Long Wave Run-up

With the devastating effects of the 2004 Sumatra Tsunami, tsunami research is at an all time high. Tsunami forecasting and modeling has become exceedingly important in the anticipation of major disasters. Tsunami inundation modeling, how a tsunami invades a coastal area, is an extremely useful tool for the prevention of major disaster in tsunami laden zones. Using a new free-surface hydrodynamic modeling code called GPU-SPHysics, accurate inundation and propagation models of tsunamis can be modeled at very high resolutions. GPU-SPHysics takes advantage of the extremely powerful computational power of a GPU (Graphics Processing Unit) and calculates the dynamics of fluids based on SPH (Smoothed Particle Hydrodynamics). The implementation of SPH on the GPU not only creates accurate, three-dimensional models but stunning visualizations of a tsunami wave breaking on beaches or other structures. Using the data from these models, coastal communities will be well prepared for any magnitude of tsunami that they may encounter by adjusting their infrastructure and disaster preparation to accommodate for this common disaster and potentially save many lives. To utilize GPU-SPHysics' models accurately, they must first be verified. NOAA (The National Oceanic and Atmospheric Administration) has provided benchmarks for tsunami inundation and propagation models. These benchmarks consist of analytic tests, laboratory tests and field tests. A key benchmark for GPU-SPHysics to be verified against is the solitary wave inundation on a sloping beach iv experiment. The solitary wave best represents the leading wave of a tsunami; hence it is vital to test other inundations that involve more complex structures than sloping beaches. Through visual analysis, the GPU-SPHysics solitary wave model, accurate to a small deviation, has been verified using the analytic calculation for maximum runup as provided by Synolakis. To verify other benchmarks provided by NOAA, GPU-SPHysics must be tested against multiple experiments. Once GPU-SPHysics has been verified for multiple data sets, it can be considered an accurate tool for hazard analysis.

Dispersive effects during long wave run-up on a plane beach are studied. We take an advantage of experimental data collection of different wave types (single pulses, sinusoidal waves, bi-harmonic waves, and frequency modulated wave trains) and simulate their run-up using two models: (i) nondispersive nonlinear shallow water theory and (ii) dispersive Boussinesq type model based on the modified Peregrine system. It is shown, that for long positive pulses, dispersive effects are not so important and nonlinear shallow water theory can be used. However, for periodic sinusoidal and bi-harmonic pulses of the same period, the dispersive effects result in significant wave transformation during its propagation, but do not have a strong impact on its maximal run-up height. Overall, for maximum wave run-up height, we could not find a preference of dispersive model against the nondispersive one, and, therefore, suggest using nonlinear shallow water model for long wave run-up height estimation.

The present study focused on generation of representative waves of tsunamis using GPU-based SPH numerical method. In this regard, solitary waves, as traditional representative of leading waves of tsunamis, were firstly generated in SPH model by a piston wave-maker moving based on an implicit equation solved by numerical code. Since it was proved that solitary waves are remarkably shorter and steeper than real-world tsunami waves, a new approach was also presented to reproduce the very long wave of a real tsunami. In this method, the tsunami time series was approximated by a theoretical relation based on the combination of several solitons. The relation was then used to solve the linearized trajectory equation of a wave-maker for generation of the intended time series of tsunami wave in the SPH model. The generation of solitary wave in SPH model was evaluated by comparing different simulated waves with analytical ones and it was seen that the solitary waves are successfully generated...

The large-scale laboratory experiments were performed in a 30 m-wide, 25 m-long, and 60 cm-deep wave basin. Waves were realistically created in the tank by a horizontal wave generator with 60 different paddles each 46 cm-wide and moving independently. These experiments provided run-up observations for validating numerical models and supplemented comparisons with analytical results. Smoothed particle hydrodynamics (SPH) is a popular meshfree, Lagrangian method with attractive features in modelling fluid dynamics. The SPH method is capable of dealing with problems with free surface, deformable boundary, moving interface, wave propagation and solid simulation. A weakly incompressible fluid flow SPH model was employed in this paper to investigate the run-up heights of nearshore tsunamis in the vicinity of a circular island. The predicted numerical results have been verified by comparing to available laboratory measurements. A good agreement has been observed.

