Publications
92 results found
Zhang C, Zhang J, Angeloudis A, et al., 2023, Physical Modelling of Tidal Stream Turbine Wake Structures under Yaw Conditions, Energies, Vol: 16
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 under varying yaw conditions. Two scenarios, including a single turbine and a set of two turbines in alignment, were configured and compared. The turbine thrust force results confirmed that an increasing yaw angle results in a decrease in the turbine streamwise force and an increase in the turbine spanwise force. The velocity distributionfrom the single turbine scenario showed that the wake deflection and velocity deficit recovery rate increased at a rate proportional to the yaw angle. The two-turbine scenario results indicated that the deployment of an upstream non-yawed turbine significantly limited the downstream wake steering (i.e., the wake area behind the downstream turbine). Interestingly, a yawed downstream turbine was seen to influence the steering of both the upstream and the downstream wakes. These systematically derived data could be regarded as useful references for the numerical modelling and optimisation of large arrays.
Zhang C, Angeloudis A, Kramer SC, et al., 2023, Investigating the effect of the sediment transport on tidal turbine array performance, Pages: 189-196
A two-dimensional hydrodynamic model is coupled with a suspended and bedload sediment transport model within the Thetis coastal ocean modelling framework. In investigating the effect of sediment transport on turbine array performance, we consider two artificial scenarios of 16 turbines deployed in aligned and staggered layouts to explore the impact of morphodynamics on power conversion. An optimisation algorithm is then applied to improve the position of turbines to maximize power output. Comparing this optimisation for a case with and without sediment transport we study the effect of morphodynamics on optimal layouts. The results show that sediment transport can significantly influence the performance of the aligned layout turbine array. As for the layout optimisation process, the inclusion of sediment transport makes little difference to the final results, while the computational cost becomes substantial when including the sediment model within the optimisation, even for a steady state case.
Zhang C, Kramer SC, Angeloudis A, et al., 2022, Improving tidal turbine array performance through the optimisation of layout and yaw angles, International Marine Energy Journal, Vol: 5, Pages: 273-280
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 array design optimisation. An idealised rectangular channel test case is studied to demonstrate this optimisation framework. Located in the centre of the computational domain, arrays comprised of 12 turbines are tested in aligned and staggered layouts. The setups are initially optimised based on their yaw angles alone. In turn, turbine coordinates and yaw angles are also optimized simultaneously. Results indicate that for an aligned turbine array case under steady state conditions, the energy output can be increased by approximately 80% when considering yaw angle optimisation alone. For the staggered turbine ar-ray, 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.
Chen F, Davies DR, Goes S, et al., 2022, Comparing the Dynamics of Free Subduction in Cartesian and Spherical Domains, Geochemistry, Geophysics, Geosystems, Vol: 23
The effects of sphericity are regularly neglected in numerical and laboratory studies that examine the factors controlling subduction dynamics. Most existing studies have been executed in a Cartesian domain, with the small number of simulations undertaken in a spherical shell incorporating plates with an oversimplified rheology, limiting their applicability. Here, we simulate free-subduction of composite visco-plastic plates in 3-D Cartesian and spherical shell domains, to examine the role of sphericity in dictating the dynamics of subduction, and highlight the limitations of Cartesian models. We identify two irreconcilable differences between Cartesian and spherical models, which limit the suitability of Cartesian-based studies: (a) the presence of sidewall boundaries in Cartesian models, which modify the flow regime; and (b) the reduction of space with depth in spherical shells, alongside the radial gravity direction, which cannot be captured in Cartesian domains. Although Cartesian models generally predict comparable subduction regimes and slab morphologies to their spherical counterparts, there are significant quantitative discrepancies. We find that simulations in Cartesian domains that exceed Earth's dimensions overestimate trench retreat. Conversely, due to boundary effects, simulations in smaller Cartesian domains overestimate the variation of trench curvature driven by plate width. Importantly, spherical models consistently predict higher sinking velocities and a reduction in slab width with depth, particularly for wider subduction systems, enhancing along-strike slab buckling and trench curvature. Results imply that sphericity must be considered for understanding the dynamics of Earth's wider subduction systems, and is already a significant factor for slabs of width 2,400 km.
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.
Chen F, Davies DR, Goes S, et al., 2022, How Slab Age and Width Combine to Dictate the Dynamics and Evolution of Subduction Systems: A 3-D Spherical Study, GEOCHEMISTRY GEOPHYSICS GEOSYSTEMS, Vol: 23
Chen F, Davies DR, Goes S, et al., 2022, Comparing the Dynamics of Free Subduction in Cartesian and Spherical Domains
Halilovic S, Böttcher F, Kramer S, et al., 2022, Well layout optimization for groundwater heat pump systems using the adjoint approach, Energy Conversion and Management, Vol: 268, ISSN: 0196-8904
Groundwater heat pump systems cause thermal anomalies in the aquifer that can impact upon downstream systems and reduce their efficiency. Therefore, it is important to optimally position the extraction and injection wells of such systems to avoid negative interactions and maximize the thermal potential of the aquifer. This paper presents a new method to determine optimal well layouts of groundwater heat pumps using the adjoint approach, which is an efficient way to solve the underlying PDE-constrained optimization problem. An integral part of the method is the numerical groundwater simulation, which here is based on the finite element method. In addition, a multi-start initialization strategy is introduced in an attempt tobetter reach the global optimum. The method is applied to a real case study with 10 groundwater heat pumps, i.e. 20 wells, and two optimization scenarios with different natural groundwater temperatures. In both scenarios, the optimization method successfully determines a well layout that maximizes groundwater temperatures at all extraction wells. Comparing the results from these scenarios demonstrates that hydro-geological conditions can have a significant impact on the optimal well layout. The proposed method is equally applicable to systems with multiple extraction and injection wells and can be extended to various other shallow geothermal applications, such as combined heating and cooling systems.
