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A multi-phase smoothed particle hydrodynamics (SPH) formulation in combination with a granular rheological model is applied to simulate the 2007 Chehalis Lake landslide and the subsequent tsunami. ...

This paper investigates the applicability of Smoothed Particle Hydrodynamics (SPH) for regular wave overtopping. The best practices for creating a 3-D wave simulation using SPH are investigated, fo...

In this work, the SPH method is used in 2D to evaluate the pump characteristics of free surface water waves above a submerged plate. The configuration considered here consists of an infinite wave t...

The turbulent plunging jet of a nearly incompressible fluid into a stagnant fluid is of great importance in many practical applications, especially for the engineering of hydropower. As an example, the dynamic load exerted by the impact of turbulent high-velocity jets into a pool must be estimated to evaluate the potential destabilization of a rock bed or dam's structure. Modelling plunging jets in the laboratory presents a challenge due to the complex two-phase environment, which requires models to be built at near-prototype scales. This paper deals with the application of a three-dimensional weakly compressible smoothed particle hydrodynamics (SPH) model to study a circular jet impinging into a water flat pool, at a near-prototype scale. To identify the level of reliability of the computed parameters, validation of the pool bottom pressures is carried out by comparison with existing experimental data. The self-similarity of the jet's centreline velocity is correctly reproduced and the computed maximum dynamic pressures near the stagnation point are reasonably accurate. The differences observed are mainly attributed to the non-consideration of the air phase.

We address the question of cosmogenic tsunamis, i.e., tsunamis due to the fall of an asteroid in the ocean, in particular on the Atlantic coasts of Europe. We apply Ward and Asphaug's method (Deep-Sea Res II 49:1073–1079, 2002) for assessing this probabilistic return period of tsunami waves, with simplifying assumptions allowing writing their results in the form of analytic formulae, some of them involving simple integrals to be computed by numerical quadrature. We also account for uncertainties, (still following Ward and Asphaug (Deep-Sea Res II 49:1073–1079, 2002) on a simplified line. An upper bound of continental shelf shoaling is estimated ad hoc. The influence of several parameters is also analyzed, in particular the effect of tide is briefly addressed.

A series of experiments were conducted in a wind-wave tank facility in Marseilles (France) to study the effects of preexisting swell conditions (represented by long mechanically-generated waves) on wind-wave growth with fetch. Both monochromatic and irregular (JONSWAP-type) long wave conditions with different values of wave steepness have been generated in the presence of a constant wind forcing, for several wind velocities. A spectral analysis of temporal wave signals combined with airflow measurements allowed to study the evolution of both wave systems with the aim of identifying the interaction mechanisms transportable to prototype scale. In particular, a specific method is used to separate the two wave systems in the measured bimodal spectra. In fetch-limited conditions, pure wind-wave growth is in accordance with anterior experiments, but differs from the prototype scale in terms of energy and frequency variations with fetch. Monochromatic long waves are shown to reduce the energy of the wind-waves significantly, as it was observed in anterior laboratory experiments. The addition of JONSWAP-type long waves instead results in a downshift of the wind-wave peak frequency but no significant energy reduction. Overall, it is observed that the presence of long waves affects the wind-wave energy and frequency variations with fetch. Finally, in the presence of JONSWAP-type long waves, variations of wind-wave energy and peak frequency with fetch appear in close agreement with the wind-wave growth observed at prototype scale both in terms of variations and nondimensional magnitude.

