The state-of-the-art formulas for mean wave overtopping (q) assessment typically require wave conditions at the toe of the structure as input. However, for structures built either on land or in very shallow water, obtaining accurate estimates of wave height and period at the structure toe often proves difficult and requires the use of either physical modeling or high-resolution numerical wave models. Here, we follow Goda's method to establish an accurate prediction methodology for both vertical and sloping structures based entirely on deep-water characteristics—where the influence of the foreshore is captured by directly incorporating the foreshore slope and the relative water depth at the structure toe (htoe/Hm0,deep). Findings show that q decreases exponentially with htoe/Hm0,deep due to the decrease of the incident wave energy; however, the rate of reduction in q decreases for structures built on land or in extremely shallow water (htoe/Hm0,deep = 0.1) due to the increased influence of wave-induced setup and infragravity waves—which act as long-period fluctuations in mean water level—generated by nonlinear wave transformation over the foreshore., This work is part of the Perspectief research program All-Risk with Project No. B2 which is (partly) financed by NWO Domain Applied and Engineering Sciences, in collaboration with the following private and public partners: the Dutch Ministry of Infrastructure and Water Management (RWS); Deltares; STOWA; the regional water authority, Noorderzijlvest; the regional water authority, Vechtstromen; It Fryske Gea; HKV consultants; Natuurmonumenten; and waterboard HHNK. Dr. Corrado Altomare acknowledges funding from the European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie, Grant No. 792370, Peer Reviewed, Postprint (published version)

Due to ongoing climate change, overtopping risk is increasing. In order to have effective countermeasures, it is useful to understand overtopping processes in details. In this study overtopping flow on a dike with gentle and shallow foreshores are investigated using a non-hydrostatic wave-flow model, SWASH (an acronym of Simulating WAves till SHore). The SWASH model in 2DV (i.e., flume like configuration) is first validated using the data of long crested wave cases with second order wave generation in the physical model test conducted. After that it is used to produce overtopping flow in different wave conditions and bathymetries. The results indicated that the overtopping risk is better characterized by the time dependent h (overtopping flow depth) and u (overtopping flow velocity) instead of hmax (maximum overtopping flow depth) and umax (maximum overtopping flow velocity), which led to overestimation of the risk. The time dependent u and h are strongly influenced by the dike configuration, namely by the promenade width and the existence of a vertical wall on the promenade: the simulation shows that the vertical wall induces seaward velocity on the dike which might be an extra risk during extreme events., This research was part of the CREST (Climate REsilient CoaST) project (http://www.crestproject.be/en), funded by the Flemish Agency for Innovation by Science and Technology, grant number 150028. Corrado Altomare acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No.: 792370., Peer Reviewed, Postprint (published version)

Treball elaborat dins el programa Horizon 2020, amb l'ajut Marie Skłodowska-Curie Individual Fellowship, The main scientific objective of DURCWAVE project is to define new design criteria for wave action by modelling wave overtopping and post-overtopping processes of these urban defences., Award-winning, Postprint (published version)

The data refer to an experimental campaign carried out to characterize the forces involved in the failure of the Pont del Petroli (Badalona, Catalonia) due to the storm Gloria happened in the night of the 20 January 2020. The experiments were carried out in the CIEM (Canal d’Investigació i Experimentació Marítima) wave flume in the Laboratory of Maritime Engineering of the UPC (Universitat Politecnica de Catalunya - BarcelonaTech, Barcelona, Catalonia)., Data include measurements of water surface elevation along the wave flume and wave loading (forces + pressures) on elements of the pier. Both raw and post-processed data are provided., 1

In this work the numerical model DualSPHysics has been applied to study the complex phenomenon of wave overtopping characterising dike-promenade coastal defence layout. The model has been first validated, by comparing the results versus laboratory data obtained during a project campaign at the Maritime Engineering Laboratory of Universitat Politècnica de Catalunya – BarcelonaTech (LIM/UPC). The experimental campaign aimed to describe flow characteristics for the current dike and beach layout. Numerical modelling was employed to extend the experimental database beyond the range of tested conditions. In this work, a new Density Diffusion Scheme and the new modified Dynamic Boundary Conditions are applied to model wave-structure interaction. A real sea state was simulated, corresponding to a train of random waves having a duration equal to 1000 waves (= 1300s in real time). Cumulative overtopping volumes and mean discharges are calculated and compared with the experimental ones, showing a very good agreement and accuracy in not showing before in previous studies on wave overtopping with SPH-based solvers. One test case has been employed for further analysis. The model applicability and impact has been focused on reducing discharge under tolerable values by modifying the structural and beach layout. One solution corresponds to hard countermeasures to reduce overtopping discharge, employing a storm wall located on the dike crest. The other one is representative of soft countermeasures, namely beach nourishment, where the beach profile has been changed to shallower conditions to provoke more intense wave breaking and dissipate the incoming wave energy. Both alternatives guarantee tolerable discharges for coastal safety., This research was funded by European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No.: 792370., Postprint (published version)

The work highlights the importance of directional spreading effects on wave overtopping estimation in shallow and mild sloping foreshores. Wave short-crestedness leads, in general, to a reduction of mean overtopping discharges on coastal structures. In the present work, the case of a sea dike with gentle foreshore in very and extremely shallow water conditions is analysed. Physical model tests have been carried out in order to investigate the effect of directional spreading on overtopping and incident wave characteristics. In the present experimental campaign, the effect of wave spreading has only been investigated for perpendicular wave attack. Results show that directional spreading is proved to cause a reduction of average discharge of sea dikes with gentle and shallow foreshore. Expressions for the reduction factor for directional spreading are derived, fitted on the tested database. The use of this reduction factor leads to more accurate prediction and avoids overtopping overestimation, however reduction-factor formulations are overtopping-formula depending., Peer Reviewed, Postprint (author's final draft)

The present work employs the so-called Evolutionary Polynomial Regression (EPR) algorithm to build up a formula for the assessment of mean wave overtopping discharge for smooth sea dikes and vertical walls. EPR is a data-mining tool that combines and integrates numerical regression and genetic programming. This technique is here employed to dig into the relationship between the mean discharge and main hydraulic and structural parameters that characterize the problem under study. The parameters are chosen based on the existing and most used semi-empirical formulas for wave overtopping assessment. Besides the structural freeboard or local wave height, the unified models highlight the importance of local water depth and wave period in combination with foreshore slope and dike slope on the overtopping phenomena, which are combined in a unique parameter that is defined either as equivalent or imaginary slope. The obtained models aim to represent a trade-off between accuracy and parsimony. The final formula is simple but can be employed for a preliminary assessment of overtopping rates, covering the full range of dike slopes, from mild to vertical walls, and of water depths from the shoreline to deep water, including structures with emergent toes., This research was funded by European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No.: 792370., Peer Reviewed, Postprint (published version)

In January 2020, the footbridge connecting the seaward platform of the Pont del Petroli pier to Badalona beach collapsed due to the severe sea storm named Gloria. Approximately 15 m of the footbridge fell into the sea as a result of prolonged wave action and strong impacts. To understand the complex interaction between waves and structures that led to the pier’s collapse during the storm, a composite modelling approach was developed. The loads on each pier element were initially evaluated using the meshless DualSPHysics code, which employs the Smoothed Particle Hydrodynamics (SPH) method. This evaluation was conducted under severe wave conditions analogous to those experienced during the storm. Numerical models informed the design of an experimental campaign carried out at the Maritime Engineering Laboratory of Universitat Politècnica de Catalunya—BarcelonaTech, using the CIEM large-scale wave flume facility in Barcelona, Spain. Post-storm bathymetric surveys revealed significant alterations in the seabed profile near the affected infrastructure, including sediment deposition and a reduction in water depth from 10 m to 8 m. Consequently, it was anticipated that wave transformation and breaking in the vicinity of the structure would be substantially affected. To explore this phenomenon, various extreme wave impacts were experimentally simulated using focused wave groups. The physical model findings unveiled the forces that the pier endured during the storm Gloria. The results indicate that wave phases influence individual waves, with waves that are biased and asymmetric experiencing higher peaks than those focused on the crest. This insight helps to explain the structural failure of the footbridge during the storm and underscores the importance of considering wave phase impacts in the design and assessment of coastal infrastructure. The combined numerical and experimental approach provides a comprehensive understanding of the forces at play, contributing valuable knowledge to the field of coastal engineering and infrastructure resilience., The author(s) declare that financial support was received for the research, authorship, and/or publication of this article. The experimental campaign was partially funded by European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No: 792370. CA acknowledges funding from the Spanish government and the European Social Found (ESF) under the programme “Ramón y Cajal 2020” (RYC 2020-030197-I/AEI/10.13039/501100011033) and within the project GLORIA PID 2020-115030RJ-I00 “Adquirir conocimientos sobre el riesgo de rebase para las zonas costeras urbanizadas” (MCIN/AEI/10.13039/501100011033)., Peer Reviewed, Postprint (published version)

