# SPH Modeling of Water-Related Natural Hazards

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Two-Phase Coupled Dynamics

#### 2.1. Scouring and Sediment Transport

_{s}, and a magnification factor, η, representing the numerical parameters to be tuned. When the apparent viscosity is lower than the maximum viscosity, the sediment is treated as a non-Newtonian fluid of Bingham type and solid particles are set in motion with constant viscosity μ

_{s}(green curve in Figure 1). The strategy of introducing an upper viscosity limit for the sediment was also followed in [51] in the WCSPH simulation of complex problems in the field of marine engineering; below this maximum limit, the work in [51] adopted a variable apparent viscosity calculated through the M–C theory for the soil phase. The SH critical condition does not require the introduction of a numerical threshold for the viscosity of the solid phase. However, in [7], both the M–C and SH approaches require tuning of the mechanical parameters of the bottom sediment such as the angle of internal friction, φ, and sediment viscosity, μ

_{s}, that became numerical parameters to fit the experimental eroded profile. This may be not be practical when calibration data are not available for the investigated problem.

_{s}of the solid (granular) phase and is characteristic of bed-load transport and fast landslides (see also Section 2.2). In the frictional regime, the mixture (or apparent) viscosity, μ, is calculated as a weighted sum of the pure fluid viscosity μ

_{f}, and the frictional viscosity μ

_{fr}, the latter being evaluated on the basis of the mean effective stress σ’

_{m}, angle of internal friction φ, and the second invariant I

_{2}of the rate of the deformation tensor of the sediment. The frictional viscosity increases as the shear rate tends to zero, in accordance with the pseudo-plastic rheological behavior (dashed blue curve in Figure 1). To avoid the unbounded growth of apparent viscosity of the mixture, a threshold (or maximum) viscosity μ

_{max}is introduced with a physical meaning. Threshold viscosity acts when approaching the zero shear rate; mixture particles with an apparent viscosity higher than the threshold viscosity are considered in the elastic–plastic regime of soil deformation where the kinetic energy of solid particles is relatively small and the frictional regime of the packing limit in the KTGF does not apply. For these reasons, the threshold viscosity is assigned to those particles that are excluded from the SPH computation (continuous red curve in Figure 1; below μ

_{max}, the red curve coincides with the dashed blue curve of the pseudoplastic model). The excluded particles represent a fixed boundary with suitable values of the relevant physical properties and are included in the neighbor list of the nearby moving particle. The value of the threshold viscosity does not require tuning or calibration, but it should be selected for the specific problem; the value assigned to the threshold viscosity is the higher value that does not influence the numerical results significantly. Further increase of the value assigned to the threshold viscosity only affects the computational time because it determines an increase in the maximum value that can be assumed by the apparent mixture viscosity during the computation. The relationship between the mixture viscosity and the time step value that assures the stability of the adopted explicit time-stepping scheme is given by Equation 2.33 in [8]. When the numerical stability of the time integration scheme is dominated by the viscous criterion, the threshold viscosity reduces the computational time.

_{HBP}of the sediment:

_{c}in the HBP model was evaluated in two different calibration procedures depending on the erosion criterion that holds for modeling the yielding mechanism of sediment. The qualitative representation of Equation (1) with n < 1 is denoted by the blue dashed curve in Figure 1.

_{bcr}, replacing the yield stress parameter τ

_{c}, in the HBP model.

_{y}, replacing the yield stress parameter, τ

_{c}, in the HBP model to be defined to determine the apparent viscosity for the sediment.

_{v}, computed for an interface particle as the ratio of the sediment particle volume to the total particle volume within the interaction domain. The onset of suspended transport is determined by c

_{v}falling below the threshold value of 0.3 and the suspended sediment viscosity is computed through [54] the experimental colloidal equation, which is more simple to implement with respect to the piece-wise function adopted in [51]. The density of suspended particles is computed by solving the mass balance equation. Even if, in some cases, the percentage gap between the experimental and numerically predicted maximum scouring depth is significant, it can be seen that the scour process is affected by several random factors and therefore reliable predictions of scouring effects are quite difficult to obtain, even with experimental modeling. The sediment dynamics models based on a synthetic rheological law (e.g., [6]) assume the same rheological behavior for the bed-load transport (frictional regime of KTGF), suspension for dense granular flows (kinetic-collisional regime of KTGF),a and suspension for diluted granular flows (kinetic regime of KTGF). This feature provides advantages and drawbacks with respect to KTGF-based sediment dynamics models (e.g., [8]). The model of [6] can reproduce several sediment transport regimes (not only bed-load transport), but is not coherent with KTGF, some parameters require tuning procedures, and non-transported granular material (e.g., landslides) is not treated.

^{3}has been suggested for the reasonable initial density of the TWPs based on studies of bottom sediment movement. Figure 2 shows that the proposed ISPH model can simulate the real-time processes of the 2D overflow induced scouring. The detailed comparisons between numerical and experimental data can be found in [2].

