Periodic Reporting for period 2 - EAGRE (Eagre/Aegir: high-seas wave-impact modelling)
Période du rapport: 2022-01-01 au 2023-12-31
The EU project ``Eagre: high-seas wave-impact modelling'' (project no. 859983) has established numerical wavetanks with which we have analysed the effects of extreme waves and wave-wind-turbine interactions, for deployment in the maritime-engineering sector. The project has been founded on an active collaboration between the University of Leeds and the Maritime Research Institute Netherlands (MARIN).
Wave modelling is societally important in terms of the safety and reliability of offshore industries and shipping at sea. Minimising damage to marine structures is not only crucial for cost-effective and efficient operations in the maritime-engineering sector but also equally important in the mitigation of both environmental disasters and potential loss of life at sea.
Research on establishing and testing numerical wavetanks has been based on new techniques involving variational principles (VPs) as well as software modelling tools at MARIN, for both physical continuum modelling and computational implementations. Advantages of using VPs have been that they have provided stable, robust and efficient numerical methods, implemented in an automated manner in the fine-element environment Firedrake. The distinctively challenging aspect has been the dynamic interaction of evolving unknown boundaries of fluid and solid components, resolution with cutting-edge mathematical theory and numerical techniques. Our numerical models have been validated against data from wavetank measurements, including a new dataset on fluid-structure interactions (FSI). This automated implementation of numerical schemes using VPs and the acquisition of new FSI data are the highlights of our project.
Wave modelling is societally important in terms of the safety and reliability of offshore industries and shipping at sea. Minimising damage to marine structures is not only crucial for cost-effective and efficient operations in the maritime-engineering sector but also equally important in the mitigation of both environmental disasters and potential loss of life at sea.
Research on establishing and testing numerical wavetanks has been based on new techniques involving variational principles (VPs) as well as software modelling tools at MARIN, for both physical continuum modelling and computational implementations. Advantages of using VPs have been that they have provided stable, robust and efficient numerical methods, implemented in an automated manner in the fine-element environment Firedrake. The distinctively challenging aspect has been the dynamic interaction of evolving unknown boundaries of fluid and solid components, resolution with cutting-edge mathematical theory and numerical techniques. Our numerical models have been validated against data from wavetank measurements, including a new dataset on fluid-structure interactions (FSI). This automated implementation of numerical schemes using VPs and the acquisition of new FSI data are the highlights of our project.
Against this background, results obtained in the two research stream are as follows:
Extreme waves:
- Models for the interactions between waves and currents with constant vorticity have been derived in detail based on variational and Hamiltonian analysis, including a description of how a variational, finite-element potential-flow wavetank can be extended to include constant-vorticity currents in a two-dimensional vertical plane.
- A numerical wavetank has been (re)defined based on discretising the relevant Luke's variational principle (VP) in space and time.
- Coordinate transformations and dynamic mesh motions have been explored since these lead to an implementational innovation with potential high gains in computational efficiency, of which the main exploration is reported elsewhere (in the other subproject).
- A series of benchmark problems has been investigated, including various improvements, with enhanced performance, to the numerical formulation and its associated code.
- New test cases concerning short-crested waves have been defined in detail, which includes a novel analysis of exact solutions of the Kadomtsev-Petviashvilli (KP) equation; such exact solutions have defined the initial conditions for simulations within the numerical potential-flow wavetank. These finings were published in two publications in the journal Water Waves.
- A robust wavebreaking parameterisation based on diffusivity has been analysed; it has led to a preliminary investigation of a potentially new alternative based on augmented Hamiltonian dynamics. In addition, we have refined coupled potential-flow and shallow-water model, the latter at the beach where wavebreaking is occurring.
Wave-Turbine Impact:
- With reference to wave-impact on a wind-turbine mast modelled as a hyperelastic beam, the theoretical and numerical formulation of the coupled dynamics of water waves and beam motion have been investigated using variational principles (VPs). Due to the complexities involved, and for didactic training purposes, the methodology has been developed by considering a hierarchy of increasingly-complex dynamical problems, as follows.
- The VP of the nonlinear hyperelastic beam was investigated in separation, including some preliminary numerical tests.
-A first theoretical formulation, based on the relevant VP, was made of the coupled dynamics.
- A digression was made investigating the generation of water waves by a waveflap. Its numerical formulation requires a coordinate transformation and its discretisation is related to that for the coupled wave-beam problem. It results in a final time-discrete VP directly of use for a numerical discretisation. This was published in a first refereed (OMAE) conference proceeding.
- Full theoretical and numerical formulations are considered of the coupled problem, again using VPs, in which various computational-grid-transformation strategies are explored.
- Novel FSI experiments were designed and performed at MARIn. Results were presented in a second, refereed OMAE proceeding, on GitHub as well as a larger archived report.
- Using bespoke MARIN software, first validation of the nbew data set were made, for which a conference paper has been submitted to the ASME conference.
The above haw culminated in the delivery and validation, to MARIN and maritime-engineering consulting, of numerical wavetanks and new datasets for advanced computer modelling of extreme waves at sea and wave-impact on offshore wind-turbine masts. all tools have been made available in public repositories, to attract academic attention and usage in related research sectors.
Extreme waves:
- Models for the interactions between waves and currents with constant vorticity have been derived in detail based on variational and Hamiltonian analysis, including a description of how a variational, finite-element potential-flow wavetank can be extended to include constant-vorticity currents in a two-dimensional vertical plane.