The final publication is available at Springer via http://dx.doi.org/10.1007/s40571-021-00404-2, DualSPHysics is a weakly compressible smoothed particle hydrodynamics (SPH) Navier–Stokes solver initially conceived to deal with coastal engineering problems, especially those related to wave impact with coastal structures. Since the first release back in 2011, DualSPHysics has shown to be robust and accurate for simulating extreme wave events along with a continuous improvement in efficiency thanks to the exploitation of hardware such as graphics processing units for scientific computing or the coupling with wave propagating models such as SWASH and OceanWave3D. Numerous additional functionalities have also been included in the DualSPHysics package over the last few years which allow the simulation of fluid-driven objects. The use of the discrete element method has allowed the solver to simulate the interaction among different bodies (sliding rocks, for example), which provides a unique tool to analyse debris flows. In addition, the recent coupling with other solvers like Project Chrono or MoorDyn has been a milestone in the development of the solver. Project Chrono allows the simulation of articulated structures with joints, hinges, sliders and springs and MoorDyn allows simulating moored structures. Both functionalities make DualSPHysics especially suited for the simulation of offshore energy harvesting devices. Lately, the present state of maturity of the solver goes beyond single-phase simulations, allowing multi-phase simulations with gas–liquid and a combination of Newtonian and non-Newtonian models expanding further the capabilities and range of applications for the DualSPHysics solver. These advances and functionalities make DualSPHysics an advanced meshless solver with emphasis on free-surface flow modelling., This work was partially financed by the Ministry of Economy and Competitiveness of the Government of Spain under project “WELCOME ENE2016-75074-C2-1-R” and financed by Xunta de Galicia (Spain) under project ED431C 2017/64 ″Programa de Consolidación e Estructuración de Unidades de Investigación Competitivas (Grupos de Referencia Competitiva)" co-funded by European Regional Development Fund (ERDF). We are grateful for funding from the European Union Horizon 2020 programme under the ENERXICO Project, Grant Agreement No. 828947 and the Mexican CONACYT- SENER Hidrocarburos Grant Agreement No. B-S-69926. Dr. J. M. Domínguez acknowledges funding from Spanish government under the program “Juan de la Cierva-incorporación 2017” (IJCI-2017-32592). Dr. C. Altomare acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No.: 792370., Peer Reviewed, Postprint (author's final draft)

Physical model experiments were conducted in a wave tank at Flanders Hydraulics Research, Antwerp, Belgium, to characterize the wave overtopping and impact force on vertical quay walls and sloping sea dike (1:2.5) under very oblique wave attack (angle between 45° and 80°). This study was triggered by the scarce scientific literature on the overtopping and force reduction due to very oblique waves since large reduction is expected for both when compared with the perpendicular wave attack. The study aimed to compare the results from the experimental tests with formulas derived from previous experiments and applicable to a Belgian harbor generic case. The influence of storm return walls and crest berm width on top of the dikes has been analyzed in combination with the wave obliqueness. The results indicate significant reduction of the overtopping due to very oblique waves and new reduction coefficients were proposed. When compared with formulas from previous studies the proposed coefficients indicate the best fit for the overtopping reduction. Position of the storm return wall respect to the quay edge rather than its height was found to be more important for preventing wave induced overtopping. The force reduction is up to approximately 50% for the oblique waves with respect to the perpendicular wave impact and reduction coefficients were proposed for two different configurations a sea dike and vertical quay wall, respectively., This research was funded by Agentschap voor Maritieme Dienstverlening en Kust (MDK)—Coastal Division, project WL2012_00_050. Corrado Altomare acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No.:792370., Peer Reviewed, Postprint (published version)

Smoothed Particle Hydrodynamics (SPH) method is used here to simulate a heaving point-absorber with a Power Take-Off system (PTO). The SPH-based code DualSPHysics is first validated with experimental data of regular waves interacting with the point-absorber. Comparison between the numerical and experimental heave displacement and velocity of the device show a good agreement for a given regular wave condition and different configurations of the PTO system. The validated numerical tool is then employed to investigate the efficiency of the proposed system. The efficiency, which is defined here as the ratio between the power absorbed by the point-absorber and its theoretical maximum, is obtained for different wave conditions and several arrangements of the PTO. Finally, the effects of highly energetic sea states on the buoy are examined through alternative configurations of the initial system. A survivability study is performed by computing the horizontal and vertical forces exerted by focused waves on the wave energy converter (WEC). The yield criterion is used to determine that submerging the heaving buoy at a certain depth is the most effective strategy to reduce the loads acting on the WEC and its structure, while keeping the WEC floating at still water level is the worst-case scenario., Agencia Estatal de Investigación | Ref. ENE2016-75074-C2-1-R, Agencia Estatal de Investigación | Ref. IJCI-2017-32592, Xunta de Galicia | Ref. ED431C 2017/64

In this work the Weakly Compressible SPH-based (WCSPH) model DualSPHysics has been validated and applied to study the random wave overtopping of dike-promenade layout in shallow water conditions. Data from physical model tests carried out in a small-scale wave flume have been used for model validation. The results have been compared in terms of water surface elevation, mean discharges and individual overtopping volumes distribution. The selected geometrical layout is representative of the coastal area of Premià de Mar, in Catalonia (Spain). This stretch of the coast presents both railways and a bike path very close to the shore and therefore exposed to possible sea storms. For the first time an SPH-based model has been employed to reproduce long-lasting wave overtopping tests, made of time series of 1000 irregular waves, which are representative of real sea states. The density diffusion scheme and the modified Dynamic Boundary Conditions have been applied in the present simulations. By employing standard setup for SPH modelling of wave-structure interaction problems of a very long duration, stable simulations and accurate results have been attained.

DualSPHysics is a weakly compressible smoothed particle hydrodynamics (SPH) Navier–Stokes solver initially conceived to deal with coastal engineering problems, especially those related to wave impact with coastal structures. Since the first release back in 2011, DualSPHysics has shown to be robust and accurate for simulating extreme wave events along with a continuous improvement in efficiency thanks to the exploitation of hardware such as graphics processing units for scientific computing or the coupling with wave propagating models such as SWASH and OceanWave3D. Numerous additional functionalities have also been included in the DualSPHysics package over the last few years which allow the simulation of fluid-driven objects. The use of the discrete element method has allowed the solver to simulate the interaction among different bodies (sliding rocks, for example), which provides a unique tool to analyse debris flows. In addition, the recent coupling with other solvers like Project Chrono or MoorDyn has been a milestone in the development of the solver. Project Chrono allows the simulation of articulated structures with joints, hinges, sliders and springs and MoorDyn allows simulating moored structures. Both functionalities make DualSPHysics especially suited for the simulation of offshore energy harvesting devices. Lately, the present state of maturity of the solver goes beyond single-phase simulations, allowing multi-phase simulations with gas–liquid and a combination of Newtonian and non-Newtonian models expanding further the capabilities and range of applications for the DualSPHysics solver. These advances and functionalities make DualSPHysics an advanced meshless solver with emphasis on free-surface flow modelling., Ministerio de Economía, Industria y Competitividad | Ref. ENE2016-75074-C2-1-R, Ministerio de Ciencia, Innovación y Universidades | Ref. IJCI-2017-32592, Xunta de Galicia | Ref. ED431C 2017/64

