Matthew D. Piggott

• MMath, PhD
• Professor at Imperial College London

Unstructured grid data are essential for modelling complex geometries and dynamics in computational physics. Yet, their inherent irregularity presents significant challenges for conventional machine learning (ML) techniques. This paper provides a comprehensive review of advanced ML methodologies designed to handle unstructured grid data in high-dim...

Tidal stream turbines may operate under yawed conditions due to variability in ocean current directions. Insight into the wake structure of yawed turbines can be essential to ensure efficient tidal stream energy extraction, especially for turbine arrays where wake interactions emerge. We studied experimentally the effects of turbines operating unde...

Coastal response to anthropogenic climate change is of central importance to the infrastructure and inhabitants in these areas. Despite being globally ubiquitous, the stability of rock coasts has been largely neglected, and the expected acceleration of cliff erosion following sea-level rise has not been tested with empirical data, until now. We hav...

The white chalk cliffs on the south coast of England are one of the most iconic coastlines in the world. Rock coasts located in a weak lithology, such as chalk, are likely to be most vulnerable to climate change-triggered accelerations in cliff retreat rates. In order to make future forecasts of cliff retreat rates as a response to climate change,...

For tidal-stream energy to become a competitive renewable energy source, clustering multiple turbines into arrays is paramount. Array optimisation is thus critical for achieving maximum power performance and reducing cost of energy. However, ascertaining an optimal array layout is a complex problem, subject to specific site hydrodynamics and multip...

Purpose: To examine the accuracy and sensitivity of tidal array performance assessment by numerical techniques applying goal-oriented mesh adaptation.Methods: The goal-oriented framework is designed to give rise to adaptive meshes upon which a given diagnostic quantity of interest (QoI) can be accurately captured, whilst maintaining a low overall c...

When choosing an appropriate hydrodynamic model, there is always a compromise between accuracy and computational cost, with high fidelity models being more expensive than low fidelity ones. However, when assessing uncertainty, we can use a multifidelity approach to take advantage of the accuracy of high fidelity models and the computational efficie...

This paper presents a methodology that uses site-specific topographic and cosmogenic 10Be data to perform multi-objective model optimisation of a coupled coastal evolution and cosmogenic radionuclide production model. Optimal parameter estimation of the coupled model minimises discrepancies between model simulations and measured data to reveal the...

Accurately representing the bottom friction effect is a significant challenge in numerical tidal models. Bottom friction effects are commonly defined via parameter estimation techniques. However, the bottom friction coefficient (BFC) can be related to the roughness of the sea bed. Therefore, sedimentological data can be beneficial in estimating BFC...

This review provides a critical, multi-faceted assessment of the practical contribution tidal stream energy can make to the UK and British Channel Islands future energy mix. Evidence is presented that broadly supports the latest national-scale practical resource estimate, of 34 TWh/year, equivalent to 11% of the UK’s current annual electricity dema...

Combined convection–radiation is a common phenomenon in many engineering problems. A differentially–heated rectangular enclosure is a widely–used benchmark for testing numerical techniques developed for solving the coupled momentum and energy equations related to combined convection–radiation. Previous studies have tended to describe the phenomenon...

The development of reliable, sophisticated hydro-morphodynamic models is essential for protecting the coastal environment against hazards such as flooding and erosion. There exists a high degree of uncertainty associated with the application of these models, in part due to incomplete knowledge of various physical, empirical and numerical closure re...

As the tidal energy industry moves from demonstrator arrays comprising just a few turbines to large-scale arrays made up of potentially hundreds of turbines, there is a need to optimise both the number of turbines and their spatial distribution in order to minimise cost of energy. Optimising array design manually may be feasible for small arrays, b...

For tidal-stream energy to become a competitive renewable energy source, clustering multiple turbines into arrays is paramount. As a result, array optimisation is critical for achieving maximum power performance and reducing cost of energy. However, ascertaining an optimal array layout is a highly complex problem, subject to specific site hydrodyna...

This paper presents a methodology that uses site-specific topographic and cosmogenic 10Be data to perform multi-objective model optimisation of a coupled coastal evolution and cosmogenic radionuclide production model. Optimal parameter estimation of the coupled model minimises discrepancies between model simulations and measured data to reveal the...

The Maldives faces a unique range of environmental challenges. While the country is almost entirely dependent upon oceanic resources with more than 99% of the area covered by ocean, the absence of a suitable bathymetric map of the seafloor of the Maldives severely limits the adoption and application of modern scientific methods for the prediction o...

