75 results found
Clare MCA, Wallwork JG, Kramer SC, et al., 2022, Multi-scale hydro-morphodynamic modelling using mesh movement methods, GEM: International Journal on Geomathematics, Vol: 13, ISSN: 1869-2672
Hydro-morphodynamic modelling is an important tool that can be used in the protection of coastal zones. The models can be required to resolve spatial scales ranging from sub-metre to hundreds of kilometres and are computationally expensive. In this work, we apply mesh movement methods to a depth-averaged hydro-morphodynamic model for the first time, in order to tackle both these issues. Mesh movement methods are particularly well-suited to coastal problems as they allow the mesh to move in response to evolving flow and morphology structures. This new capability is demonstrated using test cases that exhibit complex evolving bathymetries and have moving wet-dry interfaces. In order to be able to simulate sediment transport in wet-dry domains, a new conservative discretisation approach has been developed as part of this work, as well as a sediment slide mechanism. For all test cases, we demonstrate how mesh movement methods can be used to reduce discretisation error and computational cost. We also show that the optimum parameter choices in the mesh movement monitor functions are fairly predictable based upon the physical characteristics of the test case, facilitating the use of mesh movement methods on further problems.
Zhang J, Zhang C, Angeloudis A, et al., 2022, Interactions between tidal stream turbine arrays and their hydrodynamic impact around Zhoushan Island, China, Ocean Engineering, Vol: 246, Pages: 110431-110431, ISSN: 0029-8018
Mackie L, Kramer SC, Piggott MD, et al., 2021, Assessing impacts of tidal power lagoons of a consistent design, OCEAN ENGINEERING, Vol: 240, ISSN: 0029-8018
Goss ZL, Coles DS, Kramer SC, et al., 2021, Efficient economic optimisation of large-scale tidal stream arrays, APPLIED ENERGY, Vol: 295, ISSN: 0306-2619
Duvernay T, Davies DR, Mathews CR, et al., 2021, Linking Intraplate Volcanism to Lithospheric Structure and Asthenospheric Flow, GEOCHEMISTRY GEOPHYSICS GEOSYSTEMS, Vol: 22
Zhang C, Kramer SC, Angeloudis A, et al., 2021, Improving tidal turbine array performance through the optimisation of layout and yaw angles, European Wave and Tidal Energy Conference, Pages: 2205-1-2205-7-2205-1-2205-7, ISSN: 2706-6932
Tidal stream currents change in magnitude and direction during flood and ebb tides. Setting the most appropriate yaw angles for a tidal turbine is not only important to account for the performance of a single turbine, but can also be significant for the interactions between the turbines within an array. In this paper, a partial differentiation equation (PDE) constrained optimisation approach is established based on the Thetis coastal ocean modelling framework. The PDE constraint takes the form here of the two-dimensional, depth-averaged shallow water equations which are used to simulate tidal elevations and currents in the presence of tidal stream turbine arrays. The Sequential Least Squares Programming (SLSQP) algorithm is applied with a gradient obtained via the adjoint method in order to perform design optimisation. An idealised rectangular channel test case is studied to demonstrate this optimisation framework. Located in the centre of the computational domain, turbine arrays comprised of 12 turbines are tested in aligned and staggered layouts. The setups are initially optimised based on their yaw angles alone; their locations and yaw angles are also optimized simultaneously to improve the array overall performance. Results indicate that for the aligned turbine array case, the energy output can be increased by approximately 80% when considering yaw angle optimisation alone. For the staggered turbine array, the increase is approximately 30%. The yaw optimised staggered array is able to outperform the yaw optimised aligned array by approximately 8%. If both layout and the yaw angles of the turbines are considered within the optimisation then the increase is more significant compared with optimising yaw angle alone.
Kramer S, Davies R, Wilson C, 2021, Analytical solutions for mantle flow in cylindrical and spherical shells, Geoscientific Model Development, Vol: 14, Pages: 1899-1919, ISSN: 1991-959X
Computational models of mantle convection must accurately represent curved boundaries and the associated boundary conditions of a 3-D spherical shell, bounded by Earth's surface and the core–mantle boundary. This is also true for comparable models in a simplified 2-D cylindrical geometry. It is of fundamental importance that the codes underlying these models are carefully verified prior to their application in a geodynamical context, for which comparisons against analytical solutions are an indispensable tool. However, analytical solutions for the Stokes equations in these geometries, based upon simple source terms that adhere to physically realistic boundary conditions, are often complex and difficult to derive. In this paper, we present the analytical solutions for a smooth polynomial source and a delta-function forcing, in combination with free-slip and zero-slip boundary conditions, for both 2-D cylindrical- and 3-D spherical-shell domains. We study the convergence of the Taylor–Hood (P2–P1) discretisation with respect to these solutions, within the finite element computational modelling framework Fluidity, and discuss an issue of suboptimal convergence in the presence of discontinuities. To facilitate the verification of numerical codes across the wider community, we provide a Python package, Assess, that evaluates the analytical solutions at arbitrary points of the domain.
