Ocean Engineering Problems Research Articles

The past, present and future of multi-scale modelling applied to wave-structure interaction in ocean engineering.

Concepts and evolution of multi-scale modelling from the perspective of wave-structure interaction have been discussed. In this regard, both domain and functional decomposition approaches have come into being. In domain decomposition, the computational domain is spatially segregated to handle the far-field using potential flow models and the near field using Navier-Stokes equations. In functional decomposition, the velocity field is separated into irrotational and rotational parts to facilitate identification of the free surface. These two approaches have been implemented alongside partitioned or monolithic schemes for modelling the structure. The applicability of multi-scale modelling approaches has been established using both mesh-based and meshless schemes. Owing to said diversity in numerical techniques, massively collaborative research has emerged, wherein comparative numerical studies are being carried out to identify shortcomings of developed codes and establish best-practices in numerical modelling. Machine learning is also being applied to handle large-scale ocean engineering problems. This paper reports on the past, present and future research consolidating the contributions made over the past 20 years. Some of these past as well as future research contributions have and shall be actualized through funding from the Newton International Fellowship as the next generation of researchers inherits the present-day expertise in multi-scale modelling. This article is part of the theme issue 'Celebrating the 15th anniversary of the Royal Society Newton International Fellowship'.

Cross-Scale Modeling of Shallow Water Flows in Coastal Areas with an Improved Local Time-Stepping Method

A shallow water equations-based model with an improved local time-stepping (LTS) scheme is developed for modeling coastal hydrodynamics across multiple scales, from large areas to detailed local regions. To enhance the stability of the shallow water model for long-duration simulations and at larger LTS gradings, a prediction-correction method using a single-layer interface that couples coarse and fine time discretizations is adopted. The proposed scheme improves computational efficiency with an acceptable additional computational burden and ensures accurate conservation of time truncation errors in a discrete sense. The model performance is verified with respect to conservation and computational efficiency through two idealized tests: the spreading of a drop of shallow water and a tidal flat/channel system. The results of both tests demonstrate that the improved LTS scheme maintains precision as the LTS grading increases, preserves conservation properties, and significantly improves computational efficiency with a speedup ratio of up to 2.615. Furthermore, we applied the LTS scheme to simulate tides at grid scales of 40,000 m to 200 m for a portion of the Northwest Pacific. The proposed model shows promise for modeling cross-scale hydrodynamics in complex coastal and ocean engineering problems.

Autonomous Marine Vehicle Operations

The world has witnessed the rapid development of autonomous marine vehicles,such as surface vehicles and underwater vehicles, which have created fruitful innovative approaches to previously unsolvable problems in marine and ocean engineering [...]

Quality measures for the evaluation of machine learning architectures on the quantification of epistemic and aleatoric uncertainties in complex dynamical systems

Machine learning methods for the construction of data-driven reduced order model models are used in an increasing variety of engineering domains, especially as a supplement to expensive computational fluid dynamics for design problems. An important check on the reliability of surrogate models is Uncertainty Quantification (UQ), a self assessed estimate of the model error. Accurate UQ allows for cost savings by reducing both the required size of training data sets and the required safety factors, while poor UQ prevents users from confidently relying on model predictions. We introduce two quality measures for the quantification of uncertainty that are suitable for high dimensional problems: the distribution of normalized residuals on validation data and the distribution of estimated uncertainties. While the distribution of estimated uncertainties evaluates how confident the model is in making predictions, the distribution of normalized residuals evaluates how accurate these uncertainty estimates are We examine several machine learning techniques, including both Gaussian processes and a family UQ-augmented neural networks: Ensemble neural networks (ENN), Bayesian neural networks (BNN), Dropout neural networks (D-NN), and Gaussian neural networks (G-NN). We evaluate UQ accuracy (distinct from model accuracy) We apply these metrics to two model data sets representative of complex dynamical systems: an ocean engineering problem in which a ship traverses irregular wave episodes, and a dispersive wave turbulence system with extreme events, the Majda–McLaughlin–Tabak model. We present conclusions concerning model architecture and hyperparameter tuning for use in applications of UQ to dynamical systems, such as active learning schemes.