This is a study of the maximum runup of cnoidal waves on plane beaches. An approximate theory is described for determining the maximum runup of nonbreaking cnoidal waves. It is shown that the linear and nonlinear theory predict mathematically identical maximum runup heights. An asymptotic result is derived for the maximum runup of solitary waves, which are one limiting form of cnoidal waves. A series of laboratory experiments is described to support the theory. Other numerical results are presented that suggest that the runup of cnoidal waves is significantly higher than the runup of monochromatic waves with the same waveheight and wavelength. Preliminary laboratory data are also presented which suggest that, for certain cnoidal waves, the maximum runup is not a monotonically varying function of the normalized wavelength.

The Port-Bouët Bay shoreline is threatened by extreme sea level (ESL) events, which result from the combination of storm tide, wave run-up, and sea level rise (SLR). This study provides comprehensive scenarios of current and future ESLs at the local scale along the bay to understand the evolution of the phenomenon and promote local adaptation. The methodological steps involve first reconstructing historical storm tide and wave run-up data using a hydrodynamic model (D-flow FM) and the empirical model of Stockdon et al. Second, the Generalized Pareto Distribution (GPD) model fitted to the Peaks-Over-Thresholds (POT) method is applied to the data to calculate extreme return levels. Third, we combine the extreme storm tide and wave run-up using the joint probability method to obtain the current ESLs. Finally, the current ESLs are integrated with recent SLR projections to provide future ESL estimates. The results show that the current ESLs are relatively high, with 100-year return level...

The problem of determining solitary waves runups is of great interest in studying coastal effects of tsunamis. A relationship between the runup and wave height, for non-breaking waves, exists in the literature (Synolakis, 1987). Nevertheless, it is difficult to predict the runup for breaking waves. Our study aims to numerically determine the runup law for breaking waves. Therefore, we developed a numerical model based on the Smoothed Particle Hydrodynamics method (SPH) in order to study the transformation of a wave propagating over a constant depth and encountering a sloping beach. SPH is a meshfree method, where all fluid quantities are carried out by points, and is very suitable for problems involving large deformations and moving interfaces. Originally developed for astrophysical problems, this numerical method proved its efficiency to simulate free surface flows. The formalism requires to consider fluid being slightly compressible and that pressure is to be evaluated from densit...

The Port-Bouët Bay shoreline is threatened by extreme sea level (ESL) events, which result from the combination of storm tide, wave run-up, and sea level rise (SLR). This study provides comprehensive scenarios of current and future ESLs at the local scale along the bay to understand the evolution of the phenomenon and promote local adaptation. The methodological steps involve first reconstructing historical storm tide and wave run-up data using a hydrodynamic model (D-flow FM) and the empirical model of Stockdon et al. Second, the Generalized Pareto Distribution (GPD) model fitted to the Peaks-Over-Thresholds (POT) method is applied to the data to calculate extreme return levels. Third, we combine the extreme storm tide and wave run-up using the joint probability method to obtain the current ESLs. Finally, the current ESLs are integrated with recent SLR projections to provide future ESL estimates. The results show that the current ESLs are relatively high, with 100-year return level...

The Port-Bouët Bay shoreline is threatened by extreme sea level (ESL) events, which result from the combination of storm tide, wave run-up, and sea level rise (SLR). This study provides comprehensive scenarios of current and future ESLs at the local scale along the bay to understand the evolution of the phenomenon and promote local adaptation. The methodological steps involve first reconstructing historical storm tide and wave run-up data using a hydrodynamic model (D-flow FM) and the empirical model of Stockdon et al. Second, the Generalized Pareto Distribution (GPD) model fitted to the Peaks-Over-Thresholds (POT) method is applied to the data to calculate extreme return levels. Third, we combine the extreme storm tide and wave run-up using the joint probability method to obtain the current ESLs. Finally, the current ESLs are integrated with recent SLR projections to provide future ESL estimates. The results show that the current ESLs are relatively high, with 100-year return level...