Pan W, Kramer SC, Piggott MD, 2021, A sigma-coordinate non-hydrostatic discontinuous finite element coastal ocean model, Ocean Modelling, Vol: 157, Pages: 1-21, ISSN: 1463-5003
A𝜎-coordinate non-hydrostatic coastal ocean model is developed using the discontinuous Galerkin fi-nite element method. With the selection of the low-order piecewise-constant PDG0and piecewise-linearPDG1discretisations in the vertical for the velocity and pressure fields, respectively, the proposed𝜎-coordinatemodel can naturally retain the wave dispersion characteristics of the widely-adopted multi-layer approach ofZijlema and Stelling (2005), which is demonstrated through both mathematical derivation and numerical tests.Under the finite element approach, higher-order vertical discretisation choices can also be readily made whichcan reduce the number of vertical layers required for the accurate representation of wave dispersion. Themodel is verified and validated through comparisons against a series of test cases with analytical solutions orexperimental measurements. All the comparisons demonstrate good agreement, indicating that the proposedmodel can accurately represent dispersive barotropic surface waves with as few as one vertical layer, and cansimulate baroclinic internal waves with reasonable accuracy using relatively coarse mesh resolution. It is alsodemonstrated that consistency in the coupling of barotropic and baroclinic flows can be properly ensured.
Kramer S, Wilson C, Davies R, et al., 2020, FluidityProject/fluidity: New test cases "Analytical solutions for mantle flow in cylindrical and spherical shells"
This release adds new test cases described in the GMD paper "Analytical solutions for mantle flow in cylindrical and spherical shells"
Angeloudis A, Kramer SC, Hawkins N, et al., 2020, On the potential of linked-basin tidal power plants: An operational and coastal modelling assessment, Renewable Energy, Vol: 155, Pages: 876-888, ISSN: 0960-1481
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 single-basin designs. In addressing this, we outline the basic principles of linked-basin power plant operation and report results from their numerical simulation. Tidal range energy operational models are applied to gauge their capabilities relative to conventional, single-basin tidal power plants. A coastal ocean model (Thetis) is then refined with linked-basin modelling capabilities. Simulations demonstrate that linked-basin systems can reduce non-generation periods at the expense of the extractable energy output relative to conventional tidal lagoons and barrages. As an example, a hypothetical case is considered for a site in the Severn Estuary, UK. The linked-basin system is seen to generate energy 80–100% of the time over a spring-neap cycle, but harnesses at best 30% of the energy of an equivalent-area single-basin design.
Pan W, Kramer S, Kärnä T, et al., 2020, Comparing non-hydrostatic extensions to a discontinuous finite element coastal ocean model, Ocean Modelling, Vol: 151, ISSN: 1463-5003
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 and uses a split-step pressure projection method for baroclinic and barotropic modes, while the second (a 2D based algorithm) adopts a novel multi-layer approach to convert a 3D problem into a combination of multiple 2D computations with only 2D triangle meshes required. Model development is carried out at high-level with the Firedrake library, using code generation techniques to automatically produce low-level code for the discretised model equations in an efficient and rapid manner. Through comparisons against several barotropic/baroclinic test cases where non hydrostatic effects are important, the implemented approaches are verified and validated, and the proposed algorithms compared. Depending on whether the problems are dominated by dispersive, baroclinic or barotropic features, recommendation are given over the use of full 3D or multi-layer 2D based approaches to achieve optimal computational accuracy and efficiency. It is demonstrated that while in general the 2D approach is well-suited for barotropic problems and dispersive free surface waves, the 3D approach is more advantageous for simulating baroclinic buoyancy-driven flows due in part to the high vertical resolution typically required to represent the active tracer fields. Keywords: Discontinuous Galerkin, Finite element, Unstructured mesh, Baroclinic flow, Non-hydrostatic, Dispersion, Free surface
Kramer S, Kärnä T, Hill J, et al., 2020, stephankramer/uptide: First release of uptide v1.0
python package for tidal calculations
Kramer S, 2020, stephankramer/assess: Version 1.0
First release of Assess, a python package that implements a number of analytical solutions to the Stokes equations in cylindrical and spherical shell domains. Documentation available from https://assess.readthedocs.io/
Wallwork JG, Barral N, Kramer SC, et al., 2020, Goal-oriented error estimation and mesh adaptation for shallow water modelling, SN Applied Sciences, Vol: 2, Pages: 1-11, ISSN: 2523-3971
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 another which yields anisotropic meshes. An implementation of these goal-oriented mesh adaptation algorithms is described, including a method for approximating the adjoint error term which arises in the error estimate. Results are presented for simulations of two model tidal farm configurations computed using the Thetis coastal ocean model (Kärnä et al. in Geosci Model Dev 11(11):4359–4382, 2018). Convergence analysis indicates that meshes resulting from the goal-oriented adaptation strategies permit accurate QoI estimation using fewer computational resources than uniform refinement.