#### 2.2. Fast Landslides and Dense Granular Flows Interacting with Water

_{2}of the rate of deformation tensor; K, μ

_{0}, and μ

_{∞}are three constant parameters that can be conveniently related to common Bingham rheological parameters, namely the yield stress τ

_{B}and viscosity μ

_{B}. From a physical point of view, μ

_{0}and μ

_{∞}denote the viscosity at very low and very high shear rate, respectively. In order to avoid numerical divergence caused by the unbounded growth of effective viscosity as the shear rate approaches zero, μ

_{eff}is limited to a suitably high threshold value, which is set to μ

_{0}= 103μ

_{B}to assure convergence. The test cases simulated in work in [63] considered the flow on inclined surfaces and analyzed the role of the Froude number [65] during the propagation phase, which may be helpful in designing the control works.

_{0}, referred to as limiting viscosity. The effect of limiting viscosity arises in the frictional regime at low deformation rates near the transition zone to the elastic–plastic regime: in this shear rate interval, a constant value μ

_{0}(lower than μ

_{max}) is assigned to the mixture viscosity (see red dot-dashed curve in Figure 1), thus reducing the computational time in the case where the viscous criterion dominates the numerical stability of the time integration scheme. There are other alternative approaches to keep control of computational time in the simulation of high-viscosity flows. In the work of [73], a semi-implicit integration scheme was proposed to overcome the severe time-stepping restrictions caused by the WCSPH explicit integration scheme when simulating highly viscous fluids, as in the case of lava flow with thermal-dependent rheology. According to this approach, only the viscous part of the momentum equation is solved implicitly, thus saving computational time and obtaining an improved quality of the results with respect to the fully explicit scheme.

_{0}, reaching a reasonable compromise with consumed computational time. This test case is provided as tutorial number 35 in the documentation of SPHERA v.9.0.0 that is freely available in [76].

