Model REEF3D Research Articles

Wave environment analysis at Norwegian harbours for land-based aquaculture facilities using a combined phase-averaging and phase-resolving numerical modelling approach

Numerical wave modelling of Norwegian coastal areas is challenging due to the drastically varying bathymetry, irregular coastline, and large domains of interest. The widely used phase-averaging models are limited by such bathymetric and topographic conditions. Phase-resolving models provide higher accuracy regarding strong nonlinear wave transformations with the trade-off of a higher computational cost. This study provides a combined phase-averaging and phase-resolving modelling approach to analyse the wave conditions for on-shore aquaculture facilities at the site candidates Fiskenes and Breivik, Andøya, Norway. The phase-averaging spectral model SWAN is used for the offshore sea state analysis based on the offshore hind-cast data. The analysis is performed on cascade nested grids, with increasing accuracy closer to the proposed harbour locations. A novel interpolation algorithm is proposed to provide comprehensive sea state information with every offshore wave directions without requiring additional simulations. The critical wave conditions are identified from SWAN and used as input to the open-source phase-resolving fully nonlinear potential flow model REEF3D::FNPF. Four scenarios are investigated and densely spaced wave gauges in the entire computational domain provide the distribution of significant wave height. The combined and cascade simulation approach helps to achieve a balance between computational efficiency and accuracy for large-scale marine environment assessment. The results show detailed wave statistics in the entire area of relevance near both harbours and provide a quantitative reference for both the site choice and the harbour design.

CFD modeling of flow and local scour around submerged bridge decks

In this study, the level set method-based, multiphase hydro- and morphodynamic numerical model REEF3D is used for the simulation of the flow conditions and local scouring around submerged bridge decks. Presence of hydraulic jumps, bridge overtopping, pressurized jets and the resulting scouring make the selected test cases especially challenging from the numerical modelling point of view. The models are validated against data from laboratory experiments. The influence of the submergence ratio on the prevailing flow and scouring is investigated. The level set method showed robustness and good accuracy for the treatment of the complex free surface as well as for the tracking of the mobile bed. The submergence ratio showed no clear correlation with the prevailing erosion/deposition patterns. As the simulations offered insights into the prevailing hydrodynamics and thus the relevance of numerical modelling was emphasized for such complex sediment transport problems.

Identification and Investigation of Extreme Events Using an Arbitrary Lagrangian–Eulerian Approach With a Laplace Equation Solver and Coupling to a Navier–Stokes Solver

AbstractIncreased deployment of offshore wind turbines is seen as an important pathway to increase green renewable energy production. Improved and rapid identification of extreme events and evaluation of hydrodynamic loads due to such events is essential to reduce the cost of energy production. Numerical modeling to pre-screen sea states and to identify the crucial events to prioritize model tests will make a major contribution to reduce design times and costs for such structures. In this effort, a highly efficient and nonlinear numerical model based on the Laplace equations is used to generate undisturbed wave kinematics. Such a simulation is used to identify extreme wave events in a sea state realization, and further, the wave loading due to such events are evaluated using Morison formula. Events screened in this manner can then be transferred to a high-resolution model such as a Navier–Stokes equation-based solver to investigate the hydrodynamics in detail. The implementation and application of such an approach in the open-source hydrodynamic model REEF3D is presented in this work.

Numerical Modelling of an Innovative Conical Pile Head Breakwater

When moderate wave activity at the shoreline is acceptable, pile breakwaters can serve as an alternative to conventional breakwaters. Increasing the size of the pile breakwater in the vicinity of the free surface increases the hydraulic efficiency, as most of the wave energy is concentrated around the free surface. Therefore, a conical pile head breakwater (CPHB) is proposed in the present study by gradually widening the diameter of the piles towards the free surface. Using the open-source computational fluid dynamics (CFD) model REEF3D, the transmission, reflection, and dissipation characteristics of the CPHB with monochromatic and irregular waves are examined. The investigation is carried out for both perforated and non-perforated CPHBs using monochromatic waves, and the numerical results are validated using experimental data. Further, optimally configured non-perforated and perforated CPHBs are investigated numerically by subjecting them to irregular waves using the Scott–Wiegel spectrum. The wave attenuation characteristics of the CPHBs are found to be better with irregular waves compared to monochromatic waves. With irregular waves, the minimum transmission coefficients for non-perforated and perforated CPHBs are 0.36 and 0.34, respectively. Overall, the CPHB appears to be a potential solution for coastal protection.