Pan W, Kramer SC, Piggott MD, et al., 2022, Modeling landslide generated waves using the discontinuous finite element method, International Journal for Numerical Methods in Fluids, Vol: 94, Pages: 1-33, ISSN: 0271-2091
A new two-layer model for impulsive wave generation by deformable granular landslides is developed based upon a discontinuous Galerkin finite element discretization. Landslide motion is modeled using a depth-averaged formulation for a shallow subaerial debris flow, which considers the bed curvature represented by the local slope angle variable and accounts for inter-granular stresses using Coulomb friction. Wave generation and propagation are simulated with the three-dimensional non-hydrostatic coastal ocean model Thetis to accurately capture key features such as wave dispersion. Two different techniques are used in treating wetting and drying (WD) processes during the landslide displacement and wave generation, respectively. For the lower-layer landslide motion across the dry bed a classical thin-layer explicit WD method is implemented, while for the resulting free-surface waves interacted with the moving landslide an implicit WD scheme is utilized to naturally circumvent the artificial pressure gradient problem which may appear in the dynamic interaction between the landslide and water if using the thin-layer method. The two-layer model is validated using a suite of test cases, with the resulting good agreement demonstrating its capability in describing both the complex behaviors of granular landslides from initiation to deposition, and the consequent wave generation and propagation.
Chen F, Davies DR, Goes S, et al., 2022, How slab age and width combine to dictate the dynamics and evolution of subduction systems: a 3-D spherical study
Davies DR, Kramer SC, Ghelichkhan S, et al., 2022, Towards automatic finite-element methods for geodynamics via Firedrake, GEOSCIENTIFIC MODEL DEVELOPMENT, Vol: 15, Pages: 5127-5166, ISSN: 1991-959X
Duvernay T, Davies DR, Mathews CR, et al., 2022, Continental Magmatism: The Surface Manifestation of Dynamic Interactions Between Cratonic Lithosphere, Mantle Plumes and Edge-Driven Convection, GEOCHEMISTRY GEOPHYSICS GEOSYSTEMS, Vol: 23
Clare MCA, Kramer SC, Cotter CJ, et al., 2022, Calibration, inversion and sensitivity analysis for hydro-morphodynamic models through the application of adjoint methods, Computers and Geosciences, Vol: 163, Pages: 1-13, ISSN: 0098-3004
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 related parameters in both the hydrodynamic and morphodynamic solvers. This uncertainty can be addressed through the application of adjoint methods. These have the notable advantage that the number and/or dimension of the uncertain parameters has almost no effect on the computational cost associated with calculating the model sensitivities. Here, we develop the first freely available and fully flexible adjoint hydro-morphodynamic model framework. This flexibility is achieved through using the pyadjoint library, which allows us to assess the uncertainty of any parameter with respect to any model functional, without further code implementation. The model is developed within the coastal ocean model Thetis constructed using the finite element code-generation library Firedrake. We present examples of how this framework can perform sensitivity analysis, inversion and calibration for a range of uncertain parameters based on the final bedlevel. These results are verified using so-called dual-twin experiments, where the ‘correct’ parameter value is used in the generation of synthetic model test data, but is unknown to the model in subsequent testing. Moreover, we show that inversion and calibration with experimental data using our framework produces physically sensible optimum parameters and that these parameters always lead to more accurate results. In particular, we demonstrate how our adjoint framework can be applied to a tsunami-like event to invert for the tsunami wave from sediment deposits.
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: 1-13, ISSN: 0029-8018
Tidal currents represent an attractive renewable energy source particularly because of their predictability. Prospective tidal stream development sites are often co-located in close proximity. Under such circumstances, in order to maximise the exploitation of the resource, multiple tidal stream turbine arrays working in tandem would be needed. In this paper, a continuous array optimisation approach based on the open source coastal ocean modelling framework Thetis is applied to derive optimal configurations for four turbine arrays around Zhoushan Islands, Zhejiang Province, China. Alternative optimisation scenarios are tested to investigate interactions between the turbine arrays and their hydrodynamic footprint. Results show that there are no obvious competition effects between these four arrays around Hulu and Taohua Island. However, significant interactions could arise among the three turbine arrays situated around Hulu Island, with a maximum decrease in average power of 42.2%. By optimising all turbine arrays simultaneously, the competition effects can be minimised and the cost of energy reduced as less turbines are required to deliver an equivalent energy output. As for the potential environmental impact, it is found that the turbine array around Taohua Island would affect a larger area than turbine arrays around Hulu Island.