This tidal stream energy industry has to date been comprised of small demonstrator projects made up of one to a four turbines. However, there are currently plans to expand to commercially sized projects with tens of turbines or more. As the industry moves to large-scale arrays for the first time, there has been a push to develop tools to optimise t...

With increased nutrient inputs to estuaries in recent decades exacerbating their susceptibility to eutrophication, assessment of the response of individual estuaries to nutrient enrichment is attracting considerable attention. Nonetheless, the impact of tidal energy extraction on estuarine nutrient dynamics and the risk of eutrophication has been l...

Changes to coastlines and bathymetry alter tidal dynamics and associated sediment transport processes, impacting upon a number of threats facing coastal regions, including flood risk and erosion. Especially vulnerable are coral atolls such as those that make up the Maldives archipelago, which has undergone significant land reclamation in recent yea...

Numerical storm surge models are essential to forecasting coastal flood hazard and informing the design of coastal defences. However, such models rely on a variety of inputs, many of which carry uncertainty, and an awareness and understanding of the sensitivity of the model outputs with respect to those uncertain inputs is necessary when interpreti...

This paper applies metric-based mesh adaptation methods to advection-dominated tracer transport modelling problems in two and three dimensions, using the finite element package Firedrake. In particular, the mesh adaptation methods considered are built upon goal-oriented estimates for the error incurred in evaluating a diagnostic quantity of interes...

Microbes play a primary role in aquatic ecosystems and biogeochemical cycles. Patchiness is a critical component of these activities, influencing biological productivity, nutrient cycling and dynamics across trophic levels. Incorporating spatial dynamics into microbial models is a long-standing challenge, particularly where small-scale turbulence i...

Microbes play a primary role in aquatic ecosystems and biogeochemical cycles. Spatial patchiness is a critical factor underlying these activities, influencing biological productivity, nutrient cycling and dynamics across trophic levels. Incorporating spatial dynamics into microbial models is a long-standing challenge, particularly where small-scale...

This article has been withdrawn at the request of the editor. Due to an error and no fault of the Authors, this article was published erroneously and the Publisher apologizes for any inconvenience this may cause. The full Elsevier Policy on Article Withdrawal can be found at https://www.elsevier.com/about/our-business/policies/article-withdrawal

Representation of the marine environment is key for reliable coastal hydrodynamic models. This study investigates the implications of common depth-averaged model configuration choices in sufficiently characterising seabed geometry and roughness. In particular, applications requiring a high level of accuracy and/or exhibiting complex flow conditions...

The development of morphodynamic models to simulate sediment transport accurately is a challenging process that is becoming ever more important because of our increasing exploitation of the coastal zone, as well as sea-level rise and the potential increase in strength and frequency of storms due to a changing climate. Morphodynamic models are highl...

A σ-coordinate non-hydrostatic coastal ocean model is developed using the discontinuous Galerkin finite element method. With the selection of the low-order piecewise-constant P0DG and piecewise-linear P1DG discretisations in the vertical for the velocity and pressure fields, respectively, the proposed σ-coordinate model can naturally retain the wav...

Particle Image Velocimetry (PIV) is a classical flow estimation problem which is widely considered and utilised, especially as a diagnostic tool in experimental fluid dynamics and the remote sensing of environmental flows. Recently, the development of deep learning based methods has inspired new approaches to tackle the PIV problem. These supervise...

The extraction of tidal energy from head differences represents a predictable and flexible option for generating electricity. Here, we investigate the generation potential of prospective tidal power plants in the UK. Originally conceived as separate projects, operating these schemes as a cooperative system could prove beneficial. Combined with the...

Changes to coastlines and bathymetry alter tidal dynamics and associated sediment transport process, impacting upon a number of threats facing coastal regions, including flood risk and erosion. Especially vulnerable are coral atolls such as those that make up the Maldives archipelago which has undergone significant land reclamation in recent years...

This review demonstrates the benefit of numerical tidal modelling, calibrated by integrated comparison to the preserved stratigraphic record, and offers a refined classification and prediction of shoreline process regimes. Wider and consistent utilisation of these concepts, and numerical simulations of other depositional processes, will further imp...

Tidal energy has the potential to form a key component of the energy production in a number of countries, including the UK. Nonetheless, the deployment of tidal energy systems is associated with potential environmental impacts as prime resource sites often coincide with unique ecosystems inhabited by sensitive organisms. Previous studies have gener...