[Abstract:] DualSPHysics is a weakly compressible smoothed particle hydrodynamics (SPH) Navier–Stokes solver initially conceived to deal with coastal engineering problems, especially those related to wave impact with coastal structures. Since the first release back in 2011, DualSPHysics has shown to be robust and accurate for simulating extreme wave events along with a continuous improvement in efficiency thanks to the exploitation of hardware such as graphics processing units for scientific computing or the coupling with wave propagating models such as SWASH and OceanWave3D. Numerous additional functionalities have also been included in the DualSPHysics package over the last few years which allow the simulation of fluid-driven objects. The use of the discrete element method has allowed the solver to simulate the interaction among different bodies (sliding rocks, for example), which provides a unique tool to analyse debris flows. In addition, the recent coupling with other solvers like Project Chrono or MoorDyn has been a milestone in the development of the solver. Project Chrono allows the simulation of articulated structures with joints, hinges, sliders and springs and MoorDyn allows simulating moored structures. Both functionalities make DualSPHysics especially suited for the simulation of offshore energy harvesting devices. Lately, the present state of maturity of the solver goes beyond single-phase simulations, allowing multi-phase simulations with gas–liquid and a combination of Newtonian and non-Newtonian models expanding further the capabilities and range of applications for the DualSPHysics solver. These advances and functionalities make DualSPHysics an advanced meshless solver with emphasis on free-surface flow modelling., This work was partially financed by the Ministry of Economy and Competitiveness of the Government of Spain under project “WELCOME ENE2016-75074-C2-1-R” and financed by Xunta de Galicia (Spain) under project ED431C 2017/64 ″Programa de Consolidación e Estructuración de Unidades de Investigación Competitivas (Grupos de Referencia Competitiva)" co-funded by European Regional Development Fund (ERDF). We are grateful for funding from the European Union Horizon 2020 programme under the ENERXICO Project, Grant Agreement No. 828947 and the Mexican CONACYT- SENER Hidrocarburos Grant Agreement No. B-S-69926. Dr. J. M. Domínguez acknowledges funding from Spanish government under the program “Juan de la Cierva-incorporación 2017” (IJCI-2017-32592). Dr. C. Altomare acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No.: 792370., Xunta de Galicia; ED431C 2017/64, México. CONACYT- SENER Hidrocarburos; B-S-69926

Due to climatic change and the increased usage of coastal areas, there is an increasing risk of dike failures along the coasts worldwide. Wave run-up plays a key role in the planning and design of a coastal structure. Coastal engineers use empirical equations for the determination of wave run-up. These formulae generally include the influence of various hydraulic, geometrical and structural parameters, but neglect the effect of the curvature of coastal dikes on wave run-up and overtopping. The scope of this research is to find the effects of the dike curvature on wave run-up for regular wave attack by employing numerical model studies for various dike-opening angles and comparing it with physical model test results. A numerical simulation is carried out using DualSPHysics, a mesh-less model and OpenFOAM, a mesh-based model. A new influence factor is introduced to determine the influence of curvature along a dike line. For convexly curved dikes (ad = 210° to 270°) under perpendicular wave attack, a higher wave run-up was observed for larger opening angles at the center of curvature whereas for concavely curved dikes (ad = 90° to 150°) under perpendicular wave attack, wave run-up increases at the center of curvature as the opening angle decreases. This research aims to contribute a more precise analysis and understanding the influence of the curvature in a dike line and thus ensuring a higher level of protection in the future development of coastal structures., Peer Reviewed

In January 2020, the footbridge connecting the seaward platform of the Pont del Petroli pier to Badalona beach collapsed due to the severe sea storm named Gloria. Approximately 15 m of the footbridge fell into the sea as a result of prolonged wave action and strong impacts. To understand the complex interaction between waves and structures that led to the pier’s collapse during the storm, a composite modelling approach was developed. The loads on each pier element were initially evaluated using the meshless DualSPHysics code, which employs the Smoothed Particle Hydrodynamics (SPH) method. This evaluation was conducted under severe wave conditions analogous to those experienced during the storm. Numerical models informed the design of an experimental campaign carried out at the Maritime Engineering Laboratory of Universitat Politècnica de Catalunya—BarcelonaTech, using the CIEM large-scale wave flume facility in Barcelona, Spain. Post-storm bathymetric surveys revealed significant alterations in the seabed profile near the affected infrastructure, including sediment deposition and a reduction in water depth from 10 m to 8 m. Consequently, it was anticipated that wave transformation and breaking in the vicinity of the structure would be substantially affected. To explore this phenomenon, various extreme wave impacts were experimentally simulated using focused wave groups. The physical model findings unveiled the forces that the pier endured during the storm Gloria. The results indicate that wave phases influence individual waves, with waves that are biased and asymmetric experiencing higher peaks than those focused on the crest. This insight helps to explain the structural failure of the footbridge during the storm and underscores the importance of considering wave phase impacts in the design and assessment of coastal infrastructure. The combined numerical and experimental approach provides a comprehensive understanding of the forces at play, contributing valuable knowledge to the field of coastal engineering and infrastructure resilience., The author(s) declare that financial support was received for the research, authorship, and/or publication of this article. The experimental campaign was partially funded by European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No: 792370. CA acknowledges funding from the Spanish government and the European Social Found (ESF) under the programme “Ramón y Cajal 2020” (RYC 2020-030197-I/AEI/10.13039/501100011033) and within the project GLORIA PID 2020-115030RJ-I00 “Adquirir conocimientos sobre el riesgo de rebase para las zonas costeras urbanizadas” (MCIN/AEI/10.13039/501100011033)., Peer Reviewed

This document represents a proposal for Eurocodes amendment, with particular focus on wave overtopping assessment and overtopping flow properties on coastal defences in urbanized low-elevation coastal areas., This document represents a proposal for Eurocodes amendment, with particular focus on wave overtopping assessment and overtopping flow properties on coastal defences in urbanized low-elevation coastal areas., This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 792370.

Measurements of the water surface elevation were taken close to the wavemaker, along the sloping foreshore and at the dike toe location by resistance type wave gauges. The overtopping flow properties thickness and velocity were measured by ultra-sonic distance sensors and high-speed cameras. Due to its large storage size, the whole set of data is provided on request., The experimental data refer to physical model tests carried out in 2019 from May to December at the wave flume CIEMito of the Maritime Engineering Laboratory (LIM) of the Universitat Politècnica de Catalunya – BarcelonaTech (UPC). The experiments aimed at characterizing the flow characteristics associated to the maximum individual overtopping volumes, due to specific storm events with different return periods. Specifically, the experiments focused on the measurements of overtopping volumes and discharges, in order to find the relation between these parameters with the corresponding overtopping flow velocities and overtopping flow depth, when the maximum overtopping event occurs on a dike during a sea state. A model geometry comprised of a sloping beach, a sloping dike and promenade was built into the CIEMito flume.

The proposed work aims to prove the capability of the DualSPHysics numerical code to deal with the interaction of slamming waves with a Wave Energy Converter (WEC). In particular, the analysed device is a point-absorber that consists of a cylindrical heaving-buoy equipped with an air damper in order to reproduce the effect of the Power Take-Off (PTO) system. Numerical vertical displacement of the cylinder under regular waves is found to be in good agreement with experimental data for different PTO systems. Different scenarios are considered to compute the loads of focused waves acting on the device with its PTO system set on hold. The yield criterion is used to determine that keeping the WEC fixed at still water level is the worst-case scenario and submerging the heaving buoy deep enough is the best-case scenario., This work was partially financed by the Ministry of Economy and Competitiveness of the Government of Spain under project “WELCOME ENE2016-75074-C2-1-R” and financed by Xunta de Galicia (Spain) under project ED431C 2017/64 ″Programa de Con-solidación e Estructuración de Unidades de Investi-gación Competitivas (Grupos de Referencia Com-petitiva)" cofunded by European Regional Development Fund (FEDER). Fruitful discussion was held during the Course 'Mod-eling free surface flows with DualSPHysics' funded by the University of Salerno, Italy under the project N. 300393CIC19VICCIONE. Dr. C. Altomare acknowledges funding from the Eu-ropean Union’s Horizon 2020 research and innova-tion programme under the Marie Sklodowska-Curie grant agreement No.: 792370., Peer Reviewed

In this work the Weakly Compressible SPH-based (WCSPH) model DualSPHysics has been validated and applied to study the random wave overtopping of dike-promenade layout in shallow water conditions. Data from physical model tests carried out in a small-scale wave flume have been used for model validation. The results have been compared in terms of water surface elevation, mean discharges and individual overtopping volumes distribution. The selected geometrical layout is representative of the coastal area of Premià de Mar, in Catalonia (Spain). This stretch of the coast presents both railways and a bike path very close to the shore and therefore exposed to possible sea storms. For the first time an SPH-based model has been employed to reproduce long-lasting wave overtopping tests, made of time series of 1000 irregular waves, which are representative of real sea states. The density diffusion scheme and the modified Dynamic Boundary Conditions have been applied in the present simulations. By employing standard setup for SPH modelling of wave-structure interaction problems of a very long duration, stable simulations and accurate results have been attained., This research was funded by European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No.: 792370., Peer Reviewed