Overtopping of fluvial dikes occurs frequently during major floods and may lead to dike failure, with severe consequences in the protected areas. Mechanisms of fluvial dike breaching remain incompletely understood, while predicting the breach hydrograph is of paramount importance for the flood risk management.Here, we present a new series of laboratory experiments, in which the evolving 3D fluvial dike geometry was monitored in detail using the laser profilometry technique. The experimental setup extends over about 20 m by 7 m and accommodates a 15 m long main channel and a 7 m-long dike section. The facility is located at LNHE of EDF-R&D (France). The present study extends former experiments by Rifai et al. (2017, 2018), which were conducted with uniform coarse sand (d50 = 1.03 mm). In the new tests, various mixtures of coarse (d50 = 1.03 mm) and fine (d50 = 0.24 mm) sands were used as dike material (Rifai et al., 2020). The fraction of fine sand was varied systematically to assess its influence on the breaching process, specifically as regards the apparent cohesion.The experimental observations reveal that the frequency of breach slope collapse tends to decrease as the fraction of fine sand is increased; but the collapsing volumes become larger. Consequently, in the tested configurations, the addition of fine sand to the dike material has virtually no effect on the overall breaching dynamics, due to compensation between less frequent but larger collapsing material volumes. In the presentation, the relative importance of the effects will be discussed in comparison with other influencing parameters such as the main channel discharge, floodplain backwater effects and the dike geometry.All experimental data, including high resolution 3D dynamic models of the breach geometry, are publicly available online (Rifai et al., 2019).ReferencesRifai, I., Erpicum, S., Archambeau, P., Violeau, D., Pirotton, M., El kadi Abderrezzak, K., & Dewals, B. (2017). Overtopping induced failure of noncohesive, homogeneous fluvial dikes. Water Resources Research, 53(4), 3373-3386.Rifai, I., El kadi Abderrezzak, K., Erpicum, S., Archambeau, P., Violeau, D., Pirotton, M., & Dewals, B. (2018). Floodplain backwater effect on overtopping induced fluvial dike failure. Water Resources Research, 54(11), 9060-9073.Rifai, I., El kadi Abderrezzak, K., Erpicum, S., Archambeau, P., Violeau, D., Pirotton, M., & Dewals, B. (2019). Flow and detailed 3D morphodynamic data from laboratory experiments of fluvial dike breaching. Scientific data, 6(1), 53.Rifai, I., El kadi Abderrezzak, K., Hager, W.H., Erpicum, S., Archambeau, P., Violeau, D., Pirotton, M., & Dewals, B. (2020). Apparent cohesion effects on overtopping-induced fluvial dike breaching. Journal of Hydraulic Research. In press. https://doi.org/10.1080/00221686.2020.1714760.

Flow overtopping can lead to the initiation of breaching and failure of fluvial dikes, causing severe inundations and damage in the protected areas. For flood risk management and prevention, the ac...

The design of appurtenant structures for dams, such as spillways, is a complex task because of the turbulent high-velocity aerated nature of the flowing water. In previous years, physical m...

We present the system of linear equations to be solved to evaluate the reflection coefficient at a sponge layer boundary with damping forces ρ f S L = − ρ β u , where β is the sponge layer function. The case of 2D waves is discussed in details and different sponge layer functions are proposed. The linear system is solved using the finite element method (FEM) at low computational cost compared to the target simulations. This method should enable the design of efficient sponge layer for any full Navier–Stokes solvers. The linear model results solved with a FEM solver are compared here to SPH simulations with good agreement. The linear model is then used to determine the reflection coefficient for different power sponge functions, length and dissipation coefficient using the FEM solver. The linear model solved by a simple FEM solver can be used to evaluate the suitable dissipation coefficients for waves ranging from shallow to deep water for a given sponge layer length. The coefficient depends on the non-dimensional frequency for Ω = ω d / g 2 . A table of suitable parameters for different sponge layer functions is provided over a large range of non-dimensional frequency and sponge layer length. A 3D application of waves is also presented with 45° incidence angle.

An elastic-viscoplastic model (Ulrich, 2013) is combined to a multi-phase SPH formulation (Hu and Adams, 2006; Ghaitanellis et al., 2015) to model granular flows and non-cohesive sediment transport. The soil is treated as a continuum exhibiting a viscoplastic behaviour. Thus, below a critical shear stress (i.e. the yield stress), the soil is assumed to behave as an isotropic linear-elastic solid. When the yield stress is exceeded, the soil flows and behaves as a shear-thinning fluid. A liquid-solid transition threshold based on the granular material properties is proposed, so as to make the model free of numerical parameter. The yield stress is obtained from Drucker–Prager criterion that requires an accurate computation of the effective stress in the soil. A novel method is proposed to compute the effective stress in SPH, solving a Laplace equation. The model is applied to a two-dimensional soil collapse (Bui et al., 2008) and a dam break over mobile beds (Spinewine and Zech, 2007). Results are compared with experimental data and a good agreement is obtained.

