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The accuracy and reliability of sediment transport models is crucial for understanding and predicting geomorphological changes in river systems, which can have important implications for conserving riverine ecosystem. This information can be used to make better informed decisions about the management of the river, as well as to predict and prepare for potential hazards such as flash flooding. In the past, various approaches have been used to model these processes for suspended and bedload sediment transport. However, many of these models have limitations including spatial and temporal scales, data requirements, model complexity, numerical stability and computational cost, particularly when it comes to simulating the transport of bedload sediments.In this study, we tried to address these limitations by testing a 2D weakly coupled numerical model for bedload transport in a real application. The model was implemented by adopting schemes presented in previous works (Vacondio et al. 2014, doi.org/10.1016/j.envsoft.2014.02.003; Juez et al. 2014, doi.org/10.1016/j.advwatres.2014.05.014). The advantage of using a weakly coupled model is that it is flexible, computationally efficient and can be used to simulate bedload transport in large-scale systems while producing consistent and reliable results over time. It is based on the finite-volume method and uses the Shallow water and Exner equations for the liquid and solid phases, respectively. High computational efficiency is guaranteed by parallelization on Graphics Processing Units.We selected the case study of the Baganza River (Italy), characterized by a catchment area of 228 km2 and a total length of 55 km. We focused on the 28 km-long stretch between Calestano and Parma, with an average slope in the order of 0.8-1.5% and grain sizes in the order of 2-30 mm. For the topography, we used high-resolution digital elevation model (DEM) from 2008, while grain size distribution data were obtained through a hybrid technique combining field sediment sampling and photogrammetry. The adopted approach for the characterization of fluvial sediments at different points along the river is desirable in order to accommodate the full range of particle sizes inside the riverbed. The inflow boundary condition is the 2008-2014 series of floods on the Baganza River, including a destructive flood that occurred in October 2014.The riverbed topography resulting from the numerical simulation was compared with the one extracted from the DEM provided by a LiDAR survey carried out after the October 2014 event. The overall fair agreement between measured and simulated results suggests the usefulness of 2D weakly coupled numerical model for simulating hydro-geomorphological processes in the Baganza River. Moreover, the hybrid technique adopted for the grain characterization provides realistic representation of the sediments and increases the accuracy and reliability of the model predictions.

This paper shows a detailed, advanced procedure to implement cost–benefit analyses (CBAs) in order to assess the effectiveness of flood mitigation measures. The town of Lodi (North of Italy) has been selected as a case study for the research work, as it was hit by a large flood in 2002 for which several data are available. In order to compute the benefits, in terms of avoided damage with the mitigation measure in place, micro-scale damage models developed within the Flood-IMPAT + project were used. The great amount of input data for such models comes from results of a two-dimensional river modelling, for what concern the hazard parameters, and from open-source database, to evaluate the vulnerability and the exposure of the hit area. The research highlights that technological-advanced, high-performance hydraulic models allow taking into account a variety of hazard scenarios, with reasonable computational time, supporting the proper accounting of the probabilistic nature of risk in CBAs. Nonetheless, such high-resolution tools support the implementation of micro-scale damage assessment models, which can provide information on the distribution of benefits in the investigated area, increasing the effectiveness of CBAs for policy making.

This article presents a multi-GPU implementation of a Finite-Volume solver on a multi-resolution grid. The implementation completely offloads the computation to the GPUs and communications between different GPUs are implemented by means of the Message Passing Interface (MPI) API. Different domain decomposition techniques have been considered and the one based on the Hilbert Space Filling Curves (HSFC) showed optimal scalability. Several optimizations are introduced: One-to-one MPI communications among MPI ranks are completely masked by GPU computations on internal cells and a novel dynamic load balancing algorithm is introduced to minimize the waiting times at global MPI synchronization barriers. Such algorithm adapts the computational load of ranks in response to dynamical changes in the execution time of blocks and in network performances; Its capability to converge to a balanced computation has been empirically shown by numerical experiments. Tests exploit up to 64 GPUs and 83M cells and achieve an efficiency of 90 percent in weak scalability and 85 percent for strong scalability. The framework is general and the results of the article can be ported to a wide range of explicit 2D Partial Differential Equations solvers.