The present work employs the so-called Evolutionary Polynomial Regression (EPR) algorithm to build up a formula for the assessment of mean wave overtopping discharge for smooth sea dikes and vertical walls. EPR is a data-mining tool that combines and integrates numerical regression and genetic programming. This technique is here employed to dig into the relationship between the mean discharge and main hydraulic and structural parameters that characterize the problem under study. The parameters are chosen based on the existing and most used semi-empirical formulas for wave overtopping assessment. Besides the structural freeboard or local wave height, the unified models highlight the importance of local water depth and wave period in combination with foreshore slope and dike slope on the overtopping phenomena, which are combined in a unique parameter that is defined either as equivalent or imaginary slope. The obtained models aim to represent a trade-off between accuracy and parsimony. The final formula is simple but can be employed for a preliminary assessment of overtopping rates, covering the full range of dike slopes, from mild to vertical walls, and of water depths from the shoreline to deep water, including structures with emergent toes., This research was funded by European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No.: 792370., Peer Reviewed

The data refer to an experimental campaign carried out to characterize the forces involved in the failure of the Pont del Petroli (Badalona, Catalonia) due to the storm Gloria happened in the night of the 20 January 2020. The experiments were carried out in the CIEM (Canal d’Investigació i Experimentació Marítima) wave flume in the Laboratory of Maritime Engineering of the UPC (Universitat Politecnica de Catalunya - BarcelonaTech, Barcelona, Catalonia)., Data include measurements of water surface elevation along the wave flume and wave loading (forces + pressures) on elements of the pier. Both raw and post-processed data are provided.

The final publication is available at Springer via http://dx.doi.org/10.1007/s40571-021-00404-2, DualSPHysics is a weakly compressible smoothed particle hydrodynamics (SPH) Navier–Stokes solver initially conceived to deal with coastal engineering problems, especially those related to wave impact with coastal structures. Since the first release back in 2011, DualSPHysics has shown to be robust and accurate for simulating extreme wave events along with a continuous improvement in efficiency thanks to the exploitation of hardware such as graphics processing units for scientific computing or the coupling with wave propagating models such as SWASH and OceanWave3D. Numerous additional functionalities have also been included in the DualSPHysics package over the last few years which allow the simulation of fluid-driven objects. The use of the discrete element method has allowed the solver to simulate the interaction among different bodies (sliding rocks, for example), which provides a unique tool to analyse debris flows. In addition, the recent coupling with other solvers like Project Chrono or MoorDyn has been a milestone in the development of the solver. Project Chrono allows the simulation of articulated structures with joints, hinges, sliders and springs and MoorDyn allows simulating moored structures. Both functionalities make DualSPHysics especially suited for the simulation of offshore energy harvesting devices. Lately, the present state of maturity of the solver goes beyond single-phase simulations, allowing multi-phase simulations with gas–liquid and a combination of Newtonian and non-Newtonian models expanding further the capabilities and range of applications for the DualSPHysics solver. These advances and functionalities make DualSPHysics an advanced meshless solver with emphasis on free-surface flow modelling., This work was partially financed by the Ministry of Economy and Competitiveness of the Government of Spain under project “WELCOME ENE2016-75074-C2-1-R” and financed by Xunta de Galicia (Spain) under project ED431C 2017/64 ″Programa de Consolidación e Estructuración de Unidades de Investigación Competitivas (Grupos de Referencia Competitiva)" co-funded by European Regional Development Fund (ERDF). We are grateful for funding from the European Union Horizon 2020 programme under the ENERXICO Project, Grant Agreement No. 828947 and the Mexican CONACYT- SENER Hidrocarburos Grant Agreement No. B-S-69926. Dr. J. M. Domínguez acknowledges funding from Spanish government under the program “Juan de la Cierva-incorporación 2017” (IJCI-2017-32592). Dr. C. Altomare acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No.: 792370., Peer Reviewed

This paper presents a brief review of grand challenges of Smoothed Particle Hydrodynamics (SPH) method. As a meshless method, SPH can simulate a large range of applications from astrophysics to free-surface flows, to complex mixing problems in industry and has had notable successes. As a young computational method, the SPH method still requires development to address important elements which prevent more widespread use. This effort has been led by members of the SPH rEsearch and engineeRing International Community (SPHERIC) who have identified SPH Grand Challenges. The SPHERIC SPH Grand Challenges (GCs) have been grouped into 5 categories: (GC1) convergence, consistency and stability, (GC2) boundary conditions, (GC3) adaptivity, (GC4) coupling to other models, and (GC5) applicability to industry. The SPH Grand Challenges have been formulated to focus the attention and activities of researchers, developers, and users around the world. The status of each SPH Grand Challenge is presented in this paper with a discussion on the areas for future development., Dr. Corrado Altomare acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 792370. A. Souto-Iglesias acknowledges the funding by the Spanish Ministry for Science, Innovation and Universities (MCIU) under Grant RTI2018-096791-B-C21 “Hidrodinámica de elementos de amortiguamiento del movimiento de aerogeneradores flotantes”. Open access funding provided by Università degli Studi di Parma within the CRUI-CARE Agreement., Peer Reviewed

Project Plan of the MSCA-IF Durcwave project, foreseen as deliverable D5.1., The DURCWAVE Project Plan Management (PMP) collects and summarize the project baselines and plan, namely: scopes, schedule, cost and human resource management. It is meant as an update of the project proposal, on the date of the project kick-off., This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 792370.

Three open source wave models are applied in 2DV to reproduce a large-scale wave flume experiment of bichromatic wave transformations over a steep-sloped dike with a mildly-sloped and very shallow foreshore: (i) the Reynolds-averaged Navier–Stokes equations solver interFoam of OpenFOAM® (OF), (ii) the weakly compressible smoothed particle hydrodynamics model DualSPHysics (DSPH) and (iii) the non-hydrostatic nonlinear shallow water equations model SWASH. An inter-model comparison is performed to determine the (standalone) applicability of the three models for this specific case, which requires the simulation of many processes simultaneously, including wave transformations over the foreshore and wave-structure interactions with the dike, promenade and vertical wall. A qualitative comparison is done based on the time series of the measured quantities along the wave flume, and snapshots of bore interactions on the promenade and impacts on the vertical wall. In addition, model performance and pattern statistics are employed to quantify the model differences. The results show that overall, OF provides the highest model skill, but has the highest computational cost. DSPH is shown to have a reduced model performance, but still comparable to OF and for a lower computational cost. Even though SWASH is a much more simplified model than both OF and DSPH, it is shown to provide very similar results: SWASH exhibits an equal capability to estimate the maximum quasi-static horizontal impact force with the highest computational efficiency, but does have an important model performance decrease compared to OF and DSPH for the force impulse., This research was part of the CREST (Climate REsilient CoaST) project (http://www.crestproject.be/en), funded by the Flemish Agency for Innovation by Science and Technology, grant number 150028. The work described in this section was supported by the European Community′s Horizon 2020 Research and Innovation Programme through the grant to HYDRALABPLUS, Contract no. 654110. C.A. acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie, grant number 792370., Peer Reviewed

Physical model experiments were conducted in a wave tank at Flanders Hydraulics Research, Antwerp, Belgium, to characterize the wave overtopping and impact force on vertical quay walls and sloping sea dike (1:2.5) under very oblique wave attack (angle between 45° and 80°). This study was triggered by the scarce scientific literature on the overtopping and force reduction due to very oblique waves since large reduction is expected for both when compared with the perpendicular wave attack. The study aimed to compare the results from the experimental tests with formulas derived from previous experiments and applicable to a Belgian harbor generic case. The influence of storm return walls and crest berm width on top of the dikes has been analyzed in combination with the wave obliqueness. The results indicate significant reduction of the overtopping due to very oblique waves and new reduction coefficients were proposed. When compared with formulas from previous studies the proposed coefficients indicate the best fit for the overtopping reduction. Position of the storm return wall respect to the quay edge rather than its height was found to be more important for preventing wave induced overtopping. The force reduction is up to approximately 50% for the oblique waves with respect to the perpendicular wave impact and reduction coefficients were proposed for two different configurations a sea dike and vertical quay wall, respectively., This research was funded by Agentschap voor Maritieme Dienstverlening en Kust (MDK)—Coastal Division, project WL2012_00_050. Corrado Altomare acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No.:792370., Peer Reviewed

Treball elaborat dins el programa Horizon 2020, amb l'ajut Marie Skłodowska-Curie Individual Fellowship, The main scientific objective of DURCWAVE project is to define new design criteria for wave action by modelling wave overtopping and post-overtopping processes of these urban defences., Award-winning

