The depth-integrated shallow water equations are frequently used for simulating geophysical flows, such as storm-surges, tsunamis and river flooding. In this paper a parallel shallow water solver using an unstructured high-order discontinuous Galerkin method is presented. The spatial discretization of the model is based on the Nektar++ spectral/hp library and the model is numerically shown to exhibit the expected exponential convergence. The parallelism of the model has been achieved within the Cactus Framework. The model has so far been executed successfully on up to 128 cores and it is shown that both weak and strong scaling are largely independent of the spatial order of the scheme. Results are also presented for the wave flume interaction with five upright cylinders.
Due to limited access to domain knowledge and domain-relevant benchmark data, the Container Stowage Planning Problem (CSPP) is notably under-researched. In particular, previous models of the CSPP have lacked two key aspects of the problem: lashing forces and paired block stowage. The former may reduce vessel capacity by up to 10%, and the latter is NP-hard. The Representative CSPP (RCSPP), which captures all critical aspects of the problem is formulated. The presented RCSPP incorporates overlooked constraints such as paired block stowage and lashing, along with an innovative method for estimating lashing forces, all while maintaining simplicity. A heuristic method, STOW, has been developed to identify solutions for the RCSPP using a specially designed benchmark suite based on real-world scenarios. STOW algorithm is an advanced search heuristic employing a diverse range of solution modification strategies, each tailored to address specific aspects of stowage optimization. Feasible solutions were successfully identified for all instances within the benchmark suite. Our initial findings emphasize the importance of accurately modeling lashing forces and employing paired block stowage. Results show that removing the lashing constraint can increase the number of containers stowed by over 7% on average, while disabling paired block stowage can result in nearly a 5% increase.
Due to limited access to domain knowledge and domain-relevant benchmark data, the Container Stowage Planning Problem (CSPP) is notably under-researched. In particular, previous models of the CSPP have lacked two key aspects of the problem: lashing forces and paired block stowage. The former may reduce vessel capacity by up to 10%, and the latter is NP-hard. The Representative CSPP (RCSPP), which captures all critical aspects of the problem is formulated. The presented RCSPP incorporates overlooked constraints such as paired block stowage and lashing, along with an innovative method for estimating lashing forces, all while maintaining simplicity. A heuristic method, STOW, has been developed to identify solutions for the RCSPP using a specially designed benchmark suite based on real-world scenarios. STOW algorithm is an advanced search heuristic employing a diverse range of solution modification strategies, each tailored to address specific aspects of stowage optimization. Feasible solutions were successfully identified for all instances within the benchmark suite. Our initial findings emphasize the importance of accurately modeling lashing forces and employing paired block stowage. Results show that removing the lashing constraint can increase the number of containers stowed by over 7% on average, while disabling paired block stowage can result in nearly a 5% increase.
We consider the Tramp Ship Routing and Scheduling Problem (TSRSP) in which we plan routes for a fleet of tramp shipping vessels operating on a combined contract and spot market. Earlier research has been fragmented due to variations in the side constraints studied. Hence we present the first unified model that can handle speed optimization, chartering costs, bunker planning, and hull cleaning. The model is solved by column generation, where the columns represent the possible routes of a vessel, while the master problem keeps track of the binding constraints. The pricing problem is solved efficiently using a time–space graph and several dominance rules. Real-life instances with up to 40 vessels, 35 geographic regions, and four months planning horizon can be solved to optimality in less than half an hour. The optimized routes increase earnings by 7% compared to historical schedules. Furthermore, policy-makers can use the model as a simulation of a rational agent behavior.
We present a depth-integrated Boussinesq model for the efficient simulation of nonlinear wave–body interaction. The model exploits a ‘unified’ Boussinesq framework, i.e. the fluid under the body is also treated with the depth-integrated approach. The unified Boussinesq approach was initially proposed by Jiang (2001) and recently analyzed by Lannes (2017). The choice of Boussinesq-type equations removes the vertical dimension of the problem, resulting in a wave–body model with adequate precision for weakly nonlinear and dispersive waves expressed in horizontal dimensions only. The framework involves the coupling of two different domains with different flow characteristics. Inside each domain, the continuous spectral/hp element method is used to solve the appropriate flow model since it allows to achieve high-order, possibly exponential, convergence for non-breaking waves. Flux-based conditions for the domain coupling are used, following the recipes provided by the discontinuous Galerkin framework. The main contribution of this work is the inclusion of floating surface-piercing bodies in the conventional depth-integrated Boussinesq framework and the use of a spectral/hp element method for high-order accurate numerical discretization in space. The model is verified using manufactured solutions and validated against published results for wave–body interaction. The model is shown to have excellent accuracy and is relevant for applications of waves interacting with wave energy devices.