Particle Image Velocimetry (PIV) is a classical flow estimation problem which is widely considered and utilised, especially as a diagnostic tool in experimental fluid dynamics and the remote sensing of environmental flows. Recently, the development of deep learning based methods has inspired new approaches to tackle the PIV problem. These supervise...

The tides are a predictable, renewable, source of energy that, if harnessed, can provide significant levels of electricity generation. The Alderney Race (AR), with current speeds that exceed 5 m s ⁻¹ during spring tides, is one of the most concentrated regions of tidal energy in the world, with the upper-bound resource estimated at 5.1 GW. Owing to...

Costs of tidal stream energy generation are anticipated to fall considerably with array expansion and time. This is due to both economies of volume, where arrays comprising of large numbers of turbines can split fixed costs over a greater number of devices, and learning rates, where the industry matures and so arrays of the same size become cheaper...

The Introduction presents motivations, significance and some key points of the research activities performed in the Alderney Race. This article is part of the theme issue ‘New insights on tidal dynamics and tidal energy harvesting in the Alderney Race’.

Characterising tidal hydrodynamics in the vicinity of submerged features can be demanding given the hostility of the marine environment. Logistical challenges in the measurement of such flows has promoted research on wake studies through physical and numerical modelling. In this study, site measurements and modelled data are combined to provide an...

Large tsunamis can be generated by submarine slides, but these events are rare on human timescales and challenging to observe. Experiments and numerical modelling offer methods to understand the mechanisms by which they generate waves and what the potential hazard might be. However, to fully capture the complex waveform generated by a submarine sli...

Numerical storm surge models are essential to forecasting coastal flood hazard and informing the design of coastal defences. However, such models rely on a variety of inputs, many of which will carry uncertainty, and an awareness and understanding of the sensitivity of the model outputs with respect to those uncertain inputs is necessary when inter...

Numerical tidal models are essential to the study of a variety of coastal ocean processes, but typically rely on uncertain inputs, including a bottom friction parameter which can in principle be spatially varying. Here we employ an adjoint-capable numerical ocean model, Thetis, and apply it to the Bristol Channel and Severn Estuary, using a spatial...

This study presents a novel goal-oriented error estimate for the nonlinear shallow water equations solved using a mixed discontinuous/continuous Galerkin approach. This error estimator takes account of the discontinuities in the discrete solution and is used to drive two metric-based mesh adaptation algorithms: one which yields isotropic meshes and...

The unstructured mesh, discontinuous Galerkin finite element discretisation based coastal ocean model, Thetis, has been extended to include non-hydrostatic (buoyancy-driven and free surface) dynamics. Two alternative approaches to achieve this are described in this work. The first (a 3D based algorithm) makes use of prismatic element based meshes a...

Single-basin tidal range power plants have the advantage of predictable energy outputs, but feature non-generation periods in every tidal cycle. Linked-basin tidal power systems can reduce this variability and consistently generate power. However, as a concept the latter are under-studied with limited information on their performance relative to si...

We consider metric-based mesh adaptation methods for steady-state partial differential equations (PDEs), solved using the finite element method in Firedrake. In this work, a number of mesh-adaptive methods are implemented within this framework, each enabling accurate approximation of a scalar quantity of interest (QoI). Through the QoI we define ad...

Simulations of landslide generated waves (LGWs) are prone to high levels of uncertainty. Here we present a probabilistic sensitivity analysis of an LGW model. The LGW model was realised through a smooth particle hydrodynamics (SPH) simulator, which is capable of modelling fluids with complex rheologies and includes flexible boundary conditions. Thi...

Single-basin tidal range power plants have the advantage of predictable energy outputs, but feature non-generation periods in every tidal cycle to facilitate the essential turbine driving head difference. Linked-basin tidal power systems can reduce this variability and consistently generate power. However, as a concept the latter are under-studied...

Tidal energy has the potential to form a key component of the energy mix of a number of countries, including the UK. Nonetheless, the deployment of tidal energy systems is associated with potential environmental impacts as prime resource sites often coincide with unique ecosystems inhabited by sensitive organisms. Preceding studies have generally f...

The development of morphodynamic models to simulate sediment transport accurately is a challenging process that is becoming ever more important because of our increasing exploitation of the coastal zone, as well as sea-level rise and the potential increase in strength and frequency of storms due to a changing climate. Morphodynamic models are highl...