Verification of a Free-Surface Pressure Term Extension to Represent Ships in a Nonhydrostatic Shallow-Water-Equations Solver

Abstract In recent years, increasing ship sizes and associated increasing wave loads have led to a demand for prediction tools quantifying the ship-induced loads on waterways. Depth-averaged numerical models, using a free-surface pressure term, are a prominent method to obtain the relevant design parameters. These models incorporate the wave deformation processes due to attributes of complex bathymetries, while allowing for an efficient simulation of large computational domains. The nonhydrostatic shallow-water-equations (SWE) model REEF3D::SFLOW uses a quadratic pressure approximation and high-order discretization schemes. This paper presents the implementation of a pressure term to account for the displacement of the free surface by solid moving objects. Two test cases verifying the implementation are shown based upon the analytical one-dimensional solution of the wave propagation due to surface pressure and the estimation of Havelock angles. These verification tests are the first step toward a holistic model, combining a large scale model with computational fluid dynamics (CFD) simulations near waterway banks.

Efficient Calculation of Hydrodynamic Loads on Offshore Wind Substructures Including Slamming Forces

Abstract Estimation of the hydrodynamic loads based on strip theory using the Morrison equation provides an inexpensive method for load estimation for the offshore industry. The advantage of this approach is that it requires only the undisturbed wave kinematics along with inertia and viscous force coefficients. Over the recent years, the development in numerical wave tank simulations makes it possible to simulate nonlinear 3-h sea states, with computational times in the order of real time. This presents the possibility to calculate loads using wave spectrum input in numerical simulations with reasonable computational time and effort. In the current paper, the open-source fully nonlinear potential flow model REEF3D::FNPF is employed for calculating the nonlinear wave kinematics. Here, the Laplace equation for the velocity potential is solved on a σ-coordinate mesh with the nonlinear free surface boundary conditions to close the system. A technique to calculate the total acceleration on the σ-coordinate grid is introduced which makes it possible to apply strip theory in a moving grid framework. With the combination of strip theory and 3-h wave simulations, a unique possibility to estimate the hydrodynamic loads in real time for all discrete positions in space within the domain of the numerical wave tank is presented in this paper. The numerical results for inline forces on an offshore wind mono-pile substructure are compared with measurements, and the new approach shows good agreement.

Numerical Investigation on Wave-Overtopping at a Double-Dike Defence Structure in Response to Climate Change-Induced Sea Level Rise

Climate change has tremendous economic and environmental impacts on coastal areas and threatens human lives and livelihoods in generally densely populated coastal communities. Climate change-induced sea level rise (SLR) is a particular risk factor for coastal and low-lying areas. Therefore, the study on the overtopping of coastal structures in a changing climate is a critical topic for coastal protection and adaptation. As most coastal areas have shallow water conditions, the open-source nonhydrostatic shallow water equation-based model REEF3D::SFLOW is applied for the numerical investigation of overtopping over a coastal structure. Validation is performed by comparing the numerical estimations with the existing experiment presented by previous studies. The time evolution of overtopping can be predicted well by the numerical model in comparison to the experimental data. The computational speed is seen to be approximately 1500 times as fast as the Navier–Stokes equation-based counterparts. Thereafter, a comprehensive study on overtopping that takes into account different climate scenarios is presented with regard to the chosen coastal structure; this offers insights for future adaptations. The numerical approach provides an efficient alternative for the coastal protection structure adaptations in the changing climate.