## 3. Flooding in Complex Topography with the Transport of Sediments

## 4. High Performance Computing Solutions for Complex Hydraulic Engineering Problems

## 5. Conclusions and Future Perspectives

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Wang, D.; Shao, S.; Li, S.; Shi, Y.; Arikawa, T.; Zhang, H. 3D ISPH erosion model for flow passing a vertical cylinder. J. Fluids Struct.
**2018**, 78, 374–399. [Google Scholar] [CrossRef] - Wang, D.; Shaowu, L.; Arikawa, T.; Gen, H. ISPH Simulation of Scour Behind Seawall Due to Continuous Tsunami Overflow. Coast. Eng. J.
**2016**, 58, 1650014. [Google Scholar] [CrossRef] - Wang, C.; Peng, C.; Meng, X. Smoothed Particle Hydrodynamics Simulation of Water-Soil Mixture Flows. J. Hydraul. Eng.
**2016**, 142, 04016032. [Google Scholar] [CrossRef] - Guandalini, R.; Agate, G.; Manenti, S.; Sibilla, S.; Gallati, M. SPH Based Approach toward the Simulation of Non-cohesive Sediment Removal by an Innovative Technique Using a Controlled Sequence of Underwater Micro-explosions. Procedia IUTAM
**2015**, 18, 28–39. [Google Scholar] [CrossRef] - Guandalini, R.; Agate, G.; Manenti, S.; Sibilla, S.; Gallati, M. Innovative numerical modeling to investigate local scouring problems induced by fluvial structures. In Proceedings of the Sixth International Conference on Bridge Maintenance, Safety and Management (IABMAS 2012), Stresa, Italy, 8–12 July 2012; pp. 3110–3116. [Google Scholar]
- Zubeldia, E.H.; Fourtakas, G.; Rogers, B.D.; Farias, M.M. Multi-phase SPH model for simulation of erosion and scouring by means of the shields and Drucker–Prager criteria. Adv. Water Resour.
**2018**, 117, 98–114. [Google Scholar] [CrossRef] - Manenti, S.; Sibilla, S.; Gallati, M.; Agate, G.; Guandalini, R. SPH simulation of sediment flushing induced by a rapid water flow. J. Hydraul. Eng.
**2012**, 138, 272–284. [Google Scholar] [CrossRef] - Amicarelli, A.; Kocak, B.; Sibilla, S.; Grabe, J. A 3D smoothed particle hydrodynamics model for erosional dam-break floods. Int. J. Comput. Fluid Dyn.
**2017**, 31, 413–434. [Google Scholar] [CrossRef] - Manenti, S.; Amicarelli, A.; Todeschini, S. WCSPH with Limiting Viscosity for Modeling Landslide Hazard at the Slopes of Artificial Reservoir. Water
**2018**, 10, 515. [Google Scholar] [CrossRef] - Tan, H.; Chen, S. A hybrid DEM-SPH model for deformable landslide and its generated surge waves. Adv. Water Resour.
**2017**, 108, 256–276. [Google Scholar] [CrossRef] - Shi, C.; An, Y.; Wu, Q.; Liu, Q.; Cao, Z. Numerical simulation of landslide-generated waves using a soil–water coupling smoothed particle hydrodynamics model. Adv. Water Resour.
**2016**, 92, 130–141. [Google Scholar] [CrossRef] - Viroulet, S.; Sauret, A.; Kimmoun, O.; Kharif, C. Granular collapse into water: Toward tsunami landslides. J. Vis.
**2013**, 16, 189–191. [Google Scholar] [CrossRef] - Capone, T.; Panizzo, A.; Monaghan, J.J. SPH modeling of water waves generated by submarine landslides. J. Hydraul. Res.
**2010**, 48, 80–84. [Google Scholar] [CrossRef] - Bordoni, M.; Meisina, C.; Valentino, R.; Bittelli, M.; Chersich, S. Site-specific to local-scale shallow landslides triggering zones assessment using TRIGRS. Nat. Hazards Earth Syst. Sci.
**2015**, 15, 1025–1050. [Google Scholar] [CrossRef][Green Version] - Zizioli, D.; Meisina, C.; Valentino, R.; Montrasio, L. Comparison between different approaches to modeling shallow landslide susceptibility: A case history in Oltrepo Pavese, Northern Italy. Nat. Hazards Earth Syst. Sci.
**2013**, 13, 559–573. [Google Scholar] [CrossRef] - Ray, R.; Deb, K.; Shaw, A. Pseudo-Spring smoothed particle hydrodynamics (SPH) based computational model for slope failure. Eng. Anal. Bound. Elem.
**2019**, 102, 139–148. [Google Scholar] [CrossRef] - Gu, S.; Zheng, X.; Ren, L.; Xie, H.; Huang, Y.; Wei, J.; Shao, S. SWE-SPHysics Simulation of Dam Break Flows at South-Gate Gorges Reservoir. Water
**2017**, 9, 387. [Google Scholar] [CrossRef] - Barreiro, A.; Domínguez, J.M.; Crespo, A.J.C.; González-Jorge, H.; Roca, D.; Gómez-Gesteira, M. Integration of UAV photogrammetry and SPH modeling of fluids to study runoff on real terrains. PLoS ONE
**2014**, 9, e111031. [Google Scholar] [CrossRef] - Vacondio, R.; Mignosa, P.; Pagani, S. 3D SPH numerical simulation of the wave generated by the Vajont rock slide. Adv. Water Res.
**2013**, 59, 146–156. [Google Scholar] [CrossRef] - Qiu, L.C.; Liu, Y.; Han, Y. A 3D Simulation of a Moving Solid in Viscous Free-Surface Flows by Coupling SPH and DEM. Math. Probl. Eng.
**2017**, 2017, 1–7. [Google Scholar] [CrossRef] - Albano, R.; Sole, A.; Mirauda, D.; Adamowski, J. Modeling large floating bodies in urban area flash-floods via a Smoothed Particle Hydrodynamics model. J. Hydrol.
**2016**, 541, 344–358. [Google Scholar] [CrossRef] - Amicarelli, A.; Albano, R.; Mirauda, D.; Agate, G.; Sole, A.; Guandalini, R. A smoothed particle hydrodynamics model for 3D solid body transport in free surface flows. Comput. Fluids
**2015**, 116, 205–228. [Google Scholar] [CrossRef] - Lu, N.; Godt, J. Hillslope Hydrology and Stability; Cambridge University Press: New York, NY, USA, 2013. [Google Scholar]
- Iverson, R.M. Landslide triggering by rain infiltration. Water Resour. Res.
