Powerful numerical simulation tools can assist in gaining a better understanding of the hydrodynamic effects acting during landing maneuvers of supply vessels at offshore structures. To this end, the panel code panMARE has been extended by a method specifically designed to include wave-body interactions considering the non-linear free surface and thus allows the simulation of landing maneuvers at offshore structures.
This extension method of panMARE has been used to successfully simulate the landing maneuver of a catamaran vessel at an offshore monopile foundation, which is visualised in Figure 1. The simulation is performed in the time domain and based on potential theory.
As part of panMARE, the method uses the existing boundary element method (BEM) and computes the rigid body's motions caused by the acting hydrodynamic loads. Thereby, the hydrodynamic loads are made up of the incoming waves, the diffraction that is caused by the monopile, and the radiation effects due to the catamaran itself. Additionally, a fender model has been implemented, which is able to consider the reaction forces caused by friction and the fender's deformation. Hereby, the model can discern between a slip and a non-slip condition of the fender.
The coordinate system and definitions used in the numerical simulation are illustrated in Figure 2, whereas the contact model is visualised in Figure 4.
The numerical results have been compared with experimental data gained from model tests of the landing maneuver, as visible in Figure 3.
In the model tests both landing craft and monopile where scaled in equal measure with the model catamaran pushing against the monopile. During the model tests the forces at the fender's attachment as well as the motions of the vessel were measured in both regular and irregular waves.
The comparison of the numerical results with the model test data has shown, that the developed method is capable of quantifying the risk of the fender slipping, as described in detail in Ferreira (2015).
The underlying theory of panMARE's free-surface extension method is only briefly summarised here. It is illustrated and explained extensively in Ferreira (2020).
The simulation method combines the boundary element method (BEM) panMARE with the Mixed Eulerian-Lagrangian (MEL) approach.Hereby, the Dirichlet boundary condition is applied on both the body and the free water surface for solving the boundary integral equation. Additionally, the acceleration potential is also solved in the numerical method as part of the solving routine. The solution of the acceleration potential ensures an accurate and robust computation of the hydrodynamic pressure. Based on the pressure's accuracy, the hydrodynamic forces and the body's motion are also computed with high precision. Furthermore, the added mass is calculated. This leads to higher numerical stability of the equation of motion's integration.
The simulation method has been validated by the following cases:
Firstly, simulations of a cylinder in waves have been performed. The numerical results have been compared with both a higher order panel method as well as experimental data and show good agreement.
Secondly, a catamaran comprised of Wigley hull forms has been simulated in head waves with forward speed and the computed forces on the hull forms, as well as the motions have been compared with experimental data. Especially for a fixed model the calculated forces showed a particularly good agreement with the measured forces. Even though some differences concerning the response amplitude operator (RAO) of non-slender hulls remained, the overall comparison of numerical and experimental results shows generally fair agreement.
Thirdly, the comparison of calculated forces and motions of a landing maneuver of a catamaran at an offshore monopile structure with experimental results has shown good agreement, as presented above.
In conclusion, the numerical method is able to solve different types of wave-body interaction problems, whereby further development is planned in order to reduce the occurrence of deviations in blunt hull non-fixed cases (see Ferreira (2020)). Future work will also focus on the transom stern of ships. Once a transom stern condition is implemented, the wave forces acting on more practical vessel geometries can be computed using panMARE.