Real-time river flood forecasting models can be useful for issuing flood alerts and reducing or preventing inundations. To this end, machine-learning (ML) methods are becoming increasingly popular thanks to their low computational requirements and to their reliance on observed data only. This work aimed to evaluate the ML models’ capability of predicting flood stages at a critical gauge station, using mainly upstream stage observations, though downstream levels should also be included to consider backwater, if present. The case study selected for this analysis was the lower stretch of the Parma River (Italy), and the forecast horizon was extended up to 9 h. The performances of three ML algorithms, namely Support Vector Regression (SVR), MultiLayer Perceptron (MLP), and Long Short-term Memory (LSTM), were compared herein in terms of accuracy and computational time. Up to 6 h ahead, all models provided sufficiently accurate predictions for practical purposes (e.g., Root Mean Square Error &lt, 15 cm, and Nash-Sutcliffe Efficiency coefficient &gt, 0.99), while peak levels were poorly predicted for longer lead times. Moreover, the results suggest that the LSTM model, despite requiring the longest training time, is the most robust and accurate in predicting peak values, and it should be preferred for setting up an operational forecasting system.

In the present work, a porosity-based numerical scheme for the Shallow Water Equations is presented. With the aim of accounting for the presence of storage areas, such as gardens, yards and dead zones, and for preferential flow pathways, both an isotropic storage porosity parameter and anisotropic friction are adopted. Particularly, the anisotropic effects due to the building alignments are evaluated defining conveyance porosities along principal directions and using them to express the friction losses in tensor form. The storage and conveyance porosities are evaluated from the geometry of the urban layout at a district scale and then assigned to computational cells rather than to cell sides, thus avoiding oversensitivity to the mesh design. The proposed formulation guarantees the C-property also in presence of wet-dry fronts. Model testing is performed analyzing schematic and idealized urban layouts, and against experimental data as well. The results obtained by the proposed anisotropic scheme are similar to a high-resolution model with resolved buildings, also in the presence of low-friction regimes, meanwhile with a remarkable reduction of the computational times.

A novel formulation for the diffusive term in the continuity equation is proposed to improve the stability of smoothed particle hydrodynamics weakly compressible scheme avoiding the introduction of empirical parameters. Densities at particle-particle interface have been computed by means of a first-order consistent total variational diminishing reconstruction and a one-dimensional Roe’s approximate Riemann solver is applied to add the correct amount of diffusion. Results of numerical tests also demonstrate that the proposed method is able to guarantee consistency both inside the fluid and close to the free surface. Furthermore, a numerical analysis of several flux limiter functions has been conducted, finding that the choice of this function is a critical point to guarantee the accuracy of the method. It has been assessed, through the monitoring of the internal energy, that the van Albada limiter is more effective in dissipating spurious density fluctuations.

An open boundary algorithm for weakly compressible Smoothed particle hydrodynamics (WCSPH) numerical models is presented. Open boundary conditions are implemented by means of buffer regions whereby physical quantities are either imposed or extrapolated from the fluid region using a first-order accurate SPH interpolation. A unique formulation has been developed which can be used for inflow, outflow, and mixed open boundary conditions. The extrapolation process from the fluid domain encompasses quantities such as velocity, density, pressure and also free-surface elevation. The algorithm has been parallelized for both CPU and general-purpose on graphics processing units (GPGPU) and it has been tested against the 2-D reference solutions of flow past a cylinder and open channel flow. Finally, its capability to simulate 2-D and 3-D complex flows such as water waves and flow past a surface-piercing extraterrestrial submarine is demonstrated.

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.