**2000**, 36, 1897–1910. [Google Scholar] [CrossRef][Green Version] - Iverson, R.M. The physics of debris flows. Rev. Geophys.
**1997**, 35, 245–296. [Google Scholar] [CrossRef][Green Version] - Inam, A.; Adamowski, J.; Prasher, S.; Halbe, J.; Malard, J.; Albano, R. Coupling of a distributed stakeholder-built system dynamics socio-economic model with SAHYSMOD for sustainable soil salinity management—Part 1: Model development. J. Hydrol.
**2017**, 55, 596–618. [Google Scholar] [CrossRef] - Shao, S. Incompressible smoothed particle hydrodynamics simulation of multi-fluid flows. Int. J. Numer. Meth. Fluids
**2012**, 69, 1715–1735. [Google Scholar] [CrossRef] - Manenti, S. Standard WCSPH for free-surface multi-phase flows with a large density ratio. Int. J. Ocean Coast. Eng.
**2018**, 1. [Google Scholar] [CrossRef] - Colagrossi, A.; Landrini, M. Numerical simulation of interfacial ows by smoothed particle hydrodynamics. J. Comput. Phys.
**2003**, 191, 448–475. [Google Scholar] [CrossRef] - Hu, X.Y.; Adams, N.A. An incompressible multi-phase SPH method. J. Comput. Phys.
**2007**, 227, 264–278. [Google Scholar] [CrossRef] - Grenier, N.; Antuono, M.; Colagrossi, A.; le Touzé, D.; Alessandrini, B. An Hamiltonian interface SPH formulation for multi-fluid and free-surface flows. J. Comput. Phys.
**2009**, 228, 380–393. [Google Scholar] [CrossRef] - Monaghan, J.J.; Ashkan, R. A simple SPH algorithm for multi-fluid ow with high density ratios. Int. J. Numer. Methods Fluids
**2013**, 71, 537–561. [Google Scholar] [CrossRef] - Bouscasse, B.; Colagrossi, A.; Marrone, S.; Souto-Iglesias, A. SPH modelling of viscous flow past a circular cylinder interacting with a free surface. Comput. Fluids
**2017**, 146, 190–212. [Google Scholar] [CrossRef] - Hamill, L. Bridge Hydraulics; E&FN Spon: New York, NY, USA, 1999. [Google Scholar]
- Persi, E.; Petaccia, G.; Fenocchi, A.; Manenti, S.; Ghilardi, P.; Sibilla, S. Hydrodynamic coefficients of yawed cylinders in open-channel flow. Flow Meas. Instrum.
**2019**, 65, 288–296. [Google Scholar] [CrossRef] - Dordoni, S.; Malerba, P.; Sgambi, L.; Manenti, S. Fuzzy reliability assessment of bridge piers in presence of scouring. In Proceedings of the 5th International Conference on Bridge Maintenance, Safety and Management, Philadelphia, PA, USA, 11–15 July 2010; pp. 1388–1395. [Google Scholar]
- Sumer, B.M.; Fredsøe, J. The Mechanics of Scour in the Marine Environment; Advanced Series on Ocean Engineering; World Scientific Publishing Company: Singapore, 2002; Volume 17. [Google Scholar]
- Whitehouse, R.J.S. Scour at Marine Structures; Thomas Telford: London, UK, 1998. [Google Scholar]
- Wang, D.; Arikawa, T.; Li, S.W.; Gen, H. Numerical Simulation on Scour behind Seawall due to Tsunami Overflow. In Proceedings of the Coastal Structures & Solutions to Coastal Disasters Joint Conference, Boston, MA, USA, 9–11 September 2015; ASCE: Reston, VA, USA, 2015. [Google Scholar]
- Li, S.W.; Wang, D. Tsunami occurrences in China and numerical simulation of a supposed tsunami process in Bohai Sea. In Proceedings of the China Ocean Engineering, Dailian, China, August 2013; pp. 490–496. Available online: http://cpfd.cnki.com.cn/Article/CPFDTOTAL-HYGC201308001076.htm (accessed on 30 August 2013).
- Sugano, T.; Nozu, A.; Kohama, E.; Shimosako, K.; Kikuchi, Y. Damage to coastal structures. Soils Found.
**2014**, 54, 883–901. [Google Scholar] [CrossRef][Green Version] - Takahashi, H.; Sassa, S.; Morikawa, Y.; Takano, D.; Maruyama, K. Stability of caisson-type breakwater foundation under tsunami-induced seepage. Soils Found.
**2014**, 54, 789–805. [Google Scholar] [CrossRef][Green Version] - Nakamura, T.; Mizutani, N. Sediment Transport Calculation Considering Laminar and Turbulent Resistance Forces Caused by Infiltration/Exfiltration and its Application to Tsunami-induced Local Scouring. J. Offshore Mech. Arct. Eng.
**2013**, 136, 011105. [Google Scholar] [CrossRef] - Oie, T.; Dong, W.; Takatani, T.; Araki, K.; Shaowu, L.; Goto, H.; Arikawa, T. Numerical simulation of scouring behind the seawall caused by tsunami overflow with accurate ISPH method. Jpn. Soc. Civ. Eng.