Submarine landslides can exhibit complex rheologies, including a finite yield stress and shear thinning, yet are often simulated numerically using a Newtonian fluid rheology and simplistic boundary conditions. Here we present improvements made to a Smoothed Particle Hydrodynamics simulator to allow the accurate simulation of submarine landslide gen...

Numerical modelling frequently involves a diagnostic quantity of interest (QoI) - often of greater importance than the PDE solution - which we seek to accurately approximate. In the case of coastal ocean modelling the power output of a tidal turbine farm is one such example. Goal-oriented error estimation and mesh adaptation can be used to provide...

Uncertainty quantification is crucial to storm surge forecasting, and is typically undertaken using ensemble methods. Such methods generally do not provide insight into the underlying patterns of model sensitivity, which we explore in this work via adjoint modelling. The unstructured-mesh coastal ocean model Thetis is first validated against tide g...

Tidal lagoons represent a form of renewable electricity generation that remain untested. In the UK, a perceived lack of value for money to the consumer triggered the government's rejection of a recent plan to build and operate a system of six tidal lagoons along the west coast of England and Wales. Tidal energy benefits from a high degree of predic...

In the drive towards a carbon-free society, tidal energy has the potential to become a valuable part of the UK energy supply. Developments are subject to intense scrutiny, and potential environmental impacts must be assessed. Unfortunately many of these impacts are still poorly understood, including the implications that come with altering the hydr...

The generation and evolution of tidally-induced vortices in coastal and estuarine regions can influence water quality and sedimentary processes. These effects must be taken into consideration in the development of coastal reservoirs, barrages and lagoons, among other environmental flow applications. Results are presented here on the fate of large-s...

Tidal range renewable power plants have the capacity to deliver predictable energy to the electricity grid, subject to the known variability of the tides. Tidal power plants inherently feature advantages that characterise hydro-power more generally, including a lifetime exceeding alternative renewable energy technologies and relatively low Operatio...

A multi-layer non-hydrostatic version of the unstructured mesh, discontinuous Galerkin finite element based coastal ocean model, Thetis, is developed. This is accomplished using the PDE solver framework, Firedrake, which is used to automatically produce the code for the discretised model equations in a rapid and efficient manner. The motivation for...

Tidal range renewable power plants have the capacity to deliver predictable energy to the electricity grid, subject to the known variability of the tides. Tidal power plants inherently feature advantages that characterise hydro-power more generally, including a lifetime exceeding alternative renewable energy technologies and relatively low Operatio...

Turbulence-resolving simulations of wind turbine wakes are presented using a high--order flow solver combined with both a standard and a novel dynamic implicit spectral vanishing viscosity (iSVV and dynamic iSVV) model to account for subgrid-scale (SGS) stresses. The numerical solutions are compared against wind tunnel measurements, which include m...

Unstructured grid ocean models are advantageous for simulating the coastal ocean and river–estuary–plume systems. However, unstructured grid models tend to be diffusive and/or computationally expensive, which limits their applicability to real-life problems. In this paper, we describe a novel discontinuous Galerkin (DG) finite element discretizatio...

Depth-averaged shallow water models are widely used for the large-scale simulation of tidal turbine arrays. The relatively low computational complexity of this approach allows for layout optimisations aimed at improving the total array power output as well as an assessment of large-scale environmental impacts. In order to assess the suitability of...

High-fidelity wind farm models typically employ large-eddy simulation (LES) formulations and turbine parametrisations (e.g. actuator disc models) to resolve the turbine wakes at spatial and temporal scales so that all flow features of engineering improtance are well-captured. Such features include the low frequency dynamic wake meandering, which pl...

This paper develops a new implementation coupling optimisation-based anisotropic mesh adaptivity algorithms to a moving mesh numerical scour model, considering both turbulent suspended and bedload sediment transport. The significant flexibility over mesh structure and resolution, in space and time, that the coupling of these approaches provides mak...

Numerical models of the flow and wakes due to turbines operating within a real‐scale offshore wind farm can lead to a prohibitively large computational cost, particularly when considering blade‐resolved simulations. With the introduction of turbine parametrizations such as the actuator disk (AD) or the actuator line (AL) models, this problem has be...

Tidal energy is one of the most predictable forms of renewable energy. Although there has been much commercial and R&D progress in tidal stream energy, tidal range is a more mature technology, with tidal range power plants having a history that extends back over 50 years. With the 2017 publication of the "Hendry Review" that examined the feasibilit...