Dynamic boundary conditions (DBC) for solid surfaces are standard in the weakly compressible smoothed particle hydrodynamics (SPH) code DualSPHysics. A stationary solid is simply represented by fixed particles with pressure from the equation of state. Boundaries are easy to set up and computations are relatively stable and efficient, providing robust numerical simulation for complex geometries. However, a small unphysical gap between the fluid and solid boundaries can form, decreasing the accuracy of pressures measured on the boundary. A method is presented where the density of solid particles is obtained from ghost positions within the fluid domain by linear extrapolation. With this approach, the gap between fluid and boundary is reduced and pressures in still water converge to hydrostatic, including the case of a bed with a sharp corner. The violent free-surface cases of a sloshing tank and dam break impact on an obstacle show pressures measured directly on solid surfaces in close agreement with experiments. The complex 3-D flow in a fish pass, with baffles to divert the flow, is simulated showing close agreement with measured water levels with weirs open and gates closed, but less close with gates open and weirs closed. This indicates the method is suitable for rapidly varying free-surface flows, but development for complex turbulent flows is necessary. The code with the modified dynamic boundary condition (mDBC) is available in DualSPHysics to run on CPUs or GPUs. Engineering and Physical Sciences Research Council | Ref. EP/P510579/1 Xunta de Galicia | Ref. ED431C 2017/64 Ministerio de Economía y Competitividad | Ref. WELCOME ENE2016-75074-C2-1-R Ministerio de Ciencia, Innovación y Universidades | Ref. IJCI-2017-32592 Ministero dell’Istruzione, dell’Università e della Ricerca | Ref. RBSI14R1GP Mexican CONACYT-SENER Hidrocarburos | Ref. B-S-69926

The capability of a GPU-parallelized numerical scheme to perform accurate and fast simulations of surface runoff in watersheds, exploiting high-resolution digital elevation models (DEMs), was investigated. The numerical computations were carried out by using an explicit finite volume numerical scheme and adopting a recent type of grid called Block-Uniform Quadtree (BUQ), capable of exploiting the computational power of GPUs with negligible overhead. Moreover, stability and zero mass error were ensured, even in the presence of very shallow water depth, by introducing a proper reconstruction of conserved variables at cell interfaces, a specific formulation of the slope source term and an explicit discretization of the friction source term. The 2D shallow water model was tested against two different literature tests and a real event that recently occurred in Italy for which field data is available. The influence of the spatial resolution adopted in different portions of the domain was also investigated for the last test. The achieved low ratio of simulation to physical times, in some cases less than 1:20, opens new perspectives for flood management strategies. Based on the result of such models, emergency plans can be designed in order to achieve a significant reduction in the economic losses generated by flood events.

With the aim of improving resilience to flooding and increasing preparedness to face levee-breach-induced inundations, this paper presents a methodology for creating a wide database of numerically simulated flooding scenarios due to embankment failures, applicable to any lowland area protected by river levees. The analysis of the detailed spatial and temporal flood data obtained from these hypothetical scenarios is expected to contribute both to the development of civil protection planning and to immediate actions during a possible future flood event (comparable to one of the available simulations in the database) for which real-time modelling may not be feasible. The most relevant criteria concerning the choice of mathematical model, grid resolution, hydrological conditions, breach parameters and locations are discussed in detail. The proposed methodology, named RESILIENCE, is applied to a 1100 km2 pilot area in northern Italy. The creation of a wide database for the study area is made possible thanks to the adoption of a GPU-accelerated shallow-water numerical model which guarantees remarkable computational efficiency (ratios of physical to computational time up to 80) even for high-resolution meshes (2.5–5 m) and very large domains (>1000 km2).

In this paper a novel methodology to estimate the unknown discharge hydrograph at the entrance of a river reach, where no information is available, is presented. The methodology is obtained by coupling an optimization procedure, based on the Bayesian Geostatistical Approach (BGA), with a forward self-developed 2D hydraulic model of the stream. In order to accurately describe the flow propagation in real rivers characterized by large floodable areas, the forward model solves the 2D Shallow Water Equations by means of a Finite Volume explicit shock-capturing algorithm. The forward code exploits the computational power of Graphics Processing Units (GPUs) achieving ratio of physical to computational time up to 1000. With the aim of enhancing the computational efficiency of the inverse estimation, the Bayesian technique is parallelized developing a procedure based on the Secure Shell (SSH) protocol which allows to take advantage of remote High Performance Computing clusters (including those available on the Cloud) equipped with GPUs. The capability of the coupled models is assessed estimating irregular and synthetic inflow hydrographs in real river reaches, taking into account also the presence of downstream corrupted observations. Finally, the capability to adopt this methodology for real cases is demonstrated by reconstructing a real flood wave in a river reach located in Northern Italy.