Numerical investigation of wave impact forces on coastal deck structures with girders along the West Coast of India in changing climate

ABSTRACT Coastal structural damage has been a serious issue in the past decades due to changes in various ocean environmental parameters and increased frequency of extreme events. The present study focuses on the estimation of wave impact forces on typical deck structures at Indian port locations in a changing climate scenario. The effect of climate change has been investigated by applying the future ocean climate characteristics, such as future wave height conditions and sea-level rise by the year 2100 using RCP 4.5 scenario obtained from the recent studies. The numerical investigations were carried out by generating solitary waves in a numerical wave tank modelled using an open-source CFD model REEF3D. Comparison of peak wave impact force and pressure distribution due to climate change on a model and prototype deck structure in the elevated condition is carried out to investigate the scale effects. Overall, the study concluded that there is a significant change in both vertical and horizontal forces on coastal deck structures due to climate change, where the percentage change varies with varying airgaps and geographical locations. Investigation on prototype scale deck shows that the model scale overestimates the positive horizontal impact force to a larger extent than the vertical impact force.

Numerical Investigation of Breaking Focused Waves and Forces on Coastal Deck Structure with Girders

In the present study, breaking focused wave groups were simulated using open-source Computational Fluid Dynamics model REEF3D in order to investigate the breaking wave impact on scaled (1:10) two-dimensional coastal deck structure with girder. The effect of environmental parameters, such as bottom slope and wave steepness on the breaking and geometric properties of high-crested spilling breakers, was investigated. The effect of the wave breaking location on the impact forces acting on the deck structure located at different airgap positions was studied for three wave impact scenarios: (i) when the wave breaking starts, (ii) when a slightly overturning crest is formed, and (iii) when the wave breaks and a fully overturning crest is formed just before hitting the preceding trough. The peak horizontal impact force was found to be higher when the wave breaks ahead of the structure and the overturning wave crest hits the deck positioned above the still water level. Additionally, the peak vertical impact force attains the peak when the deck is placed at the still water level for different stages of breaking. The peak horizontal impact force shows a parabolic trend, whereas the peak vertical impact forces show a decreasing linear trend with an increase in airgap. Finally, force coefficients are derived for calculating the peak impact force on deck with girders subjected to high-crested spilling breakers.

Hydrodynamic Coupling of Viscous and Nonviscous Numerical Wave Solutions Within the Open-Source Hydrodynamics Framework reef3d

Abstract A comprehensive understanding of the marine environment in the offshore area requires phase-resolved wave information. For far-field wave propagation, computational efficiency is crucial, as large spatial and temporal scales are involved. For the near-field extreme wave events and wave impacts, high resolution is required to resolve the flow details and turbulence. The combined use of a computationally efficient large-scale model and a high-resolution local-scale solver provides a solution that combines accuracy and efficiency. This article introduces a coupling strategy between the efficient fully nonlinear potential flow (FNPF) solver REEF3D::FNPF and the high-fidelity computational fluid dynamics (CFD) model REEF3D::CFD within the open-source hydrodynamics framework REEF3D. REEF3D::FNPF solves the Laplace equation together with the boundary conditions on a sigma-coordinate. The free surface boundary conditions are discretized using high-order finite difference methods. The Laplace equation for the velocity potential is solved with a conjugated gradient solver preconditioned with a geometric multigrid provided by the open-source library Hypre. The model is fully parallelized following the domain decomposition strategy and the message passing interface protocol. The waves calculated with the FNPF solver are used as wave generation boundary conditions for the CFD-based numerical wave tank REEF3D::CFD. The CFD model employs an interface capturing two-phase flow approach that can resolve complex wave structure interaction, including breaking wave kinematics and turbulent effects. The presented hydrodynamic coupling strategy is tested for various wave conditions and the accuracy is fully assessed.