A new semi-analytical solution is derived in a linear potential framework for simulating tsunami-like water waves caused by a dynamic sea ground deformation. The movement generating the tsunami is represented by a simplified model of the sea-floor displacement caused by a schematic seismic event. This displacement generalises the earlier work of Hammack (1973) and Todorovska and Trifunac (2001), in the sense that both the rise time ( t r ) in the vertical direction and the rupture propagation velocity ( v p ) in the horizontal direction are simultaneously included in the model. The influence of both parameters is investigated by applying the linear solution to a large range of parameter values. An analysis of the maximum amplitude of generated waves allows the identification of a resonance for no rise time ( t r ≈ 0 ) and a rupture propagation velocity close to the long wave celerity ( v p ≈ g h ), corroborating the resonance mechanism identified by Todorovska and Trifunac (2001). An empirical relationship is proposed to estimate the amplification factor as a function of the fault length. In a second step, an energetic ratio is defined representing the quantity of potential energy that is not taken into account properly when using the shallow water equations. The energetic ratio is estimated as the fraction of potential energy associated with wavelengths shorter than the long wave limit. This ratio is largest for rapid vertical motions, in particular in the vicinity of the resonant condition, suggesting that models based on the shallow water equations should not be used for these conditions. Numerical simulations using a nonlinear and dispersive wave propagation model are also performed, showing that the resonance effect still exists when nonlinear effects are included. Finally, the tsunami event of 1947 near New Zealand is analysed and shown to be close to the resonant condition, with seismic activity generating a free surface wave that could be much larger than the amplitude of the ground motion.

Accurate predictions of breach characteristics are necessary to reliably estimate the outflow hydrograph and the resulting inundation close to fluvial dikes. Laboratory experiments on the breaching of fluvial sand dikes were performed, considering a flow parallel to the dike axis. The breach was triggered by overtopping the dike crest. A detailed monitoring of the transient evolution of the breach geometry was conducted, providing key insights into the gradual and complex processes involved in fluvial dike failure. The breach develops in two phases: (1) the breach becomes gradually wider and deeper eroding on the downstream side along the main channel and (2) breach widening controlled by side slope failures, continuing in the downstream direction only. Increasing the inflow discharge in the main channel, the breach formation time decreases significantly and the erosion occurs preferentially on the downstream side. The downstream boundary condition has a strong influence on the breach geometry and the resulting outflow hydrograph.

We present a unified vision of the existing theoretical models for the turbulent plane jet, leading to new analytical profiles for scalar concentration and turbulent quantities, including a complete turbulent kinetic energy budget. Integrals of the budget terms are also computed. The present model is split into two variants. Both compare fairly well with referenced experimental data.

International audience; The numerical modelling of two-phase mixture flows with high density ratios (e.g. water/air) is challenging. Multiphase averaged models with volume fraction representation encompass a simple way of simulating such flows: mixture models with relative velocity between phases. Such approaches were implemented in SPH (Smoothed Particle Hydrodynamics) using a mass-weighted definition of the mixture velocity, but with limited validation. Instead, to handle high density ratios, a mixture model with a volumetric mixture velocity is developed in this work. To avoid conservation issues raised by the discretization of the relative material displacement contribution in the volume fraction equation, a formulation on phase volumes is derived following a finite volume reasoning. Conservativity, realizability, limit behaviour for single-phase flow are the leading principles of this derivation. Volume diffusion is added to prevent development of instabilities due to the colocated nature of SPH. This model is adapted to the semi-analytical SPH wall boundary conditions. Running on GPU, this approach is successfully applied to the separation of phases in a settling tank with low to high density ratios. An analytical solution on a two-phase mixture Poiseuille flow is also used to check the accuracy of the numerical implementation. Then, a Rayleigh-Taylor instability test case is performed to compare with multi-fluid SPH. Finally, a comparison with experimental and numerical data is made on a sand dumping case; this highlights some limits of this mixture model.