In the simulation of flooding events, mesh refinement is often required to capture local bathymetric features and/or to detail areas of interest; however, if an explicit finite volume scheme is adopted, the presence of small cells in the domain can restrict the allowable time step due to the stability condition, thus reducing the computational efficiency. With the aim of overcoming this problem, the paper proposes the application of a Local Time Stepping (LTS) strategy to a GPU-accelerated 2D shallow water numerical model able to handle non-uniform structured meshes. The algorithm is specifically designed to exploit the computational capability of GPUs, minimizing the overheads associated with the LTS implementation. The results of theoretical and field-scale test cases show that the LTS model guarantees appreciable reductions in the execution time compared to the traditional Global Time Stepping strategy, without compromising the solution accuracy.

In this paper, two emerging strategies for the reduction of the computational time of 2D large-scale flood simulations are compared, with the aim of evaluating their strengths and limitations and of suggesting guidelines for their effective application. The analysis is based on two state-of-the-art raster flood models with different governing equations and parallelization strategies: PARFLOOD, a GPU-accelerated code that solves the fully dynamic shallow water equations, and LISFLOOD-FP, which combines a parallel implementation for CPU with simplified equations (local-inertial approximation). The results of two case studies (a river flood propagation, and a lowland inundation) suggest that, at coarse grid resolutions, the parallelized simplified model LISFLOOD-FP can represent a good alternative to fully dynamic models in terms of accuracy and runtime, while the GPU-parallel code PARFLOOD is more efficient in case of high-resolution simulations with millions of cells, despite the greater complexity of the numerical scheme.

A novel augmented Riemann Solver capable of handling porosity discontinuities in 1D and 2D Shallow Water Equation (SWE) models is presented. With the aim of accurately approximating the porosity source term, a Generalized Riemann Problem is derived by adding an additional fictitious equation to the SWEs system and imposing mass and momentum conservation across the porosity discontinuity. The modified Shallow Water Equations are theoretically investigated, and the implementation of an augmented Roe Solver in a 1D Godunov-type finite volume scheme is presented. Robust treatment of transonic flows is ensured by introducing an entropy fix based on the wave pattern of the Generalized Riemann Problem. An Exact Riemann Solver is also derived in order to validate the numerical model. As an extension of the 1D scheme, an analogous 2D numerical model is also derived and validated through test cases with radial symmetry. The capability of the 1D and 2D numerical models to capture different wave patterns is assessed against several Riemann Problems with different wave patterns.

This paper presents the development of a new boundary treatment for free-surface hydrodynamics using the smoothed particle hydrodynamics (SPH) method accelerated with a graphics processing unit (GPU). The new solid boundary formulation uses a local uniform stencil (LUST) of fictitious particles that surround and move with each fluid particle and are only activated when they are located inside a boundary. This addresses the issues currently affecting boundary conditions in SPH, namely the accuracy, robustness and applicability while being amenable to easy parallelization such as on a GPU. In 3-D, the methodology uses triangles to represent the geometry with a ray tracing procedure to identify when the LUST particles are activated. A new correction is proposed to the popular density diffusion term treatment to correct for pressure errors at the boundary. The methodology is applicable to complex arbitrary geometries without the need of special treatments for corners and curvature is presented. The paper presents the results from 2-D and 3-D Poiseuille flows showing convergence rates typical for weakly compressible SPH. Still water in a complex 3-D geometry with a pyramid demonstrates the robustness of the technique with excellent agreement for the pressure distributions. The method is finally applied to the SPHERIC benchmark of a dry-bed dam-break impacting an obstacle showing satisfactory agreement and convergence for a violent flow. EPSRC, Reino Unido | Ref. EP/L014890/1 Ministry of Education, Universities and Research, Italia | Ref. RBSI14R1GP Xunta de Galicia | Ref. ED431C 2017/64 Ministerio de Economía y Competividad | Ref. ENE2016-75074-C2-1-R

With the aim of improving resilience to flooding and increasing preparedness to face levee breach-induced inundations, this paper presents a methodology to create a wide database of numerically simulated flooding scenarios due to embankment failures, applicable to any lowland area protected by river levees. The analysis of the detailed spatial and temporal flood data obtained from these hypothetical scenarios is expected to contribute both to the development of civil protection planning, and to immediate action during a possible future flood event (comparable to one of the available simulations in the database), for which a real-time simulation may not be feasible. The most relevant criteria concerning the choice of the mathematical model, the grid resolution, the hydrological conditions, the breach parameters and locations are discussed in detail. Results of the application of the proposed methodology to a 1,100 km2-pilot area in Northern Italy are presented. The creation of a wide database for the study area is made possible thanks to the adoption of a GPU-accelerated shallow water numerical model, which guarantees a great computational efficiency (ratios of physical to computational time up to 80) even for high-resolution meshes (2.5–5 m) and large domains.