An effective preconditioning strategy for volume penalized incompressible/low Mach multiphase flow solvers

The volume penalization (VP) or the Brinkman penalization (BP) method is a diffuse interface method for simulating multiphase fluid-structure interaction (FSI) problems in ocean engineering and/or phase change problems in thermal sciences and engineering. The method relies on a penalty factor (which is inversely related to body's permeability κ) that must be large to enforce rigid body velocity in the solid domain. When the penalty factor is large, the discrete system of equations becomes stiff and difficult to solve numerically. In this paper, we propose a projection method-based preconditioning strategy for solving volume penalized (VP) incompressible and low-Mach Navier-Stokes equations. The projection preconditioner enables the monolithic solution of the coupled velocity-pressure system in both single phase (uniform density and viscosity) and multiphase (variable density and viscosity) flow settings. In this approach, the penalty force is treated implicitly, which is allowed to take arbitrary large values without affecting the solver's convergence rate or causing numerical stiffness. It is made possible by including the penalty term in the pressure Poisson equation (PPE), which was not included in previous works that solved VP incompressible Navier-Stokes equations using the projection method. We show how and where the Brinkman penalty term enters the PPE by re-deriving the projection algorithm for the VP method. Solver scalability under grid refinement is demonstrated, i.e., convergence is achieved with the same number of iterations regardless of the problem size. A manufactured solution in a single phase setting is used to determine the spatial accuracy of the penalized solution. Various values of body's permeability κ are considered. Second-order pointwise accuracy is achieved for both velocity and pressure solutions for reasonably small values of κ. Error saturation occurs when κ is extremely small, but the convergence rate of the solver does not degrade. The solver converges faster as κ decreases, contrary to prior experience. Two multiphase fluid-structure interaction (FSI) problems from the ocean engineering literature are also simulated to evaluate the solver's robustness and performance (in terms of its number of iterations). The proposed solver also allows us to investigate the effect of κ on the motion of the contact line over the surface of the immersed body. It also allows us to investigate the dynamics of the free surface of a solidifying metal.

Floating hydroelastic circular plate in regular and irregular waves

An understanding of the hydroelastic response of a flexible circular plate to water waves is relevant to many problems in ocean engineering ranging from offshore wave energy converters and solar wind devices to very large floating structures such as floating airports and ice sheets. This paper describes results from physical model tests undertaken in the COAST laboratory at the University of Plymouth. Response amplitude operators (RAOs) of a floating flexible circular disk are determined for incident monochromatic and irregular wave trains, the latter defined by JONSWAP spectra. Free-surface displacements are measured using wave gauges, and the plate motion recorded using a QUALISYS® motion tracking system. Different basin depths and plate thicknesses are considered in order to quantify the effects of water depth and flexural plate rigidity on the overall dynamic behaviour of the circular disk. We present synchronous and subharmonic nonlinear responses for monochromatic waves, and displacement spectra for irregular waves. The measured wave hydrodynamics and disk hydroelastic responses match theoretical predictions based on linear potential flow theory.

On methodology and application of smoothed particle hydrodynamics in fluid, solid and biomechanics.

Smoothed particle hydrodynamics (SPH), as one of the earliest meshfree methods, has broad prospects in modeling a wide range of problems in engineering and science, including extremely large deformation problems such as explosion and high velocity impact. This paper aims to provide a comprehensive overview on the recent advances of SPH method in the fields of fluid, solid, and biomechanics. First, the theory of SPH is described, and improved algorithms of SPH with high accuracy are summarized, such as the finite particle method (FPM). Techniques used in SPH method for simulating fluid, solid and biomechanics problems are discussed. The δ-SPH method and Godunov SPH (GSPH) based on the Riemann model are described for handling instability issues in fluid dynamics. Next, the interface contact algorithm for fluid-structure interaction is also discussed. The common algorithms for improving the tensile instability and the framework of total Lagrangian SPH are examined for challenging tasks in solid mechanics. In terms of biomechanics, the governing equations and the coupling forces based on SPH method are exemplified. Then, various typical engineering applications and recent advances are elaborated. The application of fluid mainly depicts the interaction between fluid and rigid body as well as elastomer, while some complicated fluid-structure interaction ocean engineering problems are also presented. In the aspect of solid dynamics, galaxy, geotechnical mechanics, explosion and impact, and additive manufacturing are summarized. Furthermore, the recent advancements of SPH method in biomechanics, such as hemodynamically and gut health, are discussed in general. In addition, to overcome the limitations of computational efficiency and computational scale, the multiscale adaptive resolution, the parallel algorithm and the automated mesh generation are addressed. The development of SPH software in China and abroad is also summarized. Finally, the challenging task of SPH method in the future is summarized. In future research work, the establishment of multi-scale coupled SPH model and deep learning technology in solid and biodynamics will be the focus of expanding the engineering applications of SPH methods.