We present an arbitrary-order spectral element method for general-purpose simulation of non-overturning water waves, described by fully nonlinear potential theory. The method can be viewed as a high-order extension of the classical finite element method proposed by Cai et al. (1998)[5], although the numerical implementation differs greatly. Features of the proposed spectral element method include: nodal Lagrange basis functions, a general quadrature-free approach and gradient recovery using global L2projections. The quartic nonlinear terms present in the Zakharov form of the free surface conditions can cause severe aliasing problems and consequently numerical instability for marginally resolved or very steep waves. We show how the scheme can be stabilised through a combination of over-integration of the Galerkin projections and a mild spectral filtering on a per element basis. This effectively removes any aliasing driven instabilities while retaining the high-order accuracy of the numerical scheme. The additional computational cost of the over-integration is found insignificant compared to the cost of solving the Laplace problem. The model is applied to several benchmark cases in two dimensions. The results confirm the high order accuracy of the model (exponential convergence), and demonstrate the potential for accuracy and speedup. The results of numerical experiments are in excellent agreement with both analytical and experimental results for strongly nonlinear and irregular dispersive wave propagation. The benefit of using a high-order – possibly adapted – spatial discretisation for accurate water wave propagation over long times and distances is particularly attractive for marine hydrodynamics applications.
Monitoring methods, such as seabed bottom-towed cameras, sediment grabs, and benthic sledges, have limitations in spatial coverage, cause seabed disturbance, are restricted to soft-bottom substrates, and offer low flexibility for marine seabed monitoring. In this study, we investigate the potential of a non-invasive and simple underwater remotely operated vehicle (ROV) to enhance marine seabed monitoring. A tethered ROV equipped with a GoPro camera was deployed in three areas of Skagerrak at depths from 15-34 m to assess accuracy in species identification and substrate classification identified from still frames. The quality of still frames varied between areas due to turbidity, motion blur, and marine snow, which reduced the number of high-quality frames by approximately 20%. Classification of substrates and taxa identification were possible in the remaining still frames. Two different substrates were detected: sand and stone reef. Stone reefs had a lower occurrence compared to sand. A total of 10 taxa were detected in the two substrate types. The highest abundance was observed in the stone reef substrate compared to the sand substrate. Identification at the species level was limited due to the quality of the still frames, which affected the detectability of morphological traits. This study demonstrates that a widely accessible ROV can be used for marine monitoring. The ROV can be used in different substrates, and still frames provide valuable information on species composition, which can enhance the replicability of monitoring programs.
An adaptive spectral/hp discontinuous Galerkin method for the two-dimensional shallow water equations is presented. The model uses an orthogonal modal basis of arbitrary polynomial order p defined on unstructured, possibly non-conforming, triangular elements for the spatial discretization. Based on a simple error indicator constructed by the solutions of approximation order p and p-1, we allow both for the mesh size, h, and polynomial approximation order to dynamically change during the simulation. For the h-type refinement, the parent element is subdivided into four similar sibling elements. The time-stepping is performed using a third-order Runge-Kutta scheme. The performance of the hp-adaptivity is illustrated for several test cases. It is found that for the case of smooth flows, p-adaptivity is more efficient than h-adaptivity with respect to degrees of freedom and computational time.
Large and remote offshore wind farms (OWFs) usually use voltage source converter (VSC) systems to transmit electrical power to the main network. Submarine high-voltage direct current (HVDC) cables are commonly used as transmission links. As they are liable to insulation breakdown, fault location in the HVDC cables is a major issue in these systems. Exact fault location can significantly reduce the high cost of submarine HVDC cable repair in multi-terminal networks. In this paper, a novel method is presented to find the exact location of the DC faults. The fault location is calculated using extraction of new features from voltage signals of cables' sheaths and a trained artificial neural network (ANN). The results obtained from a simulation of a three-terminal HVDC system in power systems computer-aided design (PSCAD) environment show that the maximum percentage error of the proposed method is less than 1%.
The offshore de-oiling process is a vital part of current oil recovery, as it separates the profitable oil from water and ensures that the discharged water contains as little of the polluting oil as possible. With the passage of time, there is an increase in the water fraction in reservoirs that adds to the strain put on these facilities, and thus larger quantities of oil are being discharged into the oceans, which has in many studies been linked to negative effects on marine life. In many cases, such installations are controlled using non-cooperative single objective controllers which are inefficient in handling fluctuating inflows or complicated operating conditions. This work introduces a model-based robust H ∞ control solution that handles the entire de-oiling system and improves the system’s robustness towards fluctuating flow thereby improving the oil recovery and reducing the environmental impacts of the discharge. The robust H ∞ control solution was compared to a benchmark Proportional-Integral-Derivative (PID) control solution and evaluated through simulation and experiments performed on a pilot plant. This study found that the robust H ∞ control solution greatly improved the performance of the de-oiling process.