**2015**, 71, 253–258. (In Japanese) [Google Scholar] - Ettema, R.; Kirkil, G.; Muste, M. Similitude of large-scale turbulence in experiments on local scour at cylinders. J. Hydraul. Eng.
**2006**, 132, 33–40. [Google Scholar] [CrossRef] - Sun, P.N.; Colagrossi, A.; Marrone, S.; Antuono, M.; Zhang, A.M. Multi-resolution Delta-plus-SPH with tensile instability control: Towards high Reynolds number flows. Comput. Phys. Commun.
**2018**, 224, 63–80. [Google Scholar] [CrossRef] - Zhang, A.; Sun, P.; Ming, F. An SPH modeling of bubble rising and coalescing in three dimensions. Comput. Methods Appl. Mech. Eng.
**2015**, 294, 189–209. [Google Scholar] [CrossRef] - Ming, F.R.; Sun, P.N.; Zhang, A.M. Numerical investigation of rising bubbles bursting at a free surface through a multiphase SPH model. Meccanica
**2017**, 52, 2665–2684. [Google Scholar] [CrossRef] - Ran, Q.; Tong, J.; Shao, S.; Fu, X.; Xu, Y. Incompressible SPH scour model for movable bed dam break flows. Adv. Water Resour.
**2015**, 82, 39–50. [Google Scholar] [CrossRef][Green Version] - Gotoh, H.; Ikari, H.; Memita, T.; Sakai, T. Lagrangian Particle Method for Simulation of Wave Overtopping on a Vertical Seawall. Coast. Eng. J.
**2005**, 47, 157–181. [Google Scholar] [CrossRef] - Ulrich, C.; Leonardi, M.; Rung, T. Multi-physics SPH simulation of complex marine-engineering hydrodynamic problems. Ocean Eng.
**2013**, 64, 109–121. [Google Scholar] [CrossRef] - Crespo, A.J.C.; Domínguez, J.M.; Rogers, B.D.; Gómez-Gesteira, M.; Longshaw, S.; Canelas, R.; Vacondio, R.; Barreiro, A.; García-Feal, O. DualSPHysics: Open-source parallel CFD solver based on smoothed particle hydrodynamics (SPH). Comput. Phys. Commun.
**2015**, 187, 204–216. [Google Scholar] [CrossRef] - Fourtakas, G.; Rogers, B.D. Modeling multi-phase liquid-sediment scour and resuspension induced by rapid flows using Smoothed Particle Hydrodynamics (SPH) accelerated with a Graphics Processing Unit (GPU). Adv. Water Resour.
**2016**, 92, 186–199. [Google Scholar] [CrossRef] - Vand, V. Viscosity of solutions and suspensions. I. Theory. J. Phys. Colloid Chem.
**1948**, 52, 277–299. [Google Scholar] [CrossRef] [PubMed] - Todeschini, S. Trends in long daily rainfall series of Lombardia (Northern Italy) affecting urban stormwater control. Int. J. Climatol.
**2012**, 32, 900–919. [Google Scholar] [CrossRef] - Todeschini, S.; Papiri, S.; Ciaponi, C. Placement Strategies and Cumulative Effects of Wet-weather Control Practices for Intermunicipal Sewerage Systems. Water Resour. Manag.
**2018**, 32, 2885–2900. [Google Scholar] [CrossRef] - Stancanelli, L.M.; Peres, D.J.; Cancelliere, A.; Foti, E. A combined triggering-propagation modeling approach for the assessment of rainfall induced debris flow susceptibility. J. Hydrol.
**2017**, 550, 130–143. [Google Scholar] [CrossRef][Green Version] - Baum, R.L.; Savage, W.Z.; Godt, J.W. TRIGRS—A FORTRAN Program for Transient Rainfall Infiltration and Grid-Based Regional Slope-Stability Analysis, Version 2.0; U.S. Geological Survey: Reston, VA, USA, 2008.
- O’Brien, J. Flo-2d User’s Manual, version 2006.01; flo-2d Software. Inc.: Nutrioso, AZ, USA, 2006. [Google Scholar]
- Dai, F.C.; Lee, C.F.; Ngai, Y.Y. Landslide risk assessment and management: An overview. Eng. Geol.
**2002**, 64, 65–87. [Google Scholar] [CrossRef] - Pastor, M.; Haddad, B.; Sorbino, G.; Cuomo, S.; Drempetic, V. A depth-integrated, coupled SPH model for flow-like landslides and related phenomena. Int. J. Numer. Anal. Methods Geomech.
**2009**, 33, 143–172. [Google Scholar] [CrossRef] - Pastor, M.; Quecedo, M.; González, E.; Herreros, I.; Merodo, J.A.F.; Mira, P. A simple approximation to bottom friction for Bingham fluid depth integrated models. J. Hydraul. Eng.
**2004**, 130, 149–155. [Google Scholar] [CrossRef] - Rendina, I.; Viccione, G.; Cascini, L. Kinematics of flow mass movements on inclined surfaces. Theor. Comput. Fluid Dyn.
**2019**, 33, 107–123. [Google Scholar] [CrossRef] - Shao, S.; Lo, E.Y.M. Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface. Adv. Water Resour.
**2003**, 26, 787–800. [Google Scholar] [CrossRef] - Albano, R.; Craciun, I.; Mancusi, L.; Sole, A.; Ozunu, A. Flood damage assessment and uncertainity analysis: the case study of 2006 flood in Ilisua Basin in Romania. Carpath. J. Earth. Environ. Sci.
**2017**, 2, 12. [Google Scholar] - Di Risio, M.; Bellotti, G.; Panizzo, A.; de Girolamo, P. Three-dimensional experiments on landslide generated waves at a sloping coast. Coast. Eng.
**2009**, 56, 659–671. [Google Scholar] [CrossRef] - Panizzo, A.; de Girolamo, P.; di Risio, M.; Maistri, A.; Petaccia, A. Great landslide events in Italian artificial reservoirs. Nat. Hazards Earth Syst. Sci.