Representation of 3-h Offshore Short-Crested Wave Field in the Fully Nonlinear Potential Flow Model REEF3D::FNPF

Abstract Stochastic wave properties are crucial for the design of offshore structures. Short-crested seas are commonly seen at the sites of offshore structures, especially during storm events. A long time duration is required in order to obtain the statistical properties, which is challenging for numerical simulations. In this scenario, a potential flow solver is ideal due to its computational efficiency. A procedure of reproducing accurate short-crested sea states using the open-source fully nonlinear potential flow model REEF3D::FNPF is presented in the paper. The procedure examines the sensitivity of the resolutions in space and time as well as the arrangements of wave gauge arrays. A narrow band power spectrum and a mildly spreading directional spreading function are simulated, and an equal energy method is used to generate input waves and avoid phase-locking. REEF3D::FNPF solves the Laplace equation together with the boundary conditions using a finite difference method. A sigma grid is used in the vertical direction and the vertical grid clustering follows the principle of constant truncation error. High-order discretization methods are implemented in space and time. Message passing interface is used for high performance computation using multiple processors. Three-hour simulations are performed in full-scale at a hypothetic offshore site with constant water depth. The significant wave height, peak period, kurtosis, skewness and ergodicity are examined in the numerically generated wave field. The stochastic wave properties in the numerical wave tank (NWT) using REEF3D::FNPF match the input wave conditions with high fidelity.

Reduction of the wave propagation error of a sigma grid based numerical tank using a vertical spacing based on the constant truncation error

Numerical wave models that solve the Laplace equation for the velocity potential with a σ-grid in the vertical direction have been proven to be flexible and efficient. However, it is observed that the dispersion relation is sensitive to the variation of the vertical σ-grid arrangements. So far, there is no recommended practice to optimise the vertical σ-grid for a correct representation of the dispersion relation. In order to reduce the uncertainty of the dispersion relation and optimise the choice of the vertical grid distribution, a new method based on the constant truncation error of the finite difference scheme is presented in this article. The optimised vertical grids estimated by the novel method are applied in the fully nonlinear potential flow model REEF3D::FNPF to provide simulated wave surface elevations, which are compared with the measured time series in the long wave flume at SINTEF Ocean, Trondheim. Several different wave scenarios are considered, including regular waves, bichromatic waves, trichromatic waves as well as irregular waves. The wavemaker motions in the physical flume are used to generate waves in the numerical wave tank of REEF3D::FNPF. The proposed truncation error method is seen to effectively mitigate the dispersion (phase) error in all scenarios and the simulations show high accuracy in comparison with the experimental data.

Numerical investigation of extreme wave impact on coastal bridge deck using focused waves

Horizontal and vertical impact forces on a coastal bridge deck with girders due to asymmetric and nonlinear wave loads induced by the action of focused wave groups have been investigated using open-source CFD model REEF3D. An extensive parametric study was conducted to investigate the variation of horizontal and vertical impact forces induced on bridge deck by steep focused waves. Results indicate that with increasing wave heights, while the horizontal positive force increases, the peak vertical uplift and downward forces decrease. Longer wave periods impart higher peak vertical uplift forces and horizontal positive forces. The bridge deck location at still water level, submerged and partially submerged cases are considered for the numerical study and the results are compared with the design formulae of American Association of State Highway and Transportation Officials (AASHTO). For both submerged and partially submerged scenarios, AASHTO formulae were found to highly overestimate the peak horizontal impact forces for lower wave heights and they were found to give better results for higher wave heights. In case of peak vertical impact forces, AASHTO formulae highly underestimate for lower wave heights and moderately capture the peak vertical impact force at higher wave heights and airgaps.