As smoothed particle hydrodynamics (SPH) becomes increasingly popular for complex flow analysis the need to improve efficiency particularly for 3-D problems is becoming greater. Automatic adaptivity with variable particle size is therefore desirable. In this paper, a novel 3-D splitting and coalescing algorithm is developed which minimizes density error while conserving both mass and momentum using a variational principle. Accuracy is increased in refined areas unaffected by coarser particle distributions elsewhere. For particle splitting, the key criteria are the number of split (daughter) particles, their distribution, spacing and kernel size. Four different splitting arrangements are investigated including a cubic stencil with 8 particles, a cubic stencil with an additional 6 located at the face centres, an icosahedron-shaped arrangement with 14 particles, and a dodecahedron-shaped arrangement with 20 particles where particles are located at the vertices. The error analysis also examines whether retaining a particle at the centre of the arrangement is necessary revealing that regardless of the stencil adopted, to minimize the density error a daughter particle should be placed at the same position of the original particle. The optimum configuration is found to be the icosahedron-shaped arrangement while commonly used smoothing kernels such as the cubic and quintic splines and Wendland produce similar density errors, so that the optimal refinement stencil is effectively independent of the kernel choice. A new 3-D coalescing scheme completes the algorithm such that the particle resolution can be either increased or reduced locally. The SPH splitting and coalescing scheme, is tested with Poiseuille flow showing negligible loss of convergence accuracy in the refined area and the lid driven cavity for a wide range of Reynolds number showing good agreement with reference solutions again with local accuracy defined by particle distribution.

In the present work, a novel DOT ADER numerical solver capable of handling porosity and bottom discontinuities in the framework of the 1D porous Shallow Water Equations (SWEs) is presented. In order to ensure the preservation of the water at rest condition, a new set of well-balanced governing equations based on the isotropic porosity parameter is derived. The effects exerted by the bed slope and porosity variation source terms are accurately accounted for inside the Riemann solver: to this purpose, an augmented Riemann problem is created by adding two fictitious equations stating the invariance of porosity and bottom in time to the SWEs system. With the aim of computing the non-conservative fluxes, which in the augmented system replace the original source terms, meanwhile ensuring robustness, stability and accuracy, a novel approximate numerical scheme, based on the entropy-satisfying DOT family, is introduced. The extension of the novel Riemann solver, which strictly conserves mass, to a second order of accuracy in both space and time is addressed in the ADER framework. The fulfillment of the C-property condition (i.e. the exact preservation of an initial quiescent flow) in the presence of a discontinuous porosity field and over a non-flat bottom with abrupt variation is theoretically proved and numerically verified. The capability of the proposed numerical scheme to simulate some Riemann problems developing across porosity discontinuities and bed steps is finally assessed.

Flood propagation in rivers is strongly influenced by the presence of bridges and other hydraulic structures. Among the available approaches for including these elements in numerical models, the adoption of Internal Boundary Conditions (IBC), given its ability to capture backwater, is suitable for field-scale analyses for flood hazard assessment. In this paper, the implementation of internal boundary conditions in the two-dimensional shallow water code named “PARFLOOD” is presented. The application to experimental and real test cases shows that the proposed IBC model can handle both low and high flow conditions for bridges, while being flexible for other types of structures (e.g. flow-through dams). Moreover, the model is computationally efficient (physical/computational time ratio around 20–30 for domains with ~106 cells), thanks to the code parallelization on GPU.

This contribution is concerned with a novel, purely methodological strategy enabling to automatically adjust the local spatial resolution in Smoothed Particle Hydrodynamics (SPH). It is built upon the fact that the accuracy of the SPH interpolation is related to zeroth- and first-order moments. Ensuing from this knowledge, a suitable measure of the SPH spatial discretization error has been derived. Using this measure as an adaptivity criterion allows to dynamically adjust the local resolution in such a way that a uniform distribution of the spatial discretization error over the model domain is achieved. This is demonstrated in the present paper. To that end, the theoretical foundation of the proposed adaptivity criterion is discussed first. After that, its applicability to both SPH fluid and solid simulations is thoroughly examined.