The Pont del Petroli is a dismissed pier in the area of Badalona, Spain, with high historical and social value. This structure was heavily damaged in January 2020 during the storm Gloria that hit southeastern Spain with remarkable strength. The reconstruction of the pier requires the assessment and characterization of the wave loading that determined the structural failure. Therefore, a state-of-the-art Computational Fluid Dynamic (CFD) code was employed herein as an aid for a planned experimental campaign that will be carried out at the Maritime Engineering Laboratory of Universitat Politècnica de Catalunya-BarcelonaTech (LIM/UPC). The numerical model is based on Smoothed Particle Hydrodynamics (SPH) and has been employed to simulate conditions very similar to those that manifested during the storm Gloria. The high computational cost for a full 3-D simulation has been alleviated by means of inlet boundary conditions, allowing wave generation very close to the structure. Numerical results reveal forces higher than the design loads of the pier, including both self-weight and accidental loads. This demonstrates that the main failure mechanism that led to severe structural damage of the pier during the storm is related to the exceeded lateral soil resistance. To the best of the authors’ knowledge, this research represents the first known application of SPH open boundary conditions to model a real-world engineering case., This research was funded by European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No.: 792370., Peer Reviewed

The state-of-the-art formulas for mean wave overtopping (q) assessment typically require wave conditions at the toe of the structure as input. However, for structures built either on land or in very shallow water, obtaining accurate estimates of wave height and period at the structure toe often proves difficult and requires the use of either physical modeling or high-resolution numerical wave models. Here, we follow Goda's method to establish an accurate prediction methodology for both vertical and sloping structures based entirely on deep-water characteristics—where the influence of the foreshore is captured by directly incorporating the foreshore slope and the relative water depth at the structure toe (htoe/Hm0,deep). Findings show that q decreases exponentially with htoe/Hm0,deep due to the decrease of the incident wave energy; however, the rate of reduction in q decreases for structures built on land or in extremely shallow water (htoe/Hm0,deep = 0.1) due to the increased influence of wave-induced setup and infragravity waves—which act as long-period fluctuations in mean water level—generated by nonlinear wave transformation over the foreshore., This work is part of the Perspectief research program All-Risk with Project No. B2 which is (partly) financed by NWO Domain Applied and Engineering Sciences, in collaboration with the following private and public partners: the Dutch Ministry of Infrastructure and Water Management (RWS); Deltares; STOWA; the regional water authority, Noorderzijlvest; the regional water authority, Vechtstromen; It Fryske Gea; HKV consultants; Natuurmonumenten; and waterboard HHNK. Dr. Corrado Altomare acknowledges funding from the European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie, Grant No. 792370, Peer Reviewed

In this paper, a Reynolds-averaged Navier–Stokes (RANS) equations solver, interFoam of OpenFOAM®, is validated for wave interactions with a dike, including a promenade and vertical wall, on a shallow foreshore. Such a coastal defence system is comprised of both an impermeable dike and a beach in front of it, forming the shallow foreshore depth at the dike toe. This case necessitates the simulation of several processes simultaneously: wave propagation, wave breaking over the beach slope, and wave interactions with the sea dike, consisting of wave overtopping, bore interactions on the promenade, and bore impacts on the dike-mounted vertical wall at the end of the promenade (storm wall or building). The validation is done using rare large-scale experimental data. Model performance and pattern statistics are employed to quantify the ability of the numerical model to reproduce the experimental data. In the evaluation method, a repeated test is used to estimate the experimental uncertainty. The solver interFoam is shown to generally have a very good model performance rating. A detailed analysis of the complex processes preceding the impacts on the vertical wall proves that a correct reproduction of the horizontal impact force and pressures is highly dependent on the accuracy of reproducing the bore interactions., This research was part of the CREST (Climate REsilient CoaST) project (http://www.crestproject.be/en), funded by the Flemish Agency for Innovation by Science and Technology, grant number 150028. The work described in this section was supported by the European Community’s Horizon 2020 Research and Innovation Programme through the grant to HYDRALABPLUS, Contract no. 654110. C.A. acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie, grant number 792370., Peer Reviewed

Smoothed Particle Hydrodynamics (SPH) method is used here to simulate a heaving point-absorber with a Power Take-Off system (PTO). The SPH-based code DualSPHysics is first validated with experimental data of regular waves interacting with the point-absorber. Comparison between the numerical and experimental heave displacement and velocity of the device show a good agreement for a given regular wave condition and different configurations of the PTO system. The validated numerical tool is then employed to investigate the efficiency of the proposed system. The efficiency, which is defined here as the ratio between the power absorbed by the point-absorber and its theoretical maximum, is obtained for different wave conditions and several arrangements of the PTO. Finally, the effects of highly energetic sea states on the buoy are examined through alternative configurations of the initial system. A survivability study is performed by computing the horizontal and vertical forces exerted by focused waves on the wave energy converter (WEC). The yield criterion is used to determine that submerging the heaving buoy at a certain depth is the most effective strategy to reduce the loads acting on the WEC and its structure, while keeping the WEC floating at still water level is the worst-case scenario., This work was partially financed by the Ministry of Economy and Competitiveness of the Government of Spain under project “WELCOME ENE2016-75074-C2-1-R″ and financed by Xunta de Galicia (Spain) under project ED431C 2017/64 ″Programa de Consolidación e Estructuración de Unidades de Investigación Competitivas (Grupos de Referencia Competitiva)" cofunded by European Regional Development Fund (ERDF). Dr. C. Altomare acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No.: 792370. Dr J. M. Domínguez acknowledges funding from Spanish government under the program “Juan de la Cierva-incorporación 2017” (IJCI-2017-32592)., Peer Reviewed

In this study we investigated the capabilities of the mesh-free, Lagrangian particle method (Smoothed Particle Hydrodynamics, SPH) to simulate the detailed hydrodynamic processes generated by both spilling and plunging breaking waves within the surf zone. The weakly-compressible SPH code DualSPHysics was applied to simulate wave breaking over two distinct bathymetric profiles (a plane beach and fringing reef) and compared to experimental flume measurements of waves, flows, and mean water levels. Despite the simulations spanning very different wave breaking conditions (including an extreme case with violently plunging waves on an effectively dry reef slope), the model was able to reproduce a wide range of relevant surf zone hydrodynamic processes using a fixed set of numerical parameters. This included accurate predictions of the nonlinear evolution of wave shapes (e.g., asymmetry and skewness properties), rates of wave dissipation within the surf zone, and wave setup distributions. By using this mesh-free approach, the model was able to resolve the critical crest region within the breaking waves, which provided robust predictions of the wave-induced mass fluxes within the surf zone responsible for the undertow. Within this breaking crest region, the model results capture how the potential energy of the organized wave motion is initially converted to kinetic energy and then dissipated, which reproduces the distribution of wave forces responsible for wave setup generation across the surf zone. Overall, the results reveal how the mesh-free SPH approach can accurately reproduce the detailed wave breaking processes with comparable skill to state-of-the-art mesh-based Computational Fluid Dynamics (CFD) models, and thus can be applied to provide valuable new physical insight into surf zone dynamics., Peer Reviewed

Design criteria for coastal defenses exposed to wave overtopping are usually assessed by mean overtopping discharges and maximum individual overtopping volumes. However, it is often difficult to give clear and precise limits of tolerable overtopping for all kinds of layouts. A few studies analyzed the relationship between wave overtopping flows and hazard levels for people on sea dikes, confirming that one single value of admissible mean discharge or individual overtopping volume is not a sufficient indicator of the hazard, but detailed characterization of flow velocities and depths is required. This work presents the results of an experimental campaign aiming at analyzing the validity of the safety limits and design criteria for overtopping discharge applied to an urbanized stretch of the Catalan coast, exposed to significant overtopping events every stormy season. The work compares different safety criteria for pedestrians. The results prove that the safety of pedestrians on a sea dike can be still guaranteed, even for overtopping volumes larger than 1,000 L/m. Sea storms characterized by deep-water wave height between 3.6 and 4.5 m lead to overtopping flow depth values larger than 1 m and flow velocities up to 20 m/s. However, pedestrian hazard is proved to be linked to the combination of overtopping flow velocity and flow depth rather than to single maximum values of one of these parameters. The use of stability curves to assess people’s stability under overtopping waves is therefore advised., This research was funded by European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No.: 792370. The authors would like to acknowledge the students Mauro Campagnola and Maria Luigia Robustelli, who carried out the experimental campaign under the guidance and supervision of C.A, and the technical/research staff of LIM/UPC, in particular Joaquim Sospedra, Oscar Galego and José M. Alsina for their support and assistance for the model constructions and setup of measurement systems., Peer Reviewed