International audience; This paper presents the development and validation of a three-dimensional numerical wave tank devoted to studying wave-structure interaction problems. It is based on the fully nonlinear potential flow theory, here solved by a boundary element approach and using unstructured triangular meshes of the domain's boundaries. Time updating is based on a second-order explicit Taylor series expansion. The method is parallelized using the Message Passing Interface (MPI) in order to take advantage of multi-processor systems. For radiation problems, with cylindrical bodies moving in prescribed motion, the free-surface is updated with a fully Lagrangian scheme, and is able to reproduce reference results for nonlinear forces exerted on the moving body. For diffraction problems, semi-Lagrangian time-updating is used, and reproduces nonlinear effects for diffraction on monopiles. Finally, we study the nonlinear wave loads on a fixed semi-submersible structure, thereby illustrating the possibility to apply the proposed numerical model for the design of offshore structures and floaters.

Air entrainment within water is a common feature of flows over hydraulic works – spill over a dam, wave breaking on a dike, etc. – and its accurate modeling is a key to better design such structures. The Smoothed Particle Hydrodynamics (SPH) method appears as a natural way to model such highly distorted flows. To avoid computationally prohibitive costs related to the full discretization of bubbles or drops, a mixture model for high density ratio flows relying on a volume-based formulation with relative velocity between phases has first been developed and validated in Fonty et al. (Proceedings of 13th international SPHERIC workshop. Galway, Ireland, 2018; Int J Multiph Flow 111:158–174, 2019. https://doi.org/10.1016/j.ijmultiphaseflow.2018.11.007 ). Instead of having a once and for all assigned phase as in multifluid SPH, each particle now carries both phases through their respective volume fractions. In the present work, in order to handle practical air entrainment application cases, the open boundary formulation described in Ferrand et al. (Comput Phys Commun 210:29–44, 2017. https://doi.org/10.1016/j.cpc.2016.09.009 ) is adapted to this mixture model. Then, after introducing turbulence through a $$k{-}\epsilon$$ model, a specific closure on the air bubbles relative velocity is proposed including a Stokesian drag term and turbulent diffusion. This model is then applied to two cases of air entrainment: a stepped spillway for interfacial aeration and a plunging jet for local aeration. Finally a 3D industrial test case of discharge-control structure at the La Coche power plant (France) is considered. While valuable insights are obtained for the volume fraction field, further investigations are required to improve the modeling of the flow dynamics.

In this paper, the SPH (Smoothed Particle Hydrodynamics) method is applied to predict the flow features in dam spillways and energy dissipators. Two study cases were simulated using the 3D WCSPH co...

In order to address the question of the SPH (Smoothed Particle Hydrodynamics) Laplacian conditioning, a spectral analysis of this discrete operator is performed. In the case of periodic Cartesian particle network, the eigenfunctions and eigenvalues of the SPH Laplacian are found on theoretical grounds. The theory agrees well with numerical eigenvalues. The effects of particle disorder and non-periodicity conditions are then investigated from numerical viewpoint. It is found that the matrix condition number is proportional to the square of the particle number per unit length, irrespective of the space dimension and kernel choice.

Traditionally, the initialization of seismically generated tsunamis is done by setting the initial free surface deformation as identical to the final deformation of the sea floor. However, numerous effects are neglected through this method, in particular the dynamics of the sea floor deformation. Here, two temporal parameters characterizing the sea floor deformation are defined: the rise time tr (vertical motion) and the rupture velocity Vp (horizontal motion). These parameters have already been theoretically introduced by Hammack (1973) and Todorovska and Trifunac (2001), respectively. For a simplified and schematic motion of the sea floor using simultaneously both parameters, a theoretical linear analysis developed in Le Gal et al. (2017) showed a resonance phenomenon for which the amplitude of the generated wave becomes significantly larger than the amplitude of the sea floor deformation. This phenomenon concerns deformation with small rise times and rupture velocities close to the linear long wave velocity g h . The aim of the present study is to investigate the influence of a kinematic deformation, using both parameters, during historical tsunamis with numerical nonlinear shallow water simulations. This work corroborates Le Gal et al.’s theoretical schematic analysis. For this purpose, two events are studied: the March 1947 New Zealand and the 2011 Japan tsunamis.