The Port-Bouët Bay shoreline is threatened by extreme sea level (ESL) events, which result from the combination of storm tide, wave run-up, and sea level rise (SLR). This study provides comprehensive scenarios of current and future ESLs at the local scale along the bay to understand the
evolution of the phenomenon and promote local adaptation. The methodological steps involve first reconstructing historical storm tide and wave run-up data using a hydrodynamic model (D-flow FM) and the empirical model of Stockdon et al. Second, the Generalized Pareto Distribution (GPD) model fitted to the Peaks-Over-Thresholds (POT) method is applied to the data to calculate extreme return levels. Third, we combine the extreme storm tide and wave run-up using the joint probability method to obtain the current ESLs. Finally, the current ESLs are integrated with recent SLR projections to provide future ESL estimates. The results show that the current ESLs are relatively high, with 100-year
return levels of 4.37 m ± 0.51, 4.97 m ± 0.57, and 4.48 m ± 0.5 at Vridi, Petit-Bassam, and Sogefiha respectively. By end-century, under the SSP1-2.6, SSP2-4.5, and SSP5-8.5 scenarios, the future SLR is expected to increase the current ESLs by 0.49 m, 0.62 m, and 0.84 m, respectively. This could lead to a more frequent occurrence of the current 100-year return period, happening once every 2 years by 2100, especially under SSP5-8.5. The developed SLR scenarios can be used to assess the potential
coastal flood risk in the study area for sustainable and effective coastal management and planning.

The present study focused on generation of representative waves of tsunamis using GPU-based SPH numerical method. In this regard, solitary waves, as traditional representative of leading waves of tsunamis, were firstly generated in SPH model by a piston wave-maker moving based on an implicit equation solved by numerical code. Since it was proved that solitary waves are remarkably shorter and steeper than real-world tsunami waves, a new approach was also presented to reproduce the very long wave of a real tsunami. In this method, the tsunami time series was approximated by a theoretical relation based on the combination of several solitons. The relation was then used to solve the linearized trajectory equation of a wave-maker for generation of the intended time series of tsunami wave in the SPH model. The generation of solitary wave in SPH model was evaluated by comparing different simulated waves with analytical ones and it was seen that the solitary waves are successfully generated...

In this paper, a solitary wave propagation problem running up on a range of relatively steep slopes to gentle slopes is investigated. Boussinesq solitary wave generation method is used in five beach slopes with the still water heights of 15.0-68.6 cm and relative wave heights of 0.046-0.348. The incompressible smoothed particle hydrodynamics method is utilized as the numerical method. Simulation results are compared with analytical results and experimental data in terms of free surface displacement, maximum run up, shoreline movement and fluid particle velocity. Surface profile results agree reasonably with the analytical results at run down and horizontal particle velocities coincide with the experimental data. Furthermore, the results of maximum run up show that for moderate and large wave heights, Lagrangian numerical results pursuit the maximum run up of the experimental data with acceptable accuracy.

Tsunamis are among the most destructive natural hazards and can cause massive damage to the coastal communities. This paper presents a first numerical study on the tsunami-like solitary wave impinging and overtopping based on the mesh-free Consistent Particle Method (CPM). The distinct feature of CPM is that it computes the spatial derivatives in a way consistent with the Taylor series expansion and hence achieves good numerical consistency and accuracy. This largely alleviates the spurious pressure fluctuation that is a key issue for the particle method. Validated by the benchmark example of solitary wave impact on a seawall, the CPM model is shown to be able to capture the highly deformed breaking wave and the impact pressure associated with wave impinging and overtopping. Using the numerical model, a parametric study of the effect of seawall cross-sectional geometry on the characteristics of wave overtopping is conducted. It is found that a higher water level can lead to much more intensive overtopping volume and kinetic energy of the overtopping flow, which implies that the coastal areas are at higher risk as the sea level rises. For the purpose of engineering interest, a simple and practical way to estimate the intensity of a real tsunami is presented in terms of the volume and energy of the bulge part of the incident wave.