**2005**, 5, 733–740. [Google Scholar] [CrossRef][Green Version] - Fritz, H.M.; Hager, W.H.; Minor, H.E. Lituya Bay case: Rockslide impact and wave run-up. Sci. Tsunami Hazards
**2001**, 19, 3–22. [Google Scholar] - Marrone, S.; Antuono, M.; Colagrossi, A.; Colicchio, G.; le Touzé, D.; Graziani, G. δ-SPH model for simulating violent impact flows. Comput. Methods Appl. Mech. Eng.
**2011**, 200, 1526–1542. [Google Scholar] [CrossRef] - Heinrich, P. Nonlinear water waves generated by submarine and aerial landslides. J. Waterw. Port Coast. Ocean Eng.
**1992**, 118, 249–266. [Google Scholar] [CrossRef] - Xu, W.J.; Dong, X.Y.; Ding, W.T. Analysis of fluid-particle interaction in granular materials using coupled SPH-DEM method. Powder Technol.
**2019**, 353, 459–472. [Google Scholar] [CrossRef] - Canelas, R.B.; Dominiguez, J.M.; Crespo, A.J.C.; Gomez-Gesteira, M.; Ferreira, R.M.L. Resolved Simulation of a granular-fluid flow with a coupled SPH-DCDEM model. J. Hydraul. Eng.
**2017**, 143, 6017012. [Google Scholar] [CrossRef] - Zago, V.; Bilotta, G.; Hérault, A.; Dalrymple, R.A.; Fortuna, L.; Cappello, A.; Ganci, G.; del Negro, C. Semi-implicit 3D SPH on GPU for lava flows. J. Comp. Phys.
**2018**, 375, 854–870. [Google Scholar] [CrossRef] - Manenti, S.; Pierobon, E.; Gallati, M.; Sibilla, S.; D’Alpaos, L.; Macchi, E.; Todeschini, S. Vajont Disaster: Smoothed Particle Hydrodynamics Modeling of the Postevent 2D Experiments. J. Hydraul. Eng.
**2016**, 142, 5015007. [Google Scholar] [CrossRef] - Amicarelli, A.; Manenti, S.; Albano, R.; Agate, G.; Paggi, M.; Longoni, L.; Mirauda, D.; Ziane, L.; Viccione, G.; Todeschini, S.; et al. SPHERA v.9.0.0: A Computational Fluid Dynamics research code, based on the Smoothed Particle Hydrodynamics mesh-less method. Comput. Phys. Commun.
**2019**. submitted. [Google Scholar] - SPHERA v.9.0.0 (RSE SpA). Available online: https://github.com/AndreaAmicarelliRSE/SPHERA (accessed on 21 February 2019).
- Aristodemo, F.; Merignolo, D.D.; Groenenboom, P.; Schiavo, A.L.; Veltri, P.; Veltri, M. Assessment of Dynamic Pressures at Vertical and Perforated Breakwaters through Diffusive SPH Schemes. Math. Probl. Eng.
**2015**, 2015, 1–10. [Google Scholar] [CrossRef] - Chauchat, J.; Médale, M. A three-dimensional numerical model for incompressible two-phase flow of a granular bed submitted to a laminar shearing flow. Comput. Methods Appl. Mech. Eng.
**2010**, 199, 439–449. [Google Scholar] [CrossRef][Green Version] - Fraccarollo, L.; Capart, H.; Zech, Y. A Godunov method for the computation of erosional shallow water transients. Int. J. Numer. Meth. Fluids
**2003**, 41, 951–976. [Google Scholar] [CrossRef] - Soares-Frazão, S.; Zech, Y. Experimental study of dam-break flow against an isolated obstacle. J. Hydraul. Res.
**2007**, 45 (Suppl. 1), 27–36. [Google Scholar] [CrossRef] - Lin, P.; Wu, Y.; Bai, J.; Lin, Q. A numerical study of dam-break flow and sediment transport from a quake lake. J. Earthq. Tsunami
**2011**, 5, 401–428. [Google Scholar] [CrossRef] - Wu, W.; Jiang, E.; China, P.R.; Wang, S.S. Depth-averaged 2-D calculation of flow and sediment transport in the lower Yellow River. Int. J. River Basin Manag.
**2004**, 2, 51–59. [Google Scholar] [CrossRef] - Armstrong, L.; Gu, S.; Luo, K. Study of wall-to-bed heat transfer in a bubbling fluidised bed using the kinetic theory of granular flow. Int. J. Heat Mass Transf.
**2010**, 53, 4949–4959. [Google Scholar] [CrossRef] - GDAL (OSGEO). Available online: https://github.com/OSGeo/gdal (accessed on 16 April 2019).
- DEM2xyz (RSE SpA). Available online: https://github.com/AndreaAmicarelliRSE/DEM2xyz (accessed on 16 April 2019).
- Paraview (Kitware). Available online: https://github.com/Kitware/ParaView (accessed on 16 April 2019).
- Grid Interpolator (RSE SpA). Available online: https://github.com/AndreaAmicarelliRSE/Grid_Interpolator (accessed on 16 April 2019).
- SRTM3/DTED1 (USGS). Available online: http://earthexplorer.usgs.gov/ (accessed on 16 April 2019).
- Baker, M.; Buyya, R. Cluster Computing at a Glance. In High Performance Cluster Computing—Architectures and Systems; Prentice Hall PTR: Upper Saddle River, NJ, USA, 1999; pp. 3–47. [Google Scholar]
- Nickolls, J.; Buck, I.; Garland, M.; Skadron, K. Scalable Parallel Programming with CUDA. Queue GPU Comput.