The capability of a GPU-parallelized numerical scheme to produce accurate and fast simulations of floodings induced by levee breaches in large domains, adopting high-resolution digital terrain maps, is investigated. The good predictive skills of the presented 2D shallow-water model were proven with regard to the inundation caused by a levee breach that occurred on the Secchia River, Italy, in January 2014. The numerical computations were carried out on a domain of about 180 km2 adopting a Cartesian grid of approximately 7.2 M cells with size 5 m. The results of the simulation were validated against several field data and observations, including a high-resolution synthetic aperture radar image. A ratio of simulation to physical times of about 1/15 was achieved; this kind of simulation tool opens up new perspectives in the devising and implementing of flood event management strategies for civil protection purposes and with the aim of minimizing the economic loss.

In this paper, a new method to impose 2-D solid wall boundary conditions in smoothed particle hydrodynamics is presented. The wall is discretised by means of a set of virtual particles and is simulated by a local point symmetry approach. The extension of a previously published modified virtual boundary particle (MVBP) method guarantees that arbitrarily complex domains can be readily discretised guaranteeing approximate zeroth and first-order consistency. To achieve this, three important new modifications are introduced: (i) the complete support is ensured not only for particles within one smoothing length distance, h, from the boundary but also for particles located at a distance greater than h but still within the support of the kernel; (ii) for a non-uniform fluid particle distribution, the fictitious particles are generated with a uniform stencil (unlike the previous algorithms) that can maintain a uniform shear stress on a particle-moving parallel to the wall in a steady flow; and (iii) the particle properties (density, mass and velocity) are defined using a local point of symmetry to satisfy the hydrostatic conditions and the Cauchy boundary condition for pressure. The extended MVBP model is demonstrated for cases including hydrostatic conditions for still water in a tank with a wedge and for curved boundaries, where significant improved behaviour is obtained in comparison with the conventional boundary techniques. Finally, the capability of the numerical scheme to simulate a dam break simulation is also shown. Copyright © 2015 John Wiley & Sons, Ltd.

DualSPHysics is a hardware accelerated Smoothed Particle Hydrodynamics code developed to solve free-surface flow problems. DualSPHysics is an open-source code developed and released under the terms of GNU General Public License (GPLv3). Along with the source code, a complete documentation that makes easy the compilation and execution of the source files is also distributed. The code has been shown to be efficient and reliable. The parallel power computing of Graphics Computing Units (GPUs) is used to accelerate DualSPHysics by up to two orders of magnitude compared to the performance of the serial version. Program summary Program title: DualSPHysics Catalogue identifier: AEUS_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEUS_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU General Public License No. of lines in distributed program, including test data, etc.: 121,399 No. of bytes in distributed program, including test data, etc.: 12,324,308 Distribution format: tar.gz Programming language: C++ and CUDA. Computer: Tested on CPU Intel X5500 and GPUs: GTX 480, GTX 680, Tesla K20 and GTX Titan. Operating system: Any system with a C++ and NVCC compiler, tested on Linux distribution Centos 6.5 CUDA: Tested on versions 4.0, 4.1, 4.2, 5.0 and 5.5 with driver version 331.38. Has the code been vectorised or parallelised?: Different threads of CPU or number of cores of GPU. RAM: Tens of MB to several GB, depending on problem Classification: 4.12. Nature of problem: The DualSPHysics code has been developed to study free-surface flows requiring high computational cost. Solution method: DualSPHysics is an implementation of Smoothed Particle Hydrodynamics, which is a Lagrangian meshless particle method. Running time: 6 h on 8 processors of Intel X5500 (15 min on GTX Titan) for the dam-break case with 1 million particles simulating 1.5 s of physical time (more than 26,000 steps).

A 3D numerical modeling of the wave generated by the Vajont slide, one of the most destructive ever occurred, is presented in this paper. A meshless Lagrangian Smoothed Particle Hydrodynamics (SPH) technique was adopted to simulate the highly fragmented violent flow generated by the falling slide in the artificial reservoir. The speed-up achievable via General Purpose Graphic Processing Units (GP-GPU) allowed to adopt the adequate resolution to describe the phenomenon. The comparison with the data available in literature showed that the results of the numerical simulation reproduce satisfactorily the maximum run-up, also the water surface elevation in the residual lake after the event. Moreover, the 3D velocity field of the flow during the event and the discharge hydrograph which overtopped the dam, were obtained.