Kärnä T, Kramer S, Mitchell L, et al., 2020, thetisproject/thetis: Thetis coastal ocean model
This version is used in paper "A comparison of Bayesian inference and gradient-based approaches for friction parameter estimation."This release is specifically created to document the version of Thetis used in a particular set of experiments. Please do not cite this as a general source for Thetis. See https://thetisproject.org/publications.html for how to cite Thetis in your work.
Du Feu R, funke S, Kramer S, et al., 2019, The trade-off between tidal-turbine array yield and environmental impact: A habitat suitability modelling approach, Renewable Energy, Vol: 143, Pages: 390-403, ISSN: 1879-0682
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 hydrodynamics. Here, methods are proposed to quantify ecological impact and to incorporate its minimisation into the array design process. Four tidal developments in the Pentland Firth are modelled with the array optimisation tool OpenTidalFarm, that designs arrays to generate the maximum possible profit. Maximum entropy modelling is used to create habitat suitability maps for species that respond to changes in bedshear stress. Changes in habitat suitability caused by an altered tidal regime are assessed. OpenTidalFarm is adapted to simultaneously optimise array design to maximise both this habitat suitability and to maximise the profit of the array. The problem is thus posed as a multi-objective optimisation problem, and a set of Pareto solutions found, allowing trade-offs between these two objectives to be identified. The methods proposed generate array designs that have reduced negative impact, or even positive impact, on the habitat suitability of specific species or habitats of interest.
Davies DR, Valentine AP, Kramer SC, et al., 2019, Earth's multi-scale topographic response to global mantle flow, NATURE GEOSCIENCE, Vol: 12, Pages: 845-+, ISSN: 1752-0894
Goss Z, Warder S, Angeloudis A, et al., 2019, Tidal modelling with Thetis: preliminary English Channel benchmarking, Tidal modelling with Thetis: preliminary English Channelbenchmarking
This report describes the application and benchmarking of the Thetis coastal ocean model fortidal modelling, and makes use of a test case based upon the English Channel. Comparisonsare made between model predictions and tide gauge data at a number of locations across theEnglish Channel. A preliminary investigation of the impact of mesh resolution and bathymetrydata is given. A demonstration is also provided of Thetis’s ability to use adjoint technologyto optimise model predictions through the assimilation of observational data. In the examplepresented here the bottom friction field is optimised to provide an improved match betweenthe model results and tide gauge data. This adjoint based optimisation capability may alsobe used to optimise the location, size and design of tidal power generation schemes.
Vouriot C, Angeloudis A, Kramer S, et al., 2019, Fate of large-scale vortices in idealized tidal lagoons, Environmental Fluid Mechanics, Vol: 19, Pages: 329-348, ISSN: 1567-7419
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-scale vortices within confined tidally-forced domains. A computational approach is employed using the Thetis depth-averaged coastal ocean modeling framework. Initially, two test cases serve to demonstrate model capability in capturing the formation of dipoles downstream of oscillatory flow channels. Diagnostic quantities of vorticity and localized circulation are used to track the 2-D vortex evolution and dissipation. This approach is then applied to tidal lagoon geometries, where flows through the inlet induce a pair of counter rotating vortices (dipoles). Idealized model geometries and inlet conditions are used to determine the impact of three design parameters on large-scale vortical structures: (a) the lagoon geometry aspect ratio in the horizontal plane, (b) the inlet width and (c) the bathymetry profile as the coastline is approached. The dependence of vortex flushing behavior on the dimensionless ratio Wi/UT (where Wi is the width of the inlet channel, U is the maximum velocity and T is the tidal period) is reaffirmed, while the side walls and the sloping bathymetry are found to affect the vortex dissipation process.
