The increasing demand for renewable energy sources presents challenges to the offshore wind industry. As wind turbine generators grow in size, their foundations must scale accordingly. The growing monopile weights are posing risks to existing jack-up vessels that install these components. The increasing weight of monopiles results in larger deck loads, which requires engineers to assess the structural integrity of these vessels using the finite element method. However, due to the substantial size of these vessels, finite element models require significant computational resources. Therefore, efficient methods are needed to reduce model size and complexity.

While the literature does not specifically address finite element techniques for jack-up vessels, similar challenges have been extensively studied in the field of aerospace engineering. Such finite element techniques include, surrogate models, adaptive mesh refinement, submodelling, substructuring and model order reduction. The application of these techniques is mainly due to the significant size of the structures they are used to deal with, resulting in a reduction of computational time. A combination of substructuring and model order reduction results in a superelement. Its potential in this engineering discipline is the main reason for its selection in this research.

To understand the behaviour of superelements and their impact on computational time and accuracy, an exploratory study was conducted, comparing the results to a reference model without superelements. Parameters that potentially influence the performance and outcome of the results are studied. These parameters include model complexity (1D versus 2D finite elements), the number of superelements applied to the model, the mesh size of the superelement, the number of modes incorporated in the superelements solution, and the connection type. Based on the outcome of the exploratory study, the parameters are reevaluated and used to validate the applicability to an existing model of a jack-up vessel via a case study.

The case study utilises the outcomes of the exploratory study to a real-world model of a jack-up vessel. Several locations at the structural elements of a jack-up vessel are compared while reducing the size of the model's stiffness matrix with five variations. The first serves as the reference model with no superelements. The second introduces superelements for the legs, the third adds the stern, the fourth incorporates the bow, and the fifth further includes detailed deck geometry to the superelement of the stern already made in the third iteration. As a result, the stiffness matrix decreases up to 42%, reducing the computational time by 47% in the fifth variation. However, the fifth variation shows inaccuracies in total deformation and underestimates the von Mises stress by up to 15%. In contrast, the fourth variation demonstrated a more reliable balance between efficiency and accuracy, with a 21% reduction in the size of the stiffness matrix, a 23% improvement in computational time per single run, and deformation and stress deviations of 3% and 10%, respectively.

A more representative measure for evaluating computational efficiency is the scenario in which an engineer is required to solve a model 50 times due to changes in its geometry. In this case, the superelements computational time is included, but it should be noted that this is only required for the initial run. The cumulative computational time for variation four demonstrates that the application of superelements becomes more efficient than the conventional approach from the sixth run onwards. This results in a 26% increase in efficiency over 50 runs.

This study shows that superelements can effectively reduce model size and computational effort when assessing jack-up vessels' structural integrity. While accuracy deviations must be evaluated carefully, this research presents that superelements can substantially increase the efficiency with minimal loss in accuracy. This suggests that superelements are a promising method to apply for structural integrity analysis on large structures such as jack-up vessels.

Large-scale cultivation of seaweed presents opportunities for multiple global challenges currently at play. Cultivated seaweed can provide a sustainable source of protein for humans and cattle without competing for land, freshwater supply or the use of fertilisers. Kelp forests are known to be a solid basis for an elaborate biome that supports biodiversity in areas that have been damaged by over-fishing or rising sea temperatures. Additionally, kelp forests can lock-in large amounts of Blue Carbon, expanding the oceans’ buffering capacity to mitigate anthropogenic emissions. Furthermore, with their densely seeded lines, offshore kelp farms are found to attenuate wave amplitude, thus providing coastal protection and benefits like increased workability for offshore operations. Both academic publications and industry reviews underline the potential of this sector and significant growth in cultivation is expected in the near future.

Methods currently used for quantification of the damping effects of large-scale offshore kelp farms are diverse and entail varying degrees of accuracy and computational cost. Experimental observations that support the outcomes of these methods are limited to scaled experiments in wave flumes, with various methods used to mimic vegetation. No convergence is found in the most suitable methods for application to large-scale offshore kelp farms.
This research presents a novel modelling framework based upon the Finite Element method, implemented using Julia Programming Language. The effects of the vegetation on the wave climate are represented with a Darcy-Forchheimer term borrowed from porous medium flow theory, including a linear and a quadratic resistance term. The framework comprises a numerical wave tank, using the incompressible Navier Stokes equations. The single-phase model captures the free surface using the coupling of dynamic pressure with a virtual elevation variable through a linearized transpiration boundary condition. Wave energy dissipation is shown to increase significantly by moving the farm structure close to the water surface. Similarly, a decrease in relative water depth - compared to the vegetated height - increases damping potential. Wave period is found to be of strong influence on dissipation, where short waves are attenuated more. Scaling vegetation length with wave length, however, diminishes the reduction in damping of longer waves. Conversely, wave amplitude is shown to be of less influence on the transmission of amplitude through a vegetated patch.
The framework presents a method that is easily scalable, flexible in application on a wide range of flows and vegetation characteristics, and at reasonable computational cost. Introduction of both the linear and quadratic terms extends applicability compared to traditional methods. The approach is verified using convergence studies, application of the model is validated by comparison to existing experimental data. It is shown that experimental set-ups can be reproduced effectively, and simulation results coincide with experimental findings. Validation of outcomes on scales larger than common wave tanks was found unfeasible due to a lack of measurement data. A theoretical case study was performed to predict wave damping of a full-scale kelp farm, demonstrating promising potential with up to 40% wave energy reduction at the local peak wave period.

Further research into the establishment of the Darcy- and Forchheimer-coefficients is recommended. A preliminary range of values has been found, based upon calibration on existing experiments that represent realistic ranges of vegetation characteristics. Furthermore, the main conditions of the flow and vegetation that dictate damping potential are identified. On this basis, research into a physics-based determination of the coefficients is recommended. Additionally, full-scale measurements are advised to validate application on future kelp farm designs.
Through this novel approach, the range of application is increased compared to existing methods, while straightforward setup and usage are governed, and limited computational costs allow for simulation without the need for a dedicated computer setup. The framework is shown to be robust by generating consistent simulation results. In summary, the established framework shows to be a good alternative to existing approaches to investigate the wave damping potential of large-scale offshore kelp farms.