SPHydro: Promoting smoothed particle hydrodynamics method toward extensive applications in ocean engineering

This paper aims at presenting a general-purpose-oriented and fully parallelized meshless framework to simulate complex Fluid–Structure Interaction (FSI) problems in ocean engineering. In this framework, a Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) solver is combined with several advanced pre- and post-processing techniques. Based on the framework, we have been developing our in-house WCSPH-FSI package named SPHydro for solving hydrodynamic problems involving complex FSI processes in an accurate, efficient, and convenient manner. Three benchmarks are performed to qualitatively and quantitatively validate the accuracy and convergence of SPHydro. In addition, several practical applications are also provided to further highlight the generality and applicability of SPHydro in ocean engineering simulations. It is demonstrated that SPHydro holds satisfactory performance in solving complex FSI problems in ocean engineering and that the present framework can be further developed to tackle more complex FSI problems for general engineering applications due to its high flexibility and extensibility.

Research Progress of SPH Simulations for Complex Multiphase Flows in Ocean Engineering

Complex multiphase flow problems in ocean engineering have long been challenging topics. Problems such as large deformations at interfaces, multi-media interfaces, and multiple physical processes are difficult to simulate. Mesh-based algorithms could have limitations in dealing with multiphase interface capture and large interface deformations. On the contrary, the Smoothed Particle Hydrodynamics (SPH) method, as a Lagrangian meshless particle method, has some merit and flexibility in capturing multiphase interfaces and dealing with large boundary deformations. In recent years, with the improvement of SPH theory and numerical models, the SPH method has made significant advances and breakthroughs in terms of theoretical completeness and computational stability, which starts to be widely used in ocean engineering problems, including multiphase flows under atmospheric pressure, high-pressure multiphase flows, phase-change multiphase flows, granular multiphase flows and so on. In this paper, we review the progress of SPH theory and models in multiphase flow simulations, discussing the problems and challenges faced by the method, prospecting to future research works, and aiming to provide a reference for subsequent research.

Machine learning for naval architecture, ocean and marine engineering

Machine learning (ML)-based techniques have found significant impact in many fields of engineering and sciences, where data-sets are available from experiments and high-fidelity numerical simulations. Those data-sets are generally utilised in a machine learning model to extract information about the underlying physics and derive functional relationships mapping input variables to target quantities of interest. Commonplace machine learning algorithms utilised in scientific machine learning (SciML) include neural networks, support vector machines, regression trees, random forests, etc. The focus of this article is to review the applications of ML in naval architecture, ocean and marine engineering problems; and identify priority directions of research. We discuss the applications of machine learning algorithms for different problems such as wave height prediction, calculation of wind loads on ships, damage detection of offshore platforms, calculation of ship-added resistance and various other applications in coastal and marine environments. The details of the data-sets including the source of data-sets utilised in the ML model development are included. The features used as the inputs to the ML models are presented in detail and finally, the methods employed in optimisation of the ML models were also discussed. Based on this comprehensive analysis, we point out future directions of research that may be fruitful for the application of ML to ocean and marine engineering problems.