This work aims at modelling buoyant, laminar or turbulent flows, using a 2D Incompressible Smoothed Particle Hydrodynamics (ISPH) model with accurate wall boundary conditions. The buoyancy effects are modelled through the Boussinesq approximation coupled to a heat equation, which makes it possible to apply an incompressible algorithm to compute the pressure field from a Poisson equation. Based on our previous work (Leroy et al., 2014), we extend the unified semi-analytical wall boundary conditions to the present model. The latter is also combined to a Reynolds-Averaged Navier-Stokes approach to treat turbulent flows. The k − turbulence model is used, where buoyancy is modelled through an additional term in the k − equations like in mesh-based methods. We propose a unified framework to prescribe isothermal (Dirichlet) or imposed heat flux (Neumann) wall boundary conditions in ISPH. To illustrate this, a theoretical case is presented (laminar heated Poiseuille flow), where excellent agreement with the theoretical solution is obtained. Several benchmark cases are then proposed: a lock-exchange flow, two laminar and one turbulent flow in differentially heated cavities, and finally a turbulent heated Poiseuille flow. Comparisons are provided with a Finite-Volume (FV) approach using an open-source industrial code.

International audience

We demonstrate the accuracy and convergence of a new numerical model solving wave-structure interactions based on the fully non-linear potential flow (FNPF) theory coupled to a rigid body motion approach. This work extends an earlier model proposed by Guerber et al. (Eng Anal Bound Elements 36(7):1151–1163, 2012), restricted to fully submerged structures, by allowing to solve for freely floating bodies on the free surface. Although we are currently extending the model to three dimensions (3D), the work reported here only considers two-dimensional (2D) problems. We first introduce the FNPF model, originally developed in 2D by Grilli et al. (Eng Anal Bound Elements 6(2):97–107, 1989), Grilli and Subramanya (Comput Mech 17(6):374–391, 1996), and later extended to 3D by Grilli et al. (Int J Numer Methods Fluids 35(7):829–867, 2001). We present the implementation by Guerber et al. (Eng Anal Bound Elements 36(7):1151–1163, 2012) in the 2D-FNPF model of van Daalen’s implicit method for fluid-structure interactions [see van Daalen (Numerical and theoretical studies of water waves and floating bodies, PhD thesis, Universiteit Twente, The Netherlands 1993) and Tanizawa (Proceedings of 4th Osaka colloquium on seakeeping performance of ships 2000)]. We then detail the numerical scheme used for coupling the FNPF model to the motion of a floating rigid body. Moreover, we propose a new numerical strategy for advancing the free surface front inspired by symplectic integrators, which achieves a much better performance for energy conservation. The developed algorithm is first applied to forced motion cases, for which analytical and experimental results can be found in the literature and used as benchmarks. The accuracy of the numerical solution for the fluid and applied forces is then discussed for cases with small or large amplitude motion. In the latter case, a preliminary investigation of non-linear effects is performed for the classical application of a semi-circular heaving cylinder, by comparing the computed hydrodynamic force to the experimental measurements of Yamashita (J Soc Nav Arch 141:61–70, 1977). In particular, the comparison of the magnitude of the force harmonics, up to the third order, shows the importance of simulating non-linear interactions, which become important as the ratio of the radius of the cylinder over the wavelength increases. In a second set of applications, we assess the model accuracy in dealing with freely floating bodies. As a first test case, we consider the decaying motion of a freely heaving horizontal circular cylinder released from a non-equilibrium position above the free surface. In this more demanding computations, we verify that total energy fluid-plus-body motion is well conserved, which confirms the accuracy of the fluid-structure interaction algorithm. As a second test case, we consider the free motion of a rectangular barge in waves and compute the first-order response amplitude operators.