**2008**, 6, 40–53. [Google Scholar] [CrossRef][Green Version] - Nickolls, J.; Dally, W.J. The GPU computing era. IEEE Micro
**2010**, 30, 56–69. [Google Scholar] [CrossRef] - Monaghan, J.J. Smoothed particle hydrodynamics. Ann. Rev. Astronom. Astrophys.
**1992**, 30, 543–574. [Google Scholar] [CrossRef] - Koshizuka, S.; Oka, Y. Moving Particle Semi-Implicit Method for Fragmentation of Incompressible Fluid. Nucl. Sci. Eng.
**1996**, 123, 421–434. [Google Scholar] [CrossRef] - Viccione, G.; Bovolin, V.; Carratelli, E.P. Defining and optimizing algorithms for neighbouring particle identification in SPH fluid simulations. Int. J. Numer. Methods Fluids
**2008**, 58, 625–638. [Google Scholar] [CrossRef] - Domínguez, J.M.; Crespo, A.J.C.; Gómez-Gesteira, M.; Marongiu, J.C. Neighbour lists in smoothed particle hydrodynamics. Int. J. Numer. Methods Fluids
**2011**, 67, 2026–2042. [Google Scholar] [CrossRef] - Winkler, D.; Rezavand, M.; Rauch, W. Neighbour lists for smoothed particle hydrodynamics on GPUs. Comput. Phys. Commun.
**2018**, 225, 140–148. [Google Scholar] [CrossRef] - Wang, D.; Zhou, Y.; Shao, S. Efficient Implementation of Smoothed Particle Hydrodynamics (SPH) with Plane Sweep Algorithm. Commun. Comput. Phys.
**2016**, 19, 770–800. [Google Scholar] [CrossRef] - Xia, X.; Liang, Q. A GPU-accelerated smoothed particle hydrodynamics (SPH) model for the shallow water equations. Environ. Model. Softw.
**2016**, 75, 28–43. [Google Scholar] [CrossRef] - Gonnet, P. Efficient and Scalable Algorithms for Smoothed Particle Hydrodynamics on Hybrid Shared/Distributed-Memory Architectures. SIAM J. Sci. Comput.
**2014**, 37, C95–C121. [Google Scholar] [CrossRef] - Joselli, M.; Junior, J.R.d.; Clua, E.W.; Montenegro, A.; Lage, M.; Pagliosa, P. Neighborhood grid: A novel data structure for fluids animation with GPU computing. J. Parallel Distrib. Comput.
**2015**, 75, 20–28. [Google Scholar] [CrossRef] - Wenbo, C.; Yao, Y.; Zhang, Y. Performance analysis of parallel smoothed particle hydrodynamics on multi-core CPUs. In Proceedings of the 2014 International Conference on Cloud Computing and Internet of Things, Changchun, China, 13–14 December 201.
- Nishiura, D.; Furuichi, M.; Sakaguchi, H. Computational performance of a smoothed particle hydrodynamics simulation for shared-memory parallel computing. Comput. Phys. Commun.
**2015**, 194, 18–32. [Google Scholar] [CrossRef] - Ferrari, A.; Dumbser, M.; Toro, E.F.; Armanini, A. A new 3D parallel SPH scheme for free surface flows. Comput. Fluids
**2009**, 38, 1203–1217. [Google Scholar] [CrossRef] - Cherfils, J.M.; Pinon, G.; Rivoalen, E. JOSEPHINE: A parallel SPH code for free-surface flows. Comput. Phys. Commun.
**2012**, 183, 1468–1480. [Google Scholar] [CrossRef] - Oger, G.; Le Touzé, D.; Guibert, D.; De Leffe, M.; Biddiscombe, J.; Soumagne, J.; Piccinali, J.-G. On distributed memory MPI-based parallelization of SPH codes in massive HPC context. Comput. Phys. Commun.
**2016**, 200, 1–14. [Google Scholar] [CrossRef] - Egorova, M.S.; Dyachkov, S.A.; Parshikov, A.N.; Zhakhovsky, V.V. Parallel SPH modeling using dynamic domain decomposition and load balancing displacement of Voronoi subdomains. Comput. Phys. Commun.
**2019**, 234, 112–125. [Google Scholar] [CrossRef] - Yeylaghi, S.; Moa, B.; Oshkai, P.; Buckham, B.; Crawford, C. ISPH modeling for hydrodynamic applications using a new MPI-based parallel approach. J. Ocean Eng. Mar. Energy
**2017**, 3, 35–50. [Google Scholar] [CrossRef] - Guo, X.; Rogers, B.D.; Lind, S.; Stansby, P.K. New massively parallel scheme for Incompressible Smoothed Particle Hydrodynamics (ISPH) for highly nonlinear and distorted flow. Comput. Phys. Commun.
**2018**, 233, 16–28. [Google Scholar] [CrossRef] - Fleissner, F.; Eberhard, P. Parallel load-balanced simulation for short-range interaction particle methods with hierarchical particle grouping based on orthogonal recursive bisection. Int. J. Numer. Methods Eng.
**2008**, 74, 531–553. [Google Scholar] [CrossRef] - Harada, T.; Koshizuka, S.; Kawaguchi, Y. Smoothed particle hydrodynamics on GPUs. In Proceedings of the Computer Graphics International Conference, Petròpolis, Brazil, 30 March 2007; pp. 63–70. Available online: https://pdfs.semanticscholar.org/a132/6b93316e7ce4d2580bd5e3928ce6ff24e386.pdf (accessed on 21 February 2019).
- Crespo, A.C.; Dominguez, J.M.; Barreiro, A.; Gómez-Gesteira, M.; Rogers, B.D. GPUs, a new tool of acceleration in CFD: Efficiency and reliability on smoothed particle hydrodynamics methods. PLoS ONE