In this work the numerical model DualSPHysics has been applied to study the complex phenomenon of wave overtopping characterising dike-promenade coastal defence layout. The model has been first validated, by comparing the results versus laboratory data obtained during a project campaign at the Maritime Engineering Laboratory of Universitat Politècnica de Catalunya – BarcelonaTech (LIM/UPC). The experimental campaign aimed to describe flow characteristics for the current dike and beach layout. Numerical modelling was employed to extend the experimental database beyond the range of tested conditions. In this work, a new Density Diffusion Scheme and the new modified Dynamic Boundary Conditions are applied to model wave-structure interaction. A real sea state was simulated, corresponding to a train of random waves having a duration equal to 1000 waves (= 1300s in real time). Cumulative overtopping volumes and mean discharges are calculated and compared with the experimental ones, showing a very good agreement and accuracy in not showing before in previous studies on wave overtopping with SPH-based solvers. One test case has been employed for further analysis. The model applicability and impact has been focused on reducing discharge under tolerable values by modifying the structural and beach layout. One solution corresponds to hard countermeasures to reduce overtopping discharge, employing a storm wall located on the dike crest. The other one is representative of soft countermeasures, namely beach nourishment, where the beach profile has been changed to shallower conditions to provoke more intense wave breaking and dissipate the incoming wave energy. Both alternatives guarantee tolerable discharges for coastal safety., This research was funded by European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No.: 792370.

Due to ongoing climate change, overtopping risk is increasing. In order to have effective countermeasures, it is useful to understand overtopping processes in details. In this study overtopping flow on a dike with gentle and shallow foreshores are investigated using a non-hydrostatic wave-flow model, SWASH (an acronym of Simulating WAves till SHore). The SWASH model in 2DV (i.e., flume like configuration) is first validated using the data of long crested wave cases with second order wave generation in the physical model test conducted. After that it is used to produce overtopping flow in different wave conditions and bathymetries. The results indicated that the overtopping risk is better characterized by the time dependent h (overtopping flow depth) and u (overtopping flow velocity) instead of hmax (maximum overtopping flow depth) and umax (maximum overtopping flow velocity), which led to overestimation of the risk. The time dependent u and h are strongly influenced by the dike configuration, namely by the promenade width and the existence of a vertical wall on the promenade: the simulation shows that the vertical wall induces seaward velocity on the dike which might be an extra risk during extreme events., This research was part of the CREST (Climate REsilient CoaST) project (http://www.crestproject.be/en), funded by the Flemish Agency for Innovation by Science and Technology, grant number 150028. Corrado Altomare acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No.: 792370., Peer Reviewed

An experimental campaign to study the overtopping flow properties on sea dikes has been carried out within the framework of the MSCA-IF DURCWAVE. Data of overtopping volumes and discharges have been employed to validate the SPH-based meshless and open-source DualSPHysics solver. Besides, data from other experimental campaigns (e.g. Hydralab + WaLoWa project), have been employed for further model validation of Wave-Structure-Interaction (WSI) problems., This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 792370.

The DualSPHysics project is an open-source smoothed particle hydrodynamics (SPH) code for simulating free-surface flow. The DualSPHysics code can be run on both multi-core central processing units (CPUs) or on a graphics processing unit (GPU) and is optimised to exploit the computational power of a GPU. Since its original release in 2011, DualSPHysics has been continually developed based on latest research and hence its functionality has been expanded to include an increasing range of applications. The paper presents the basic formulation and then details of all features of SPH formulations including boundary conditions, water wave generation and absorption, coupling with other models including the discrete element method, a physics engine and mooring library, and multi-phase models. Developing an SPH code with many developers in different locations presents challenges, and ensuring rigorous validation is undertaken before code releases is an important part of the development process. The validations undertaken for the DualSPHysics code are presented followed by two example applications: an armoured breakwater with moving armour units, and a wave energy converter. Both examples demonstrate the ability of SPH to include the interconnected movement of multiple objects. Finally, the paper briefly discusses the current research challenges being addressed by the DualSPHysics consortium.

This study attempts to refine a model named the Integrated Formula of Wave Overtopping and Runup Modeling (IFORM) to improve the prediction performance of mean wave overtopping discharge for a broader range of installation conditions. The empirical formula describing the relation between overtopping discharge and maximum runup has been re-examined. A set of piecewise formulas is implemented in the IFORM by optimal reconstruction of coefficients depending on the magnitude of deficit in freeboard. The refined IFORM improves the tendency to underestimate the discharge in the range of relatively high freeboard conditions, while it retains the high performance of the original IFORM in the range where the crest freeboard is relatively low. The refined model's capability for overtopping prediction is validated by comparison with various existing experimental datasets for inclined/vertical seawalls installed at relatively shallow water depth or on land. The prediction accuracy is also examined by comparison with well-known overtopping formulas. Qualitative and quantitative comparisons validate that the current model is able to reproduce the experimental observations over a broad range of overtopping conditions and that the performance of the model proposed in the present study is as good as existing representative models., This work is partially supported by the Grants-in-Aid for Scientific Research by the Japan Society for the Promotion of Science [Grant No. 19H02403 and 20K05046] and the collaborative research program of the Disaster Prevention Research Institute of Kyoto University [Grant No. 30G-09]. Dr. C. Altomare acknowledges funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No.: 792370. Suggestive comments from Prof. Hiraishi (Kyoto University), Dr. Kawasaki and Dr. Mizutani (Hydro Technology Institute Co., Ltd.) are most appreciated. Assistance rendered by Mr. Ohtani (a former student of Kanazawa University) and Ms. Ichimura (graduate student of Kanazawa University) is acknowledged. Constructive comments and suggestions from the anonymous reviewers are appreciated., Peer Reviewed

The work highlights the importance of directional spreading effects on wave overtopping estimation in shallow and mild sloping foreshores. Wave short-crestedness leads, in general, to a reduction of mean overtopping discharges on coastal structures. In the present work, the case of a sea dike with gentle foreshore in very and extremely shallow water conditions is analysed. Physical model tests have been carried out in order to investigate the effect of directional spreading on overtopping and incident wave characteristics. In the present experimental campaign, the effect of wave spreading has only been investigated for perpendicular wave attack. Results show that directional spreading is proved to cause a reduction of average discharge of sea dikes with gentle and shallow foreshore. Expressions for the reduction factor for directional spreading are derived, fitted on the tested database. The use of this reduction factor leads to more accurate prediction and avoids overtopping overestimation, however reduction-factor formulations are overtopping-formula depending., Peer Reviewed

Measurements of the water surface elevation were taken close to the wavemaker, along the sloping foreshore and at the dike toe location by resistance type wave gauges. The overtopping flow properties thickness and velocity were measured by ultra-sonic distance sensors and high-speed cameras. Due to its large storage size, the whole set of data is provided on request., The experimental data refer to physical model tests carried out in 2019 from May to December at the wave flume CIEMito of the Maritime Engineering Laboratory (LIM) of the Universitat Politècnica de Catalunya – BarcelonaTech (UPC). The experiments aimed at characterizing the flow characteristics associated to the maximum individual overtopping volumes, due to specific storm events with different return periods. Specifically, the experiments focused on the measurements of overtopping volumes and discharges, in order to find the relation between these parameters with the corresponding overtopping flow velocities and overtopping flow depth, when the maximum overtopping event occurs on a dike during a sea state. A model geometry comprised of a sloping beach, a sloping dike and promenade was built into the CIEMito flume., 1