3D numerical modelling of scour around a jacket structure with dynamic free surface capturing

This paper presents a numerical investigation of local scour with dynamic free surface capturing around a jacket structure. The hydrodynamics and resulting scour are calculated using the open-source CFD model REEF3D. The model solves the Reynolds-averaged Navier–Stokes equations with k−ω turbulence closure. The free surface is captured with the level set method. The simulated flow hydrodynamics are coupled with sediment transport algorithms. The modelling of the local scouring process is based on the bed load and the suspended load while accounting for the bed slope for the calculation of the critical bed shear stress. In order to obtain a more realistic prediction of the scour hole, a sand-slide algorithm is implemented to correct the bed slope when it exceeds the angle of repose. The grid and time step size convergence tests are performed to ensure the quality of the simulated hydrodynamics in the numerical wave tank (NWT). The model is validated for local scour around a pile in an experimental flume using different values of Keulegan–Carpenter number (KC). The results show a good agreement with the experimental data. The validated model is applied to simulate scour around a jacket structure. The key findings from the study are the modelling of flow hydrodynamics and the time development of local scour around a jacket exposed to waves and steady current.

A practical framework to assess the hydrodynamic impact of ship waves on river banks

AbstractThe temporal alteration of the hydrodynamic regime in rivers due to navigation has significant effects on riverine ecosystems. Most of the key mechanisms and interactions between hydrodynamic and ecological variables have already been revealed; however, the quantitative evaluation of biotic and abiotic variables still stands a challenge. This paper aims to present a thorough, spatiotemporal framework, involving field and computational tools, for the assessment of wave hydrodynamics in the littoral zone of rivers, where its ecological relevance is the most significant. The temporal variation of significant wave heights is derived from high‐frequency pressure measurements, offering a well‐comparable statistical evaluation of individual wave events considering the duration of different wave intensities. Acoustic Doppler velocimetry (ADV) is used for the assessment of near‐bank velocities, from which the secondary wave‐related components have been filtered offering relevant validation data for numerical modelling. The small footprint of the ADVs is extended with up‐to‐date computational fluid dynamics modelling. Wave spectra derived from the pressure measurements are used as boundary conditions for phase‐resolved irregular wave modelling with the level set method based numerical model REEF3D. The properly validated model offers the assessment of the most relevant hydrodynamic variables (e.g., velocity or turbulent kinetic energy) in a spatially extended manner, from which the hydrodynamic footprint of the wave events can be interpreted in a statistical fashion. The implementation of the proposed framework is illustrated through a case study at a Hungarian section of the Danube River.

Modeling and Simulation of Moored-Floating Structures Using the Tension Element Method

The derivation of a discrete mooring model for floating structures is presented in this paper. The method predicts the steady-state solution for the shape of an elastic cable and the tension forces under consideration of static loads. It is based on a discretization of the cable in mass points connected with straight but elastic bars. The successive approximation is applied to the resulting system of equations which leads to a significant reduction of the matrix size in comparison to the matrix of a Newton–Raphson method. The mooring model is implemented in the open-source computational fluid dynamics (CFD) model REEF3D. The solver has been used to study various problems in the field of wave hydrodynamics and fluid–structure interaction. It includes floating structures through a level set function and captures its motion using Newton and Euler equations in six degrees-of-freedom (6DOF). The fluid–structure interaction is solved explicitly using an immersed boundary method based on the ghost cell method. The applications show the accuracy of the solver and the effects of mooring on the motion of floating structures.

Breaking Wave Interaction With a Group of Four Vertical Slender Cylinders in Two Square Arrangements

The main purpose of the study is to investigate the breaking wave interaction with a group of four circular cylinders. The physical process of wave breaking involves many parameters, and an accurate numerical modeling of breaking waves and the interaction with a structure remain a challenge. In the present study, the open-source computational fluid dynamics (CFD) model REEF3D is used to simulate the breaking wave interaction with multiple cylinders. The numerical model is based on the incompressible Reynolds-averaged Navier–Stokes (RANS) equations, the level set method for the free surface, and the k–ω model for turbulence. The numerical model is validated with experimental data of large-scale experiments for the free surface elevation and the breaking wave force on a single cylinder. A good agreement is obtained between the numerical results and experimental data. Two different configurations with four cylinders are examined: in-line square configuration and diamond square configuration. For both configurations, three different tank widths and four different spacings between the cylinders are investigated. The breaking wave forces on each cylinder in the group are computed for each case for the two configurations, and the results are compared with the breaking wave force on a single isolated cylinder. Furthermore, the study investigates the water surface elevations and the free surface flow features around the cylinders. For the closely spaced cylinders in a relatively narrower tank, the cylinders in both configurations experience the maximum forces lower than the maximum force on a single cylinder. But for the widely spaced cylinder in a relatively wider tank, the forces are higher and lower for the upstream cylinders and downstream cylinders, respectively, than the maximum force on a single isolated cylinder. The results of the present study show that the interference effects from the neighboring cylinders in a group strongly influence the kinematics around and the breaking wave forces on them.