**2011**, 6, e20685. [Google Scholar] [CrossRef] [PubMed] - Hérault, A.; Bilotta, G.; Vicari, A.; Rustico, E.; del Negro, C. Numerical simulation of lava flow using a GPU SPH model. Ann. Geophys.
**2011**, 54. [Google Scholar] [CrossRef] - Mokos, A.; Rogers, B.D.; Stansby, P.K.; Domínguez, J.M. Multi-phase SPH modeling of violent hydrodynamics on GPUs. Comput. Phys. Commun.
**2015**, 196, 304–316. [Google Scholar] [CrossRef] - Winkler, D.; Meister, M.; Rezavand, M.; Rauch, W. gpuSPHASE—A shared memory caching implementation for 2D SPH using CUDA. Comput. Phys. Commun.
**2017**, 213, 165–180. [Google Scholar] [CrossRef] - Cercos-Pita, J.L. AQUAgpusph, a new free 3D SPH solver accelerated with OpenCL. Comput. Phys. Commun.
**2015**, 192, 295–312. [Google Scholar] [CrossRef] - Domínguez, J.M.; Crespo, A.J.C.; Gómez-Gesteira, M. Optimization strategies for CPU and GPU implementations of a smoothed particle hydrodynamics method. Comput. Phys. Commun.
**2013**, 184, 617–627. [Google Scholar] [CrossRef] - Qiu, L.C. OpenCL-Based GPU Acceleration of ISPH Simulation for Incompressible Flows. Appl. Mech. Mater.
**2014**, 444, 380–384. [Google Scholar] [CrossRef] - Nie, X.; Chen, L.; Xiang, T. Real-Time Incompressible Fluid Simulation on the GPU. Int. J. Comput. Games Technol.
**2015**, 2015, 417417. [Google Scholar] [CrossRef] - Chow, A.D.; Rogers, B.D.; Lind, S.J.; Stansby, P.K. Incompressible SPH (ISPH) with fast Poisson solver on a GPU. Comput. Phys. Commun.
**2018**, 226, 81–103. [Google Scholar] [CrossRef] - Hori, C.; Gotoh, H.; Ikari, H.; Khayyer, A. GPU-acceleration for Moving Particle Semi-Implicit method. Comput. Fluids
**2011**, 51, 174–183. [Google Scholar] [CrossRef][Green Version] - Kakuda, K.; Nagashima, T.; Hayashi, Y.; Obara, S.; Toyotani, J.; Miura, S. Three-dimensional fluid flow simulations using GPU-based particle method. Comput. Model. Eng. Sci.
**2013**, 95, 363–376. [Google Scholar] - Kalyanapu, A.J.; Shankar, S.; Pardyjak, E.R.; Judi, D.R.; Burian, S.J. Assessment of GPU computational enhancement to a 2D flood model. Environ. Model. Softw.
**2011**, 26, 1009–1016. [Google Scholar] [CrossRef] - Brodtkorb, A.R.; Sætra, M.L.; Altinakar, M. Efficient shallow water simulations on GPUs: Implementation, visualization, verification, and validation. Comput. Fluids
**2012**, 55, 1–12. [Google Scholar] [CrossRef] - Vacondio, R.; Palù, A.D.; Mignosa, P. GPU-enhanced finite volume shallow water solver for fast flood simulations. Environ. Model. Softw.
**2014**, 57, 60–75. [Google Scholar] [CrossRef] - García-Feal, O.; González-Cao, J.; Gómez-Gesteira, M.; Cea, L.; Domínguez, J.M.; Formella, A. An accelerated tool for flood modeling based on Iber. Water
**2018**, 10, 1459. [Google Scholar] [CrossRef] - Liu, Q.; Qin, Y.; Li, G. Fast simulation of large-scale floods based on GPU parallel computing. Water
**2018**, 10, 589. [Google Scholar] [CrossRef] - Bladé, E.; Cea, L.; Corestein, G.; Escolano, E.; Puertas, J.; Vázquez-Cendón, E.; Dolz, J.; Coll, A. Iber: Herramienta de simulación numérica del flujo en ríos. Rev. Int. Metod. Numer. Calc. Disen. Ing.
**2014**, 30, 1–10. [Google Scholar] [CrossRef] - Wolfe, M.; Lee, S.; Kim, J.; Tian, X.; Xu, R.; Chapman, B.; Chandrasekaran, S. The OpenACC data model: Preliminary study on its major challenges and implementations. Parallel Comput.
**2018**, 78, 15–27. [Google Scholar] [CrossRef] - Hérault, A.; Zhang, H.; Dalrymple, R.A.; Yang, R.; Wu, J. Numerical modeling of dam-break flood through intricate city layouts including underground spaces using GPU-based SPH method. J. Hydrodyn.
**2014**, 25, 818–828. [Google Scholar] - Liang, Q.; Xia, X.; Hou, J. Efficient urban flood simulation using a GPU-accelerated SPH model. Environ. Earth Sci.
**2015**, 74, 7285–7294. [Google Scholar] [CrossRef] - Dickson, N.G.; Karimi, K.; Hamze, F. Importance of explicit vectorization for CPU and GPU software performance. J. Comput. Phys.
**2011**, 230, 5383–5398. [Google Scholar] [CrossRef][Green Version] - Lee, V.W.; Kim, C.; Chhugani, J.; Deisher, M. Debunking the 100X GPU vs. CPU Myth: An Evaluation of Throughput Computing on CPU and GPU. ACM SIGARCH Comput. Arch. News
**2010**, 38, 451–460. [Google Scholar] [CrossRef] - Valdez-Balderas, D.; Domínguez, J.M.; Rogers, B.D.; Crespo, A.J.C. Towards accelerating smoothed particle hydrodynamics simulations for free-surface flows on multi-GPU clusters. J. Parallel Distrib. Comput.
**2013**, 73, 1483–1493. [Google Scholar] [CrossRef] - Domínguez, J.M.; Crespo, A.J.C.; Valdez-Balderas, D.; Rogers, B.D.; Gómez-Gesteira, M. New multi-GPU implementation for smoothed particle hydrodynamics on heterogeneous clusters. Comput. Phys. Commun.
**2013**, 184, 1848–1860. [Google Scholar] [CrossRef] - Rustico, E.; Bilotta, G.; Herault, A.; del Negro, C.; Gallo, G. Advances in multi-GPU smoothed particle hydrodynamics simulations. IEEE Trans. Parallel Distrib. Syst.
**2014**, 25, 43–52. [Google Scholar] [CrossRef] - Ji, Z.; Xu, F.; Takahashi, A.; Sun, Y. Large scale water entry simulation with smoothed particle hydrodynamics on single- and multi-GPU systems. Comput. Phys. Commun.
**2016**, 209, 1