Tsunamis need to be studied more carefully and quantitatively to fully understand their destructive impact on coastal areas. Numerical modeling provides an accurate and useful method to model tsunami inundations on a coastline. However, models must undergo a detailed verification and validation process to be used as an accurate hazard assessment tool. Using standards and procedures given by NOAA, a new code in hydrodynamic modeling called GPU-SPHysics can be verified and validated for use as a tsunami inundation model. GPU-SPHysics is a meshless, Lagrangian code that utilizes the computing power of the Graphics Processing Unit (GPU) to calculate high resolution hydrodynamic simulations using the equations given by Smooth Particle Hydrodynamics (SPH). GPU-SPHysics has proven to be an accurate tool in modeling complex tsunami inundations, such as the inundation on a conical island, when tested against extensive laboratory data.

The present study focused on generation of representative waves of tsunamis using GPU-based SPH numerical method. In this regard, solitary waves, as traditional representative of leading waves of tsunamis, were firstly generated in SPH model by a piston wave-maker moving based on an implicit equation solved by numerical code. Since it was proved that solitary waves are remarkably shorter and steeper than real-world tsunami waves, a new approach was also presented to reproduce the very long wave of a real tsunami. In this method, the tsunami time series was approximated by a theoretical relation based on the combination of several solitons. The relation was then used to solve the linearized trajectory equation of a wave-maker for generation of the intended time series of tsunami wave in the SPH model. The generation of solitary wave in SPH model was evaluated by comparing different simulated waves with analytical ones and it was seen that the solitary waves are successfully generated...

It is difficult to study the process of wave propagation from the deep ocean to the nearshore region using a single model due to the presence of multiple scales both in time and in space. Numerical models based on the Boussinesq equations are well known to accurately propagate waves from intermediate water depth to the nearshore region. Since they are 2D models, they are computationally efficient and can be applied to study wave transformations over large domains. Numerical models based on Smoothed Particle Hydrodynamics can inherently capture multiply connected free surfaces and hence can be naturally used to capture breaking free surfaces and estimate breaking induced runup and overtopping. Here, a hybrid model (SPHunwave) is developed combining the main advantages of a Boussinesq model (FUNWAVE) and a SPH model (SPHysics). The details of the coupling procedure along with preliminary validation tests are presented. RÉSUMÉ Il est difficile d'étudier le processus de propagation des vagues depuis l'océan profond jusqu'au bord du rivage avec un seul modèle en raison de la présence de multiples échelles de temps et d'espace. Les modèles numériques basés sur les équations de Boussinesq sont bien connus pour propager correctement les vagues depuis une profondeur intermédiaire de l'eau jusqu'à la région proche du rivage. Comme ce sont des modèles 2D, ils sont informatiquement efficaces et peuvent être appliqués à l'étude de l'évolution des vagues sur de grands domaines. Les modèles numériques basés sur la formulation SPH peuvent intrinsèquement gérer des surfaces libres multiplement connexes, ils peuvent donc naturellement traiter les déferlements et permettre l'évaluation du runup et du déversement induits. On développe ici un modèle hybride (SPHunwave) qui combine les principaux avantages d'un modèle de Boussinesq (FUNWAVE) et d'un modèle SPH (SPHysics). Les détails du procédé de couplage sont présentés ainsi que les premiers tests de validation.

Numerical simulation of wave breaking over relatively mild sloping beaches is pursued in this study with the implementation of a modern promissory method called Smoothed Particle Hydrodynamics. Validation of the method is attempted through the use and calibration of a recent free academic 'open source' code called SPHysics. Its various assumptions and parameters are adjusted to simulate experimental results. An effort is undertaken to confirm its ability to capture the near-shore wave breaking and consequent bore formation dynamics in the surf/swash zone. Inherent and calibration defects of the model are highlighted and particular upgrading measures are suggested for oncoming research.