Review of the State-of-Art of MPS Method in Ocean Engineering

When dealing with the complex deformation of free surface such as wave breaking, traditional mesh-based Computational Fluid Dynamics (CFD) methods often face problems arising alongside grid distortion and re-meshing. Therefore, the meshless method became robust for treating large displaced free surface and other boundaries caused by moving structures. The particle method, which is an important branch of meshless method, is mainly divided into the Smoothed Particle Hydrodynamics (SPH) and Moving Particle Semi-implicit (MPS) methods. Different from the SPH method, which involves continuity and treat density as a variable when building kernel functions, the kernel function in the MPS method is a weight function which treats density as a constant, and the spatial derivatives are discretized by establishing the gradient operator and Laplace operator separately. In other words, the first- or second-order continuity of the kernel functions in the MPS method is not a necessity as in SPH, though it might be desirable. At present, the MPS method has been successfully applied to various violent-free surface flow problems in ocean engineering and diverse applications have been comprehensively demonstrated in a number of review papers. This work will focus on algorithm developments of the MPS method and to provide all perspectives in terms of numerical algorithms along with their pros and cons.

Review on Applications of Machine Learning in Coastal and Ocean Engineering

Recently, an analysis method using machine learning for solving problems in coastal and ocean engineering has been highlighted. Machine learning models are effective modeling tools for predicting specific parameters by learning complex relationships based on a specified dataset. In coastal and ocean engineering, various studies have been conducted to predict dependent variables such as wave parameters, tides, storm surges, design parameters, and shoreline fluctuations. Herein, we introduce and describe the application trend of machine learning models in coastal and ocean engineering. Based on the results of various studies, machine learning models are an effective alternative to approaches involving data requirements, time-consuming fluid dynamics, and numerical models. In addition, machine learning can be successfully applied for solving various problems in coastal and ocean engineering. However, to achieve accurate predictions, model development should be conducted in addition to data preprocessing and cost calculation. Furthermore, applicability to various systems and quantifiable evaluations of uncertainty should be considered.

Generation of Stable Linear Waves in Shallow Water in a ‎Numerical Wave Tank

This paper aims to investigate numerically linear stable waves at low wave steepness in shallow water using ANSYS Fluent software. The authors mainly determined how, when, and where a linear wave will reach its stable state in shallow water. The finite volume method is used to solve the Navier-Stokes equations. The inflow velocity method and the Dirichlet boundary condition are used to generate a suitable linear wave. Numerical damping is used at the end of the tank to reduce the reflection of the wave. The accuracy and stability of the waves are judged under wave height variation between the CFD results and the analytical results. The test has been conducted in four different cases (Case 1, Case 2, Case 3, and Case 4). Wave evolution and particle velocity are obtained in the velocity field to understand the wave stability in the numerical wave tank. Numerical data are captured from the free surface to compare the surface profile and wave velocity. The results have revealed that the accuracy, stability, and consistency of the linear waves are in good agreement with the analytical solution. The relative error between the two results is 1.43% for Case 3. This research is a highly relevant source of information in realistic wave generation to design various practical systems such as wave energy converters, offshore marine structures, and many ocean engineering problems‎.

A model for underwater shaking table tests on the basis of different similar criteria

Shaking table testing is still considered a reliable approach when examining the seismic performance of structures, however, for long-span and large-scale hydraulic structures, limited by the constraints of test equipment and the influence of water, during underwater shaking table testing, if the earthquakes input, water levels and similitude law obtained on the basis of the test model and the resulting similar relationship do not fall within the operating range of the shaking table, the obtained results cannot truly reflect the dynamic response of the tested structure. To solve this problem, the improved dimensional analysis method and the finite element software ANSYS are used to study similar relationships and derive the design model of a certain bridge. Within the elastic similarity criteria, effective and feasible test models are proposed. The distortion model is designed by increasing the added mass can reduce the time scale, guarantee that the test runs smoothly, and better reflect the dynamic response of the prototype structure after such modification, however, for the long and thin model structure, the appropriate added mass adopted to ensure that within the bearing capacity of the structure and the shaking table, the elastic similarity meets the design requirements of the structure model of irregular and regular cross-sections and is suitable for the model design requirements of long-span and large-scale structures. Within the elasticity-gravity similar criteria, the distortion model designed by added mass can reflect the dynamic response of the prototype structure, which needs to be configured with certain added masses, and the bearing capacity of the model itself and the shaking table needs to be considered. The elasticity-gravity similitude law is suitable for examining regular cross-sections and short-span and small-scale test models, but the fluid-structure coupling and failure mechanism of structures can be examined. The distinctive peak acceleration will not affect the error of the dynamic response of the lacking-artificial added mass model, the distortion model and the prototype. The reinforcement ratio will not affect the error of the dynamic response of the distortion model and the prototype structure, but it will affect the error of the dynamic response of the lacking-artificial added mass model and the prototype structure. The added mass of the water triggered by the flexible movement of the structure under the action of earthquake changes the dynamic characteristics of the structure and the rigid movement of the structure triggers the water to exert an external force on the structure, which affects the dynamic characteristics and responses of the structure. This paper can provide a reference for the examine of other hydraulic structures and is beneficial to the examine of applied ocean engineering problems.