Effect of Girder Spacing and Depth on the Solitary Wave Impact on Coastal Bridge Deck for Different Airgaps

Coastal bridge damage has become a severe issue of concern in the recent past with the destruction of a considerable number of bridges under the impact of waves during tsunami and storm surges. These events have become more frequent, with waves reaching the bridge deck and causing upliftment and destruction. Past studies have demonstrated the establishment of various theoretical equations which works well for the submerged deck and regular wave types but show much scatter and uncertainty in case of a deck that is above still water level (SWL). The present study aims to generate a solitary wave to represent an extreme wave condition like a tsunami in the numerical wave tank modeled using the open source computational fluid dynamics (CFD) model REEF3D and to study the vertical impact force on the coastal bridge deck. A parametric study is carried out for increasing wave heights, girders spacing and depth for varying airgaps to analyze the effect of these parameters on the peak vertical impact force. It is observed that increasing the girder spacing and girder depth is effective in reducing the peak vertical impact force for the cases considered.

Numerical modelling of pipeline scour under the combined action of waves and current with free-surface capturing

Understanding the pipeline scour processes under the combined action of waves and current is essential for adequate scour protection measures. This paper presents the numerical modelling of pipeline scour under the co-directional combined action of waves and current including the prediction of the unsteady free surface. The numerical modelling is performed with the open-source CFD model REEF3D. The model solves the Reynolds-Averaged Navier-Stokes (RANS) equations together with the k−ω turbulence model and a sediment transport algorithm. In order to ensure the accuracy of the flow field, the model is thoroughly validated for the hydrodynamics of co-directional combined waves and current. Results for the velocity profiles show a good agreement with the experimental observations. The model is then applied to simulate the different case scenarios of the scour under waves alone, current alone, and combined waves and current. The numerical results for scour below the pipeline show good agreement with the experimental data which confirms the applicability of the model to study pipeline scour under the combined action of waves and current. A series of simulations are run for different values of the non-dimensional parameter for the combined waves and current Ucm varying between 0 and 1.0 for the given KC number. The results demonstrate the correlation between values of Ucm and (1) the flow field below the pipeline, (2) the scour depth, and (3) the temporal variation of the scouring process. The findings highlight the variation of the maximum scour depth below the pipeline with Ucm.

Numerical Modeling of Breaking Wave Kinematics and Wave Impact Pressures on a Vertical Slender Cylinder

Wave loads from breaking waves on offshore wind turbine (OWT) substructures in shallow waters still remain uncertain. The interaction of breaking waves with structures is characterized by complex free surface deformations, instantaneous impact of the water mass against the structure, and consequently large wave forces on the structures. The main objective of the paper is to investigate wave impact pressures and kinematics during the interaction of breaking waves with a vertical cylinder using the open-source computational fluid dynamics (CFD) model REEF3D. The model is based on the Reynolds-averaged Navier–Stokes (RANS) equations coupled with the level set method and k–ω turbulence model. Three wave impact conditions are considered in this study. The numerically simulated free surface deformations around the cylinder during the breaking wave interaction are also presented for different wave impact conditions. For three wave impact conditions, the wave impact pressure and the horizontal and vertical components of the particle velocity are computed in front of the cylinder and analyzed. The pressure and velocity profile at their maximum values are also examined and discussed. In addition, the total force is calculated for three breaking conditions and they are correlated with the pressure and kinematics during the interaction.