In this paper an adaptive algorithm for Smoothed Particle Hydrodynamics (SPH) for the Shallow Water Equations (SWEs) is presented. The area of a particle is inversely proportional to depth giving poor resolution in small depths without particle refinement. This is a particular limitation for flooding problems of interest here. Higher resolution is created by splitting the particles, while particle coalescing (or merging) improves efficiency by reducing the number of the particles when acceptable. The new particle coalescing procedure merges two particles together if their area becomes less than a predefined threshold value. Both particle splitting and coalescing procedures conserve mass and momentum and the smoothing length of new particles is calculated by minimizing the density error of the SPH summation. The new dynamic particle refinement procedure is assessed by testing the numerical scheme against analytical, experimental and benchmark test cases. The analytical cases show that with particle splitting and coalescing typical convergence rates remain faster than linear. For the practical test case, in comparison to using particle splitting alone, the particle coalescing procedure leads to a significant reduction of computational time, by a factor of 15. This makes the computational time of the same order as mesh-based methods with the advantage of not having to specify a mesh over a flood domain of unknown extent a priori.

In this paper a novel variable resolution method using particle splitting and coalescing for the SPH numerical solution of the Navier–Stokes equations is presented. The key idea of the scheme is to modify dynamically the particle sizes by means of splitting and coalescing (merging) individual particles to provide good resolution only where it is needed. The SPH scheme adopted is derived using the variational principle guaranteeing that both mass and momentum are conserved for particles with different smoothing lengths. A particle shifting procedure is used to prevent unacceptable anisotropic distributions of the particles and is further generalized for treating domains with variable mass particles. The algorithm has been tested against analytical solutions for Poiseuille and Taylor–Green flows showing that the shifting algorithm is effective in increasing the accuracy, and that error introduced by the splitting and coalescing is negligible. The capability of the numerical scheme for increasing efficiency is shown for more general problems: the simulations of a moving square in a box and flow past a cylinder have shown that the particle refinement procedure is able to increase the efficiency while maintaining the same level of accuracy as a uniform distribution with the most refined resolution.

A smoothed particle hydrodynamics (SPH) numerical model for shallow water equations (SWEs) is presented for simulating flood inundation owing to rapidly varying flow, such as dam breaks, tsunamis, and levee breaches. Important theoretical and numerical developments have recently been made, and the model in this paper incorporates these developments and implements open boundary conditions, resulting in a general, accurate computational tool suitable for practical application. The method is attractive for flood simulation over large domains in which the extent of inundation is unknown because computation is carried out only in wet areas and is dynamically adaptive. The open boundary algorithm is very general, on the basis of a simplified version of the characteristics method, handling both supercritical and subcritical inflow and outflow. This is tested against reference solutions for flows over a hump involving shocks. The model is then applied to two very different flood inundations resulting from...

In this paper, a smoothed particle hydrodynamics (SPH) numerical model for the shallow water equations (SWEs) with bed slope source term balancing is presented. The solution of the SWEs using SPH is attractive being a conservative, mesh-free, automatically adaptive method without special treatment for wet-dry interfaces. Recently, the capability of the SPH-SWEs numerical scheme with shock capturing and general boundary conditions has been used for predicting practical flooding problems. The balance between the bed slope source term and fluxes in shallow water models is desirable for reliable simulations of flooding over bathymetries where discontinuities are present and has received some attention in the framework of Finite Volume Eulerian models. The imbalance because of the source term resulting from the calculation of the the water depth is eradicated by means of a corrected mass, which is able to remove the error introduced by a bottom discontinuity. Two different discretizations of the momentum equation are presented herein: the first one is based on the variational formulation of the SWEs in order to obtain a fully conservative formulation, whereas the second one is obtained using a non-conservative form of the free-surface elevation gradient. In both formulations, a variable smoothing length is considered. Results are presented demonstrating the corrections preserve still water in the vicinity of either 1D or 2D bed discontinuities and provide close agreement with 1D analytical solutions for rapidly varying flows over step changes in the bed. The method is finally applied to 2D dam break flow over a square obstacle where the balanced formulation improves the agreement with experimental measurements of the free surface. ?? 2012 John Wiley & Sons, Ltd.