On removing the numerical instability induced by negative pressures in SPH simulations of typical fluid–structure interaction problems in ocean engineering

This paper is dedicated to (1) emphasizing the importance of removing the Tensile Instability (TI) induced by negative pressures in Smoothed Particle Hydrodynamics (SPH) simulations, and (2) proposing new modifications for the Tensile Instability Control (TIC) and Particle Shifting Technique (PST) to simulate Fluid–Structure Interaction (FSI) phenomena with violent free-surface evolutions. Four numerical benchmarks associated with classical FSI problems characterized by negative pressures are simulated to show how the tensile instability destroys an SPH simulation without any TI prevention strategies. Therefore, PST and TIC are adopted into the SPH simulations for the sake of suppressing the tensile instability. However, different combinations of TI prevention strategies, i.e. different combinations of PST and TIC, lead to different results, and hence detailed investigations and discussions are provided. It is demonstrated that when negative pressures are moderate, solely using either PST or TIC works well. Nonetheless, it is in favor of using both PST and TIC if an SPH simulation is characterized by extremely strong negative pressures. Furthermore, for the problems with a convex-shaped structure penetrating a free-surface, special modifications are necessary for both PST and TIC in order to obtain accurate SPH results.

Particle methods in ocean and coastal engineering

This paper aims at providing a state-of-the-art review on the applications of particle methods in hydrodynamics-related problems in ocean and coastal engineering. The problems are placed into three categories according to their physical characteristics, namely, wave hydrodynamics and corresponding mass (air, oil, etc.) transport, wave-structure interaction, and wave-current-sediment interaction. For the first category, particle-based simulations of wave generation, propagation, breaking, as well as the associated turbulence production and dissipation, air entrainment, and mass transport, are reviewed. For wave-structure interaction, extensive structural types are considered that include fixed and moving (floating) structures, rigid and deformable structures, impermeable and porous structures, etc. For the third category, the latest advances of particle methods in wave/current interaction with sediments, i.e., sediment transport and coastal morphological changes, are outlined. This article also reviews the latest developments of particle methods with respect to enhancement of numerical stability, accuracy, efficiency and consistency in order to handle the multi-physics and multi-scale problems emerging from coastal and ocean engineering practices. Finally, the future perspectives of extending particle methods to a wider range of ocean and coastal engineering applications are highlighted.

Simulation of vortex shedding around cylinders by immersed boundary-lattice Boltzmann flux solver

The hydrodynamic response accompanied with vortex shedding around circular cylinders plays a pivotal role in ocean engineering, and the numerical simulation is an essential and efficient way. The computational domain is usually in large scale for this kind of problem, and the details of flow field surrounding structures are necessary to be observed as they play key influence. Comparing with popular numerical methods for fluids such as the Navier-Stokes (N-S) solver and the lattice Boltzmann method (LBM), to some extent, the lattice Boltzmann flux solver (LBFS) inherits their advantages and removes the limitations so that the accuracy and efficiency are both ensured. In this work, the immersed boundary-lattice Boltzmann flux solver (IB-LBFS) with implicit velocity correction is implemented to simulate vortex shedding around circular cylinders. Firstly, the simulation of flow past an isolated stationary cylinder is carried out as the validation of the IB-LBFS. After that, the phenomena of flow past two stationary cylinders in two kinds of arrangements are simulated with respective spacing ratios and Reynolds numbers. The instantaneous contours of vorticity are shown to illustrate the vortex shedding, and the hydrodynamic parameters such as the drag coefficient, the lift coefficient, and the Strouhal number are given. Through comparing with previous literatures, it can be seen that the IB-LBFS is reliable and has sufficient accuracy so that it can represent the details of the flow field, for example the beat phenomenon, in this simulation, which indicates its wide application for fluid-structure interaction problems in ocean engineering.