Walker DW, Kramer SC, Biebl FRA, et al., 2019, Accelerating magnetic induction tomography-based imaging through heterogeneous parallel computing, Concurrency Computation, ISSN: 1532-0626
© 2019 John Wiley & Sons, Ltd. Magnetic Induction Tomography (MIT) is a non-invasive imaging technique, which has applications in both industrial and clinical settings. In essence, it is capable of reconstructing the electromagnetic parameters of an object from measurements made on its surface. With the exploitation of parallelism, it is possible to achieve high quality inexpensive MIT images for biomedical applications on clinically relevant time scales. In this paper we investigate the performance of different parallel implementations of the forward eddy current problem, which is the main computational component of the inverse problem through which measured voltages are converted into images. We show that a heterogeneous parallel method that exploits multiple CPUs and GPUs can provide a high level of parallel scaling, leading to considerably improved runtimes. We also show how multiple GPUs can be used in conjunction with deal.II, a widely-used open source finite element library.
Rathgeber F, Mitchell L, Luporini F, et al., 2019, OP2/PyOP2: Framework for performance-portable parallel computations on unstructured meshes
This release is specifically created to document the version of PyOP2 used in a particular set of experiments using Firedrake. Please do not cite this as a general source for Firedrake or any of its dependencies. Instead, refer to https://www.firedrakeproject.org/citing.html
Pan W, Kramer S, Piggott M, 2019, Multi-layer non-hydrostatic free surface modelling using the discontinuous Galerkin method, Ocean Modelling, Vol: 134, Pages: 68-83, ISSN: 1463-5003
A multi-layer non-hydrostatic version of the unstructured mesh, discontinuous Galerkinfinite element based coastal ocean model, Thetis, is developed. This is accomplishedusing the PDE solver framework, Firedrake, which is used to automatically produce thecode for the discretised model equations in a rapid and efficient manner. The motivationfor this work is a need to accurately simulate dispersive nearshore free surface processes.In order to resolve both frequency dispersion and non-linear effects accurately, additional non-hydrostatic terms are included in the layer-integrated hydrostatic equations,producing a form similar to the layered non-linear shallow water equations, but withextra vertical velocities at the layer interfaces. An implementation process is adoptedto easily handle the inter-layer connection, i.e. the governing equations are transformedinto a depth-integrated system through the introduction of depth-averaged variables.The model is verified and validated through comparisons against several idealisedand experimentally-based test cases. All the comparisons demonstrate good agreement,showing that the developed non-hydrostatic model has excellent capabilities in representing coastal wave phenomena including shoaling, refraction and diffraction of dispersive short waves, as well as propagation, run-up and inundation of non-linear tsunamiwaves.
Goss ZL, Piggott MD, Kramer SC, et al., 2019, Competition effects between nearby tidal turbine arrays—optimal design for alderney race, Pages: 255-262
Tidal renewable energy can be described as a fledgling industry, with the world’s pilot tidal stream turbine array only recently installed. Full-sized arrays will be developed if they prove their economic, engineering and environmental viability. Reliable numerical tools are needed to optimise power yields in arrays of potentially hundreds of turbines and assess viability of new sites and designs. To demonstrate our capability to optimise the number of turbines and their spatial distribution in a region, we focus on a test case based upon the Alderney Race. The site contains the majority of the Channel Islands resource with plans from both France and Alderney to develop adjacent arrays that could impact on each other. We present a shallow-water model of the English Channel using the Thetis ocean model. Together with the hydrodynamics modelling we employ adjoint technology to optimise the micrositing of turbines for a set of scenarios.
Angeloudis A, Hawkins N, Kramer SC, et al., 2019, Comparison of twin-basin lagoon systems against conventional tidal power plant designs, Pages: 159-168
Tidal power plant proposals present opportunities to deliver sustainable energy to the national grid in the UK and beyond. Multiple designs have been considered over the years that seek to competitively balance economic, environmental and technical challenges. Tidal range power plants have the advantage of reliable and predictable energy outputs with a certain degree of flexibility but typically feature non-generation periods in every tidal cycle. Twin-basin systems present an alternative that can significantly reduce this variability but very little information has been reported in terms of their performance to-date. In this work a coastal ocean modelling framework has been coupled with twin-basin and tidal power plant operation algorithms and is applied to compare tidal energy options. Results suggest that through use of a twin basin system the non-generation time can be substantially reduced at a notable expense to the overall energy output relative to conventional tidal lagoons and barrages.