Dam break is one of the greatest hazards causing damages in urban and rural areas throughout the world. It can happen due to design and construction errors, heavy rainfall, earthquakes or glacier melting, among other reasons. Once the dam collapses, the resulting flow can become even worse due to obstacles, like houses, walls, bridges and trees, which can be impacted and transported along with the water. The prevention or reduction of the downstream effects of a dam break due to the complex and highly energized flow has been a challenge to researchers and engineers all over the world. The present study aimed to compare two free computer programs for numerical simulation of a flow with obstacles, based on available experimental data. These programs are based on the material point method (MPM) and smoothed particle hydrodynamics (SPH), respectively. The numerical results of the two programs were in good agreement with experimental data, although important differences in computing time were observed. Therefore, these methods seem to be potential tools for the prediction of dam-break flows.

An advanced and well-equipped Moving Particle Semi-implicit which is a Lagrangian method is employed to simulate hydrodynamic behaviour of water wave evolution. Unlike most recently developed MPS models that consider inviscid or laminar flow, the present developed model is based on the turbulent nature of the fluid flow. In order to consider the turbulence stresses, three turbulence closures are included in the model, which are constant eddy viscosity, mixing length and k-ε model. The developed model was applied to different case studies including wave run-up on an inclined wall, wave train induced by wavemaker and landslide-generated wave. The model results were compared with analytical, empirical and experimental data cited in the literature and a good agreement was found. The results also showed that deploying a turbulence model could improve the stability of the MPS model. Results obtained through this research reveal that the application of k-ε model in combination with MPS method produces accurate and reliable results in addition to a stable solution for free surface prediction in wave mechanics.

Non-breaking tsunami waves run-up on steep slopes can cause severe damages to coastal structures. The estimation of the wave run-up rate caused by tsunami waves are important to understand the performance and safety issues of the breakwater in practice. In this paper, an Incompressible Smoothed Particle Hydrodynamics method (ISPH) method was utilized for the 2DV numerical modeling of nonlinear wave run-up on steep slopes. SPH is a meshless method based on particles, which is capable of high accurate modeling of free surface flows with large deformations. In developed model, mass and momentum conservation equations were solved in a Lagrangian form using a two-step fractional method. In the first step, Navier-Stokes equations were solved to compute velocity components by omitting pressure term and in the absence of incompressible condition. In the second step, the continuity constraint was satisfied and the resulting Poisson equation was solved to calculate pressure terms. Velocity values were then corrected and surface positions were computed. In the present model, a new technique was applied to allocate density to the particles for the calculations. By employing this technique, ISPH model was stablized. The developed ISPH model was first validated by the solitary wave propagation on the constant water depth and the corresponding results showed good agreement with analytical results. The convergence of the method and the sensitivity of relevant model parameters were discussed. Then, validated model was used to study the run-up of solitary waves on steep slopes by considering a coastal breakwater for various wall steepnesses (i.e. 1:1, 2:1, 4:1, 8:1 and vertical wall).

Tsunamis produce a wealth of quantitative data that can be used to improve tsunami hazard awareness and to increase the
preparedness of the population at risk. These data also allow for a performance evaluation of the coastal infrastructure and
observations of sediment transport, erosion, and deposition. The interaction of the tsunami with coastal infrastructures and with
the movable sediment bed is a three-dimensional process. Therefore, for runup and inundation prediction, three-dimensional
numerical models must be employed. In this study, we have employed Smoothed Particle Hydrodynamics (SPH) to simulate
tsunami runup on idealized geometries for the validation and exploration of three-dimensional flow structures in tsunamis. We
make use of the canonical experiments for long-wave run-up for breaking and non-breaking waves. The results of our
study prove that SPH is able to reproduce the runup of long waves for different initial and geometric conditions. We have
also investigated the applicability and the effectiveness of different viscous terms that are available in the SPH literature.
Additionally, a new breaking criterion based on numerical experiments is introduced and its similarities and differences with
existing criteria are discussed.

Numerical simulation using computers or computational simulation has increasingly become a very important approach for solving complex practical problems in engineering and science. It translates a physical problem into a discrete set of mathematical description, recreates and solves the problem on a computer, and reveals phenomena virtually according to the requirements of the analysts.