Tidal energy is one of the most predictable forms of renewable energy. Although there has been much commercial and R&D progress in tidal stream energy, tidal range is a more mature technology, with tidal range power plants having a history that extends back over 50 years. With the 2017 publication of the "Hendry Review" that examined the feasibilit...

Turbulence-resolving simulations of wind turbine wakes are presented using a high-order flow solver combined with both a standard and a novel dynamic implicit spectral vanishing viscosity (iSVV and dynamic iSVV) model to account for subgrid-scale (SGS) stresses. The numerical solutions are compared against wind tunnel measurements, which include me...

Numerical tidal modelling, when integrated with other geological datasets, can significantly inform the analysis of physical sedimentation processes and the depositional and preservational record of ancient tide‐influenced shoreline–shelf systems. This is illustrated in the Oligo–Miocene of the South China Sea, which experienced significant changes...

Tidal range power plants represent an attractive approach for the large-scale generation of electricity from the marine environment. Even though the tides and by extension the available energy resource are predictable, they are also variable in time. This variability poses a challenge regarding the optimal transient control of power plants. Here we...

Lagrangian analysis is a powerful way to analyse the output of ocean circulation models and other ocean velocity data such as from altimetry. In the Lagrangian approach, large sets of virtual particles are integrated within the three-dimensional, time-evolving velocity fields. Over several decades, a variety of tools and methods for this purpose ha...

Tidal range power plants represent an attractive approach for the large-scale generation of electricity from the marine environment. Even though the tides and by extension the available energy resource are predictable, they are also variable in time. This variability poses a challenge regarding the optimal transient control of power plants. Here we...

Unstructured grid ocean models are advantageous for simulating the coastal ocean and river-estuary-plume systems. However, unstructured grid models tend to be diffusive and/or computationally expensive which limits their applicability to real life problems. In this paper, we describe a novel discontinuous Galerkin (DG) finite element discretization...

Tidal range energy projects present an attractive means for the predictable and large-scale generation of electricity from the marine environment. In particular, proposals are under consideration in UK waters, with their feasibility currently being under high levels of scrutiny. This is due to a combination of potential environmental and socio-econ...

Renewable energy is the cornerstone of preventing dangerous climate change whilst maintaining a robust energy supply. Tidal energy will arguably play a critical role in the renewable energy portfolio as it is both predictable and reliable, and can be put in place across the globe. However, installation may impact the local and regional ecology via...

The actuator disc (ADM) and actuator line (ALM) models have long been used to parametrise turbines within mesh-based computational fluid dynamic solvers. Both models parametrise the rotor through the addition of a source term in the momentum equations to mimic the impact on momentum generated by the turbine. While ADM distributes the time-averaged...

Tidal range energy projects present an attractive means for the predictable and large-scale generation of electricity from the marine environment. In particular, proposals are under consideration in UK waters, with their feasibility currently being under high levels of scrutiny. This is due to a combination of potential environmental and socioecono...

Myths and legends across the world contain many stories of deluges and floods. Some of these have been attributed to tsunami events. Doggerland in the southern North Sea is a submerged landscape thought to have been heavily affected by a tsunami such that it was abandoned by Mesolithic human populations at the time of the event. The tsunami was gen...

The motivation for this application comes from the desire to generate renewable energy from the tides in the Earth’s oceans. Tides are a consequence of the gravitational attractions experienced within the Earth-Moon-Sun system. As this system evolves in time the cumulative gravitational forces vary and this has the effect of driving ocean (or tidal...

The use of computational models based on the numerical solution of partial differential equations (PDEs) to simulate physical processes is a powerful complement to physical experiments. Simulations can be undertaken to consider scenarios for which experiments are impossible, such as climate physics or the dynamics of black holes and galaxies.

Computationally solving an optimisation problem on Hilbert spaces requires discretisation and the application of an optimisation method to the resulting finite-dimensional problem. In this context, mesh-independent convergence of the optimisation algorithm means that, for a discretisation given on a sufficiently fine mesh, the number of iterations...

This paper introduces a new approach for investigating trade-offs between different societal objectives in the design of tidal-turbine arrays. This method is demonstrated through the trade-off between the yield of an array, and the extent to which that array alters the flow. This is posed as a multi-objective optimisation problem, and the problem i...