This work aims at improving the 2-D incompressible SPH model (ISPH) by adapting it to the unified semi-analytical wall boundary conditions proposed by Ferrand et al. [10]. The ISPH algorithm considered is as proposed by Lind et al. [25], based on the projection method with a divergence-free velocity field and using a stabilising procedure based on particle shifting. However, we consider an extension of this model to Reynolds-Averaged Navier-Stokes equations based on the k-@e turbulent closure model, as done in [10]. The discrete SPH operators are modified by the new description of the wall boundary conditions. In particular, a boundary term appears in the Laplacian operator, which makes it possible to accurately impose a von Neumann pressure wall boundary condition that corresponds to impermeability. The shifting and free-surface detection algorithms have also been adapted to the new boundary conditions. Moreover, a new way to compute the wall renormalisation factor in the frame of the unified semi-analytical boundary conditions is proposed in order to decrease the computational time. We present several verifications to the present approach, including a lid-driven cavity, a water column collapsing on a wedge and a periodic schematic fish-pass. Our results are compared to Finite Volumes methods, using Volume of Fluids in the case of free-surface flows. We briefly investigate the convergence of the method and prove its ability to model complex free-surface and turbulent flows. The results are generally improved when compared to a weakly compressible SPH model with the same boundary conditions, especially in terms of pressure prediction.

Solid wall boundary conditions have been an area of active research within the context of Smoothed Particle Hydrodynamics (SPH) for quite a while. Ferrand et al. (Int. J. Numer. Methods Fluids 71(4), 446---472, 2012) presented a novel approach using a renormalization factor in the SPH approximation. The computation of this factor depends on an integral along the boundary of the domain and in their original paper Ferrand et al. gave an analytical formulation for the 2-D case using the Wendland kernel. In this paper the formulation will be extended to 3-D, again providing analytical formulae. Due to the boundary being two dimensional a domain decomposition algorithm needs to be employed in order to obtain special integration domains. For these the analytical formulae will be presented when using the Wendland kernel. The algorithm presented within this paper is applied to several academic test-cases for which either analytical results or simulations with other methods are available. It will be shown that the present formulation produces accurate results and provides a significant improvement compared to approximative methods.

This paper assesses some recent trends in the novel numerical meshless method smoothed particle hydrodynamics, with particular focus on its potential use in modelling free-surface flows. Due to its Lagrangian nature, smoothed particle hydrodynamics (SPH) appears to be effective in solving diverse fluid-dynamic problems with highly nonlinear deformation such as wave breaking and impact, multi-phase mixing processes, jet impact, sloshing, flooding and tsunami inundation, and fluid–structure interactions. The paper considers the key areas of rapid progress and development, including the numerical formulations, SPH operators, remedies to problems within the classical formulations, novel methodologies to improve the stability and robustness of the method, boundary conditions, multi-fluid approaches, particle adaptivity, and hardware acceleration. The key ongoing challenges in SPH that must be addressed by academic research and industrial users are identified and discussed. Finally, a roadmap is propose...

We show an application of the Smoothed Particle Hydrodynamics (SPH) method to the simulation of a fully three-dimensional dam-break with floating objects. The simulation is done using GPUSPH, an implementation of the SPH method in CUDA which has been recently extended including support for fully coupled fluid/solid interaction. Boundary conditions are computed using the unified semi-analytical model proposed by Ferrand et al. SPH is also used to compute the total force and torque acting on the floating objects, which are then used to integrate the motion of the objects.

Due to the Lagrangian nature of SPH, treating inlet/outlet boundaries (that are intrinsically Eulerian) is a challenging issue. An extension to the Unified Semi-Analytical boundary conditions is presented to deal with unsteady open boundaries in confined and free-surface flows. The presented method uses Riemann invariants to calculate flow properties near the open boundaries, thus allowing the possibility to treat complex shapes. Furthermore, details are presented for a parallel implementation of this method, including particle creation and deletion , updating properties of vertices and segments, and additional constraints on the time step. Simple validation cases are then displayed to illustrate the performance of the proposed method as well as the ability to deal with complex problems such as generation of water waves and free outlets.