The solution for the shallow water equations using smoothed particle hydrodynamics is attractive, being a mesh-free, automatically adaptive method without special treatment for wetdry interfaces. However, the relatively new method is limited by the variable kernel size or smoothing length being inversely proportional to water depth causing poor resolution at small depths. Boundary conditions at solid walls have also not been well resolved. To solve the resolution problem in small depths, a particle splitting procedure was developed (conveniently into seven particles), which conserves mass and momentum by varying the smoothing length, velocity and acceleration of each refined particle. This improves predictions in the shallowest depths where the error associated with splitting is reduced by one order of magnitude in comparison to other published works. To provide good shock capturing behaviour, particle interactions are treated as a Riemann problem with Monotone Upstream-centred Scheme for Conservation Laws (MUSCL) reconstruction providing stability. For solid boundaries, the recent modified virtual boundary particle method was developed further to enable the zeroth moment to be accurately conserved where the smoothing length of particles is changing rapidly during particle splitting. The resulting method is applied to the one-dimensional and the two-dimensional axisymmetric wet-bed dam break problems showing close agreement with analytical solutions, demonstrating the need for particle splitting. To demonstrate wetting and drying in a more complex case, the scheme is applied to oscillating water in a two-dimensional parabolic basin and produces good agreement with the analytical solution. The method is finally applied to the European Concerted Action on DAm break Modelling dam-break test case representative of realistic conditions and good predictions are made of experimental measurements with a 40% reduction in the computational time when particle splitting is employed. The overall method has thus become quite sophisticated but its generality and versatility will be attractive for various shallow water problems.

SUMMARY smoothed particle hydrodynamics; boundary conditions; shallow water equations; source terms; virtual boundary particles; still waterIn this paper, an approximate modified virtual boundary particle method (MVBP) for solid boundary conditions in a two-dimensional (2-D) smoothed particle hydrodynamics (SPH) model is presented; this is a development of the original VBP method recently proposed by Ferrari et al. (Comput. Fluids 2009; 38(6): 1203–1217). The aim is to maintain the zeroth moment of the kernel function as closely as possible to unity, a property referred to as zero-consistency, for particles close to solid boundaries. The performance of the new method in approximating zero-consistency in the presence of complicated boundaries is demonstrated where we show that the MVBP method improves the accuracy of the zeroth moment by almost an order of magnitude. Shallow-water flows are an important two-dimensional (2-D) application and provide the simple test case of still water. The shallow-water equations (SWEs) are thus considered in SPH form and the zero-consistency approximation is tested for still water in domains with different boundaries: a circle and two squares, one with an additional internal angle of 300∘ and one with four internal angles of 345∘. We demonstrate that for an internal angle of 300∘, the MVBP method demonstrates numerical convergence to still-water conditions whereas both mirror particles and the VBP method cannot. The method is also demonstrated for the dynamic case of a circular dam break interacting with an outer circular wall where conventional mirror particles fail to prevent particles passing through the solid wall. The SPH SWEs are further generalized through a new method for discretizing the bed source term allowing arbitrarily complicated bathymetries. The resulting formulation is tested by considering many different bed shapes in still water: submerged and surface-piercing humps, a submerged step, a submerged and surface-piercing parabolic bed. Copyright © 2011 John Wiley & Sons, Ltd.

In this work, we present a reverse flow routing procedure, which allows estimating discharge hydrographs at upstream ungauged stations by means of information available at downstream monitored sites. The reverse routing problem is solved adopting a Bayesian Geostatistical Approach (BGA). In order to capture the complex hydrodynamic field typical of many real cases of rivers including large floodable areas, meanwhile overcoming the computational time limitations, we adopted as forward model a selfdeveloped 2D-SWE parallel numerical model (PARFLOOD) that allows achieving ratio of physical to computational time of about 500-1000. To exploit the computational capabilities of modern GPU cluster, a parallel procedure to estimate the Jacobian matrix required by the BGA approach has been implemented. The inflow hydrograph in a river reach with several meanders and floodplains has been estimated in “only” 13 hours using a HPC cluster with 10 P100 Nvidia GPUs.

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.