Three open source wave models are applied in 2DV to reproduce a large-scale wave flume experiment of bichromatic wave transformations over a steep-sloped dike with a mildly-sloped and very shallow foreshore: (i) the Reynolds-averaged Navier–Stokes equations solver interFoam of OpenFOAM® (OF), (ii) the weakly compressible smoothed particle hydrodynamics model DualSPHysics (DSPH) and (iii) the non-hydrostatic nonlinear shallow water equations model SWASH. An inter-model comparison is performed to determine the (standalone) applicability of the three models for this specific case, which requires the simulation of many processes simultaneously, including wave transformations over the foreshore and wave-structure interactions with the dike, promenade and vertical wall. A qualitative comparison is done based on the time series of the measured quantities along the wave flume, and snapshots of bore interactions on the promenade and impacts on the vertical wall. In addition, model performance and pattern statistics are employed to quantify the model differences. The results show that overall, OF provides the highest model skill, but has the highest computational cost. DSPH is shown to have a reduced model performance, but still comparable to OF and for a lower computational cost. Even though SWASH is a much more simplified model than both OF and DSPH, it is shown to provide very similar results: SWASH exhibits an equal capability to estimate the maximum quasi-static horizontal impact force with the highest computational efficiency, but does have an important model performance decrease compared to OF and DSPH for the force impulse., This research was part of the CREST (Climate REsilient CoaST) project (http://www.crestproject.be/en), funded by the Flemish Agency for Innovation by Science and Technology, grant number 150028. The work described in this section was supported by the European Community′s Horizon 2020 Research and Innovation Programme through the grant to HYDRALABPLUS, Contract no. 654110. C.A. acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie, grant number 792370., Peer Reviewed, Postprint (published version)

Due to climatic change and the increased usage of coastal areas, there is an increasing risk of dike failures along the coasts worldwide. Wave run-up plays a key role in the planning and design of a coastal structure. Coastal engineers use empirical equations for the determination of wave run-up. These formulae generally include the influence of various hydraulic, geometrical and structural parameters, but neglect the effect of the curvature of coastal dikes on wave run-up and overtopping. The scope of this research is to find the effects of the dike curvature on wave run-up for regular wave attack by employing numerical model studies for various dike-opening angles and comparing it with physical model test results. A numerical simulation is carried out using DualSPHysics, a mesh-less model and OpenFOAM, a mesh-based model. A new influence factor is introduced to determine the influence of curvature along a dike line. For convexly curved dikes (ad = 210° to 270°) under perpendicular wave attack, a higher wave run-up was observed for larger opening angles at the center of curvature whereas for concavely curved dikes (ad = 90° to 150°) under perpendicular wave attack, wave run-up increases at the center of curvature as the opening angle decreases. This research aims to contribute a more precise analysis and understanding the influence of the curvature in a dike line and thus ensuring a higher level of protection in the future development of coastal structures., Peer Reviewed, Postprint (published version)

The proposed work aims to prove the capability of the DualSPHysics numerical code to deal with the interaction of slamming waves with a Wave Energy Converter (WEC). In particular, the analysed device is a point-absorber that consists of a cylindrical heaving-buoy equipped with an air damper in order to reproduce the effect of the Power Take-Off (PTO) system. Numerical vertical displacement of the cylinder under regular waves is found to be in good agreement with experimental data for different PTO systems. Different scenarios are considered to compute the loads of focused waves acting on the device with its PTO system set on hold. The yield criterion is used to determine that keeping the WEC fixed at still water level is the worst-case scenario and submerging the heaving buoy deep enough is the best-case scenario., This work was partially financed by the Ministry of Economy and Competitiveness of the Government of Spain under project “WELCOME ENE2016-75074-C2-1-R” and financed by Xunta de Galicia (Spain) under project ED431C 2017/64 ″Programa de Con-solidación e Estructuración de Unidades de Investi-gación Competitivas (Grupos de Referencia Com-petitiva)" cofunded by European Regional Development Fund (FEDER). Fruitful discussion was held during the Course 'Mod-eling free surface flows with DualSPHysics' funded by the University of Salerno, Italy under the project N. 300393CIC19VICCIONE. Dr. C. Altomare acknowledges funding from the Eu-ropean Union’s Horizon 2020 research and innova-tion programme under the Marie Sklodowska-Curie grant agreement No.: 792370., Peer Reviewed, Postprint (published version)

Smoothed Particle Hydrodynamics (SPH) method is used here to simulate a heaving point-absorber with a Power Take-Off system (PTO). The SPH-based code DualSPHysics is first validated with experimental data of regular waves interacting with the point-absorber. Comparison between the numerical and experimental heave displacement and velocity of the device show a good agreement for a given regular wave condition and different configurations of the PTO system. The validated numerical tool is then employed to investigate the efficiency of the proposed system. The efficiency, which is defined here as the ratio between the power absorbed by the point-absorber and its theoretical maximum, is obtained for different wave conditions and several arrangements of the PTO. Finally, the effects of highly energetic sea states on the buoy are examined through alternative configurations of the initial system. A survivability study is performed by computing the horizontal and vertical forces exerted by focused waves on the wave energy converter (WEC). The yield criterion is used to determine that submerging the heaving buoy at a certain depth is the most effective strategy to reduce the loads acting on the WEC and its structure, while keeping the WEC floating at still water level is the worst-case scenario., This work was partially financed by the Ministry of Economy and Competitiveness of the Government of Spain under project “WELCOME ENE2016-75074-C2-1-R″ and financed by Xunta de Galicia (Spain) under project ED431C 2017/64 ″Programa de Consolidación e Estructuración de Unidades de Investigación Competitivas (Grupos de Referencia Competitiva)" cofunded by European Regional Development Fund (ERDF). Dr. C. Altomare acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No.: 792370. Dr J. M. Domínguez acknowledges funding from Spanish government under the program “Juan de la Cierva-incorporación 2017” (IJCI-2017-32592)., Peer Reviewed, Postprint (author's final draft)

In this study we investigated the capabilities of the mesh-free, Lagrangian particle method (Smoothed Particle Hydrodynamics, SPH) to simulate the detailed hydrodynamic processes generated by both spilling and plunging breaking waves within the surf zone. The weakly-compressible SPH code DualSPHysics was applied to simulate wave breaking over two distinct bathymetric profiles (a plane beach and fringing reef) and compared to experimental flume measurements of waves, flows, and mean water levels. Despite the simulations spanning very different wave breaking conditions (including an extreme case with violently plunging waves on an effectively dry reef slope), the model was able to reproduce a wide range of relevant surf zone hydrodynamic processes using a fixed set of numerical parameters. This included accurate predictions of the nonlinear evolution of wave shapes (e.g., asymmetry and skewness properties), rates of wave dissipation within the surf zone, and wave setup distributions. By using this mesh-free approach, the model was able to resolve the critical crest region within the breaking waves, which provided robust predictions of the wave-induced mass fluxes within the surf zone responsible for the undertow. Within this breaking crest region, the model results capture how the potential energy of the organized wave motion is initially converted to kinetic energy and then dissipated, which reproduces the distribution of wave forces responsible for wave setup generation across the surf zone. Overall, the results reveal how the mesh-free SPH approach can accurately reproduce the detailed wave breaking processes with comparable skill to state-of-the-art mesh-based Computational Fluid Dynamics (CFD) models, and thus can be applied to provide valuable new physical insight into surf zone dynamics., Peer Reviewed, Postprint (author's final draft)

Design criteria for coastal defenses exposed to wave overtopping are usually assessed by mean overtopping discharges and maximum individual overtopping volumes. However, it is often difficult to give clear and precise limits of tolerable overtopping for all kinds of layouts. A few studies analyzed the relationship between wave overtopping flows and hazard levels for people on sea dikes, confirming that one single value of admissible mean discharge or individual overtopping volume is not a sufficient indicator of the hazard, but detailed characterization of flow velocities and depths is required. This work presents the results of an experimental campaign aiming at analyzing the validity of the safety limits and design criteria for overtopping discharge applied to an urbanized stretch of the Catalan coast, exposed to significant overtopping events every stormy season. The work compares different safety criteria for pedestrians. The results prove that the safety of pedestrians on a sea dike can be still guaranteed, even for overtopping volumes larger than 1,000 L/m. Sea storms characterized by deep-water wave height between 3.6 and 4.5 m lead to overtopping flow depth values larger than 1 m and flow velocities up to 20 m/s. However, pedestrian hazard is proved to be linked to the combination of overtopping flow velocity and flow depth rather than to single maximum values of one of these parameters. The use of stability curves to assess people’s stability under overtopping waves is therefore advised., This research was funded by European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No.: 792370. The authors would like to acknowledge the students Mauro Campagnola and Maria Luigia Robustelli, who carried out the experimental campaign under the guidance and supervision of C.A, and the technical/research staff of LIM/UPC, in particular Joaquim Sospedra, Oscar Galego and José M. Alsina for their support and assistance for the model constructions and setup of measurement systems., Peer Reviewed, Postprint (published version)

An experimental campaign to study the overtopping flow properties on sea dikes has been carried out within the framework of the MSCA-IF DURCWAVE. Data of overtopping volumes and discharges have been employed to validate the SPH-based meshless and open-source DualSPHysics solver. Besides, data from other experimental campaigns (e.g. Hydralab + WaLoWa project), have been employed for further model validation of Wave-Structure-Interaction (WSI) problems., This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 792370., Preprint