Duvernay T, Davies DR, Mathews C, et al., 2022, Continental Magmatism: The Surface Manifestation of Dynamic Interactions Between Cratonic Lithosphere, Mantle Plumes and Edge-Driven Convection
Davies DR, Kramer SC, Ghelichkhan S, et al., 2022, Automating Finite Element Methods for Geodynamics via Firedrake
<jats:p>Abstract. Firedrake is an automated system for solving partial differential equations using the finite element method. By applying sophisticated performance optimisations through automatic code-generation techniques, it provides a means to create accurate, efficient, flexible, easily extensible, scalable, transparent and reproducible research software, that is ideally suited to simulating a wide-range of problems in geophysical fluid dynamics. Here, we demonstrate the applicability of Firedrake for geodynamical simulation, with a focus on mantle dynamics. The accuracy and efficiency of the approach is confirmed via comparisons against a suite of analytical and benchmark cases of systematically increasing complexity, whilst parallel scalability is demonstrated up to 12288 compute cores, where the problem size and the number of processing cores are simultaneously increased. In addition, Firedrake's flexibility is highlighted via straightforward application to different physical (e.g. complex nonlinear rheologies, compressibility) and geometrical (2-D and 3-D Cartesian and spherical domains) scenarios. Finally, a representative simulation of global mantle convection is examined, which incorporates 230 Myr of plate motion history as a kinematic surface boundary condition, confirming its suitability for addressing research problems at the frontiers of global mantle dynamics research. </jats:p>
Piggott MD, Kramer SC, Funke SW, et al., 2022, 8.10 - Optimization of Marine Renewable Energy Systems, Comprehensive Renewable Energy, Second Edition: Volume 1-9, Pages: 176-220, ISBN: 9780128197271
Optimizing marine renewable energy systems to maximize performance is key to their success. However, a range of physical, environmental, engineering, economic as well as computational challenges means that this is not straightforward. This article considers this topic, focusing on those systems whose performance is coupled to the hydrodynamics providing the resource; tidal power represents a clear example of this. In such cases system design must be optimal in relation to the resource׳s magnitude as well as its spatial and temporal variation, which are all dependent on the system׳s configuration and operation and so cannot be assumed to be known at the design stage. Designing based on the ambient resource could lead to under-performance. Coupling between the design and the resource has implications for the complexity of the optimization problem and potential hydrodynamical and environmental impacts. This coupling distinguishes many marine energy systems from other renewables which do not impact in any significant manner on the resource. The optimal design of marine energy systems thus represents a challenging and somewhat unique problem. However, feedback also opens up a number of possibilities where the resource can be ‘controlled’, to maximize the cumulative power obtained from multiple devices or plants, or to achieve some other complementary goal. Design optimization is thus critical, with many issues to consider. Due to the complexity of the problem a computational based solution is a necessity in all but the simplest scenarios. However, the coupled feedback requires that an iterative solution approach be used, which combined while the vast range of spatial and temporal scales means that methodological compromises need to be made. These compromises need to be understood, with the correct computational tool used at the appropriate point in the design process. This article reviews these challenges as well as the progress that has been made in addressi
Chen F, Davies DR, Goes S, et al., 2021, How sphericity combines with the age and width of slabs to dictate the dynamics and evolution of subduction systems on Earth
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
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- Citations: 3
Duvernay T, Davies DR, Mathews CR, et al., 2021, Linking Intraplate Volcanism to Lithospheric Structure and Asthenospheric Flow, GEOCHEMISTRY GEOPHYSICS GEOSYSTEMS, Vol: 22
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- Citations: 11
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.
Goss ZL, Coles DS, Kramer SC, et al., 2021, Efficient economic optimisation of large-scale tidal stream arrays, Applied Energy, Vol: 295, Pages: 1-17, ISSN: 0306-2619
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, but becomes an impractically large approach when the number of devices is high, especially if taking into account both the cost effectiveness of each turbine and also the coupled nature of the turbine locations and the local as well as far-field hydrodynamics.Previous work has largely focused on producing computational tools to automatically design the size and layout of large-scale tidal turbine arrays to optimise power. There has been some limited preliminary work to incorporate costs into these models, in order to improve the economic viability of tidal arrays. This paper provides the first in depth implementation and analysis of economic functionals, based upon metrics such as break even power and levelised cost of energy, used for design of explicit array sizing and spatial variation.The addition of these new economic functionals introduces complexity by increasing the number of inputs to the model, each of which are subject to their own uncertainty in value. For this reason, sensitivity analysis becomes both more important as well as more difficult to undertake. This paper presents a novel rapid methodology for deriving the optimal array design (number of turbines and their spatial distribution throughout the farm area) to minimise cost functionals, and its sensitivity to variations in the economic inputs. Importantly, the new aspects of this method introduced here do not rely on repeated model runs and iterative optimisation, two aspects that typically prove to be impractically expensive computationally. This more readily allows for the impact of changes in investor priorities to be investigated. It is also shown tha
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.
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