiments are performed and replicated using the
CEL approach, extending the same simulation setup to
a full-scale event cannot guarantee accurate modelling
of FSI forces.
Consequently, the present CEL modelling approach in LS-DYNA cannot be reliably employed as a benchmark tool to validate studies on ship collisions with FOWTs. Further research is necessary to develop S-ALE modelling methods to correctly represent FSI forces on deep draft structures such as the SPAR FOWT and be reliably used over long-duration simulations.

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