The DualSPHysics project is an open-source smoothed particle hydrodynamics (SPH) code for simulating free-surface flow. The DualSPHysics code can be run on both multi-core central processing units (CPUs) or on a graphics processing unit (GPU) and is optimised to exploit the computational power of a GPU. Since its original release in 2011, DualSPHysics has been continually developed based on latest research and hence its functionality has been expanded to include an increasing range of applications. The paper presents the basic formulation and then details of all features of SPH formulations including boundary conditions, water wave generation and absorption, coupling with other models including the discrete element method, a physics engine and mooring library, and multi-phase models. Developing an SPH code with many developers in different locations presents challenges, and ensuring rigorous validation is undertaken before code releases is an important part of the development process. The validations undertaken for the DualSPHysics code are presented followed by two example applications: an armoured breakwater with moving armour units, and a wave energy converter. Both examples demonstrate the ability of SPH to include the interconnected movement of multiple objects. Finally, the paper briefly discusses the current research challenges being addressed by the DualSPHysics consortium., Postprint (published version)

This document represents a proposal for Eurocodes amendment, with particular focus on wave overtopping assessment and overtopping flow properties on coastal defences in urbanized low-elevation coastal areas., This document represents a proposal for Eurocodes amendment, with particular focus on wave overtopping assessment and overtopping flow properties on coastal defences in urbanized low-elevation coastal areas., This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 792370., Preprint

Project Plan of the MSCA-IF Durcwave project, foreseen as deliverable D5.1., The DURCWAVE Project Plan Management (PMP) collects and summarize the project baselines and plan, namely: scopes, schedule, cost and human resource management. It is meant as an update of the project proposal, on the date of the project kick-off., This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 792370., Preprint

This study attempts to refine a model named the Integrated Formula of Wave Overtopping and Runup Modeling (IFORM) to improve the prediction performance of mean wave overtopping discharge for a broader range of installation conditions. The empirical formula describing the relation between overtopping discharge and maximum runup has been re-examined. A set of piecewise formulas is implemented in the IFORM by optimal reconstruction of coefficients depending on the magnitude of deficit in freeboard. The refined IFORM improves the tendency to underestimate the discharge in the range of relatively high freeboard conditions, while it retains the high performance of the original IFORM in the range where the crest freeboard is relatively low. The refined model's capability for overtopping prediction is validated by comparison with various existing experimental datasets for inclined/vertical seawalls installed at relatively shallow water depth or on land. The prediction accuracy is also examined by comparison with well-known overtopping formulas. Qualitative and quantitative comparisons validate that the current model is able to reproduce the experimental observations over a broad range of overtopping conditions and that the performance of the model proposed in the present study is as good as existing representative models., This work is partially supported by the Grants-in-Aid for Scientific Research by the Japan Society for the Promotion of Science [Grant No. 19H02403 and 20K05046] and the collaborative research program of the Disaster Prevention Research Institute of Kyoto University [Grant No. 30G-09]. Dr. C. Altomare acknowledges funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No.: 792370. Suggestive comments from Prof. Hiraishi (Kyoto University), Dr. Kawasaki and Dr. Mizutani (Hydro Technology Institute Co., Ltd.) are most appreciated. Assistance rendered by Mr. Ohtani (a former student of Kanazawa University) and Ms. Ichimura (graduate student of Kanazawa University) is acknowledged. Constructive comments and suggestions from the anonymous reviewers are appreciated., Peer Reviewed, Postprint (published version)

In this paper, a Reynolds-averaged Navier–Stokes (RANS) equations solver, interFoam of OpenFOAM®, is validated for wave interactions with a dike, including a promenade and vertical wall, on a shallow foreshore. Such a coastal defence system is comprised of both an impermeable dike and a beach in front of it, forming the shallow foreshore depth at the dike toe. This case necessitates the simulation of several processes simultaneously: wave propagation, wave breaking over the beach slope, and wave interactions with the sea dike, consisting of wave overtopping, bore interactions on the promenade, and bore impacts on the dike-mounted vertical wall at the end of the promenade (storm wall or building). The validation is done using rare large-scale experimental data. Model performance and pattern statistics are employed to quantify the ability of the numerical model to reproduce the experimental data. In the evaluation method, a repeated test is used to estimate the experimental uncertainty. The solver interFoam is shown to generally have a very good model performance rating. A detailed analysis of the complex processes preceding the impacts on the vertical wall proves that a correct reproduction of the horizontal impact force and pressures is highly dependent on the accuracy of reproducing the bore interactions., This research was part of the CREST (Climate REsilient CoaST) project (http://www.crestproject.be/en), funded by the Flemish Agency for Innovation by Science and Technology, grant number 150028. The work described in this section was supported by the European Community’s Horizon 2020 Research and Innovation Programme through the grant to HYDRALABPLUS, Contract no. 654110. C.A. acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie, grant number 792370., Peer Reviewed, Postprint (published version)

In this work the Weakly Compressible SPH-based (WCSPH) model DualSPHysics has been validated and applied to study the random wave overtopping of dike-promenade layout in shallow water conditions. Data from physical model tests carried out in a small-scale wave flume have been used for model validation. The results have been compared in terms of water surface elevation, mean discharges and individual overtopping volumes distribution. The selected geometrical layout is representative of the coastal area of Premià de Mar, in Catalonia (Spain). This stretch of the coast presents both railways and a bike path very close to the shore and therefore exposed to possible sea storms. For the first time an SPH-based model has been employed to reproduce long-lasting wave overtopping tests, made of time series of 1000 irregular waves, which are representative of real sea states. The density diffusion scheme and the modified Dynamic Boundary Conditions have been applied in the present simulations. By employing standard setup for SPH modelling of wave-structure interaction problems of a very long duration, stable simulations and accurate results have been attained., This research was funded by European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No.: 792370., Peer Reviewed, Postprint (published version)

The Pont del Petroli is a dismissed pier in the area of Badalona, Spain, with high historical and social value. This structure was heavily damaged in January 2020 during the storm Gloria that hit southeastern Spain with remarkable strength. The reconstruction of the pier requires the assessment and characterization of the wave loading that determined the structural failure. Therefore, a state-of-the-art Computational Fluid Dynamic (CFD) code was employed herein as an aid for a planned experimental campaign that will be carried out at the Maritime Engineering Laboratory of Universitat Politècnica de Catalunya-BarcelonaTech (LIM/UPC). The numerical model is based on Smoothed Particle Hydrodynamics (SPH) and has been employed to simulate conditions very similar to those that manifested during the storm Gloria. The high computational cost for a full 3-D simulation has been alleviated by means of inlet boundary conditions, allowing wave generation very close to the structure. Numerical results reveal forces higher than the design loads of the pier, including both self-weight and accidental loads. This demonstrates that the main failure mechanism that led to severe structural damage of the pier during the storm is related to the exceeded lateral soil resistance. To the best of the authors’ knowledge, this research represents the first known application of SPH open boundary conditions to model a real-world engineering case., This research was funded by European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No.: 792370., Peer Reviewed, Postprint (published version)

This paper presents a brief review of grand challenges of Smoothed Particle Hydrodynamics (SPH) method. As a meshless method, SPH can simulate a large range of applications from astrophysics to free-surface flows, to complex mixing problems in industry and has had notable successes. As a young computational method, the SPH method still requires development to address important elements which prevent more widespread use. This effort has been led by members of the SPH rEsearch and engineeRing International Community (SPHERIC) who have identified SPH Grand Challenges. The SPHERIC SPH Grand Challenges (GCs) have been grouped into 5 categories: (GC1) convergence, consistency and stability, (GC2) boundary conditions, (GC3) adaptivity, (GC4) coupling to other models, and (GC5) applicability to industry. The SPH Grand Challenges have been formulated to focus the attention and activities of researchers, developers, and users around the world. The status of each SPH Grand Challenge is presented in this paper with a discussion on the areas for future development., Dr. Corrado Altomare acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 792370. A. Souto-Iglesias acknowledges the funding by the Spanish Ministry for Science, Innovation and Universities (MCIU) under Grant RTI2018-096791-B-C21 “Hidrodinámica de elementos de amortiguamiento del movimiento de aerogeneradores flotantes”. Open access funding provided by Università degli Studi di Parma within the CRUI-CARE Agreement., Peer Reviewed, Postprint (published version)