Mitchell L, Ham D, Gibson T, et al., 2018, firedrakeproject/firedrake: an automated finite element system
This release is specifically created to document the version of firedrake used in a particular set of experiments using Firedrake. Please do not cite this as a general source for Firedrake or any of its dependencies. Instead, refer to https://www.firedrakeproject.org/citing.html
Kärnä T, Kramer SC, Mitchell L, et al., 2018, Thetis coastal ocean model: discontinuous Galerkin discretization for the three-dimensional hydrostatic equations, Geoscientific Model Development, Vol: 11, Pages: 4359-4382, ISSN: 1991-959X
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 for the hydrostatic equations. The formulation is fully conservative and second-order accurate in space and time. Monotonicity of the advection scheme is ensured by using a strong stability preserving time integration method and slope limiters. Compared to previous DG models advantages include a more accurate mode splitting method, revised viscosity formulation, and new second-order time integration scheme. We demonstrate that the model is capable of simulating baroclinic flows in the eddying regime with a suite of test cases. Numerical dissipation is well-controlled, being comparable or lower than in existing state-of-the-art structured grid models.
Kärnä T, Kramer SC, Mitchell L, et al., 2018, Thetis coastal ocean model: discontinuous Galerkin discretization for the three-dimensional hydrostatic equations, Geoscientific Model Development, Vol: 11, Pages: 4359-4382
<jats:p>Abstract. 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 for the hydrostatic equations. The formulation is fully conservative and second-order accurate in space and time. Monotonicity of the advection scheme is ensured by using a strong stability-preserving time integration method and slope limiters. Compared to previous DG models, advantages include a more accurate mode splitting method, revised viscosity formulation, and new second-order time integration scheme. We demonstrate that the model is capable of simulating baroclinic flows in the eddying regime with a suite of test cases. Numerical dissipation is well-controlled, being comparable or lower than in existing state-of-the-art structured grid models. </jats:p>
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. We consider simulation methods which include the main modes of operation of tidal power plants, along with algorithms to regulate the timing of these. This paper proposes a framework where simplified power plant operation models are coupled with gradient-based optimisation techniques to determine the optimal control strategy over multiple tidal cycles. The optimisation results inform coastal ocean simulations that include tidal power plants to gauge whether the benefits of an adaptive operation are preserved once their hydrodynamic impacts are also taken into consideration. The combined operation of two prospective tidal lagoon projects within the Bristol Channel and the Severn Estuary is used as an example to demonstrate the potential benefits of an energy maximisation optimisation approach. For the case studies considered, the inclusion of pumping and an adaptive operation is shown to deliver an overall increase in energy output of 20–40% compared to a conventional two-way uniform operation. The findings also demonstrate that smaller schemes stand to gain more from operational optimisation compared to designs of a larger scale.
Avdis A, Candy AS, Hill J, et al., 2017, Efficient unstructured mesh generation for marine renewable energy applications, Renewable Energy, Vol: 116, Pages: 842-856, ISSN: 0960-1481
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 changes in tidal dynamics, sediment transport pathways or bathymetric changes. In order to mitigate these effects, tidal energy devices need to be modelled in order to predict hydrodynamic changes. Robust mesh generation is a fundamental component required for developing simulations with high accuracy. However, mesh generation for coastal domains can be an elaborate procedure. Here, we describe an approach combining mesh generators with Geographical Information Systems. We demonstrate robustness and efficiency by constructing a mesh with which to examine the potential environmental impact of a tidal turbine farm installation in the Orkney Islands. The mesh is then used with two well-validated ocean models, to compare their flow predictions with and without a turbine array. The results demonstrate that it is possible to create an easy-to-use tool to generate high-quality meshes for combined coastal engineering, here tidal turbines, and coastal ocean simulations.
du Feu RJ, Funke SW, Kramer SC, et al., 2017, The trade-off between tidal-turbine array yield and impact on flow: A multi-objective optimisation problem, Renewable Energy, Vol: 114, Pages: 1247-1257, ISSN: 1879-0682
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 is investigated using the array layout optimisation tool OpenTidalFarm. Motivated by environmental concerns, OpenTidalFarm is adapted to not only maximise array yield but also to minimise the effect of the array upon the hydrodynamics of the region, specifically the flow velocity. A linear scalarisation of the multi-objective optimisation problem is solved for a series of different weightings of the two conflicting objectives. Two idealised test scenarios are evaluated and in each case a set of Pareto solutions is found. These arrays are assessed for the power they generate and the severity of change they cause in the flow velocity. These analyses allow for the identification of trade-offs between these two objectives, while the methods proposed can similarly be applied to the two key societal objectives of energy production and conservation, thus providing information that could be valuable to stakeholders and policymakers when making decisions on array design.
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