- A numerical wavetank has been (re)defined based on discretising the relevant Luke's variational principle (VP) in space and time.
- Coordinate transformations and dynamic mesh motions have been explored since these lead to an implementational innovation with potential high gains in computational efficiency, of which the main exploration is reported elsewhere (in the other subproject).
- A series of benchmark problems has been investigated, including various improvements, with enhanced performance, to the numerical formulation and its associated code.
- New test cases concerning short-crested waves have been defined in detail, which includes a novel analysis of exact solutions of the Kadomtsev-Petviashvilli (KP) equation; such exact solutions have defined the initial conditions for simulations within the numerical potential-flow wavetank. These finings were published in two publications in the journal Water Waves.
- A robust wavebreaking parameterisation based on diffusivity has been analysed; it has led to a preliminary investigation of a potentially new alternative based on augmented Hamiltonian dynamics. In addition, we have refined coupled potential-flow and shallow-water model, the latter at the beach where wavebreaking is occurring.
Wave-Turbine Impact:
- With reference to wave-impact on a wind-turbine mast modelled as a hyperelastic beam, the theoretical and numerical formulation of the coupled dynamics of water waves and beam motion have been investigated using variational principles (VPs). Due to the complexities involved, and for didactic training purposes, the methodology has been developed by considering a hierarchy of increasingly-complex dynamical problems, as follows.
- The VP of the nonlinear hyperelastic beam was investigated in separation, including some preliminary numerical tests.
-A first theoretical formulation, based on the relevant VP, was made of the coupled dynamics.
- A digression was made investigating the generation of water waves by a waveflap. Its numerical formulation requires a coordinate transformation and its discretisation is related to that for the coupled wave-beam problem. It results in a final time-discrete VP directly of use for a numerical discretisation. This was published in a first refereed (OMAE) conference proceeding.
- Full theoretical and numerical formulations are considered of the coupled problem, again using VPs, in which various computational-grid-transformation strategies are explored.
- Novel FSI experiments were designed and performed at MARIn. Results were presented in a second, refereed OMAE proceeding, on GitHub as well as a larger archived report.
- Using bespoke MARIN software, first validation of the nbew data set were made, for which a conference paper has been submitted to the ASME conference.
The above haw culminated in the delivery and validation, to MARIN and maritime-engineering consulting, of numerical wavetanks and new datasets for advanced computer modelling of extreme waves at sea and wave-impact on offshore wind-turbine masts. all tools have been made available in public repositories, to attract academic attention and usage in related research sectors.
In Leeds and MARIN the ESRs were trained in mathematics and fluid dynamics applied to maritime engineering. This emersion at MARIN included use of wave-basin facilities for acquisition of novel data. Fluid-dynamics courses were also followed at the Dutch National Burgers’ School of Fluid Dynamics. Hence, the ESRs’ employability in general and in particular for the maritime sector at large was greatly facilitated and enhanced. Two PhD dissertations are expected to be completed and ready for submission within 2024 deadlines. Both ESRs have passed their last 3rd-year graduate-school assessments prior to submission of their theses.
There have been two peer-reviewed journal publications in Water Waves, a submission to J. Comp. Phys (archived at Earth Arxiv), and two peer-reviewed and published conference publications as part of the OMAE-2023 conference. Submissions to J. Comp. Phys (revision), Open Research Europe (also archived at Earth Arxiv) and the ASME 2024 Power Conference have taken place or are foreseen in 2024. A compilation of public open-access Firedrake tutorials on wave modelling for MARIN has been made (updates ongoing), facilitating potential impact. New data sets have been made available via GitHub.
Noteworthy is that the most tangible contributions by our EU project EAGRE (besides expected business-as-usual scientific disseminations, in terms of delivering new methods/products for market or research community) are as follows:
- The novel space-time VP-approach developed and tested in the project has enormous potential beyond the water-wave applications explored, both for academic and industrial applications. This novel space-time approach leads to a vast reduction in development time and minimisation of human errors. Future applications apply to any area in which VPs are relevant but in particular also two-way coupled FSI and wave-energy devices.
- The open and freely accessible experimental data set established on Fluid-Structure-Interactions-experiments aim to be used as benchmarking by both academia and industry.
There have been two peer-reviewed journal publications in Water Waves, a submission to J. Comp. Phys (archived at Earth Arxiv), and two peer-reviewed and published conference publications as part of the OMAE-2023 conference. Submissions to J. Comp. Phys (revision), Open Research Europe (also archived at Earth Arxiv) and the ASME 2024 Power Conference have taken place or are foreseen in 2024. A compilation of public open-access Firedrake tutorials on wave modelling for MARIN has been made (updates ongoing), facilitating potential impact. New data sets have been made available via GitHub.
Noteworthy is that the most tangible contributions by our EU project EAGRE (besides expected business-as-usual scientific disseminations, in terms of delivering new methods/products for market or research community) are as follows:
- The novel space-time VP-approach developed and tested in the project has enormous potential beyond the water-wave applications explored, both for academic and industrial applications. This novel space-time approach leads to a vast reduction in development time and minimisation of human errors. Future applications apply to any area in which VPs are relevant but in particular also two-way coupled FSI and wave-energy devices.
- The open and freely accessible experimental data set established on Fluid-Structure-Interactions-experiments aim to be used as benchmarking by both academia and industry.