Multi-resolution ISPH-SPH for accurate and efficient simulation of hydroelastic fluid-structure interactions in ocean engineering

A SPH (Smoothed Particle Hydrodynamics)-based multi-resolution fully Lagrangian meshfree hydroelastic FSI (Fluid-Structure Interaction) solver is developed for accurate and adaptive reproductions of ocean engineering problems. The presented hydroelastic FSI solver comprises of projection-based ISPH (Incompressible SPH) fluid model and SPH structure model, through consideration of continuity/Navier-Stokes equations for fluid phase as well as linear/angular momentum conservation equations for structure phase. The FSI solver includes a consistent fluid-structure coupling scheme along with a novel multi-resolution scheme incorporating a common influence length, a modified SPH density definition and a SPH-based formulated SPP (Space Potential Particle) scheme in order to achieve consistent particle-based discretizations, precise satisfaction of fluid-structure interface boundary conditions and accurate volume conservation at the interface. The present ISPH fluid model corresponds to a refined version of ISPH incorporating several previously developed refined schemes, and hence the proposed FSI solver is referred to as “Enhanced Multi-resolution ISPH-SPH”. Validations are performed qualitatively/quantitatively through reproductions of classical as well as ocean engineering benchmark tests. Comparisons are also made with an MPS-based FSI solver as well as an Explicit ISPH-based one. A preliminary extension of the proposed solver to three-dimensions is also presented.

Extended variable-time-step Adams–Bashforth–Moulton method for strongly coupled fluid–structure interaction simulation

An extended variable-time-step Adams–Bashforth–Moulton (ABM) method is presented for obtaining the solution of six-degrees-of-freedom (6DoF) rigid body motion. This second-order method involves the use of one predictor and several correctors, thus requiring an iteration process during each time step. Aitken’s dynamic under-relaxation (ADUR) scheme is used to reduce the time to convergence. The initial value of the under-relaxation factor at each time step is evaluated from the values of the two previous time steps, the predictor, and the first corrector. Cooperating with the incompressible two-phase flow solver included in OpenFOAM®, the present method is capable of simulating fluid–structure interaction (FSI) problems, in which strong coupling is ensured through the outer loop of the PIMPLE algorithm. Various interface capture schemes as well as mesh motion schemes are considered. Several two- and three-dimensional cases of multi-DoF are simulated, and the recommended iteration stop condition is summarised. Finally, the method is employed to reproduce an experiment that investigates the interaction between a dam-break flow and a floating box. Satisfactory overall agreement between the numerical and experimental results is observed, which demonstrates that the method is suitable for simulating FSI problems in ocean engineering.

A 3D isogeometric FE-IBE coupling method for acoustic-structural interaction problems with complex coupling models

In this paper, Finite Element-Indirect Boundary Element (FE-IBE) coupling approach based on the Isogeometric Analysis (IGA) framework is proposed to deal with Acoustic-Structural Interaction (ASI) problems. Numerical simulation of thin-walled structures is carried out by using isogeometric Reissner-Mindlin shell theory. The isogeometric indirect boundary element method (IBEM) is used to simulate the fluid domain, and the coupling formula is established by connecting the primary variables. IBEM contains information on both sides of the boundary. Naturally, FE-IBE coupling method inherits these attractive features. FE-IBE coupling method has a wide application prospect. In general, it can not only deal with the common problems, but also solve the problems that Finite Element-Direct Boundary Element (FE-DBE) coupling method cannot handle, such as the opened boundary problems, whose inner and outer boundaries contact the liquid. In order to further expand its application range, based on the universality of the primary variables in IBEM, a more generalized coupling formula is derived to solve the hybrid problems with both the closed and opened boundaries. Numerical examples with analytical solution verify the reliability and stability of the proposed IGA FE-IBE coupling method, and two complex problems in aerospace engineering and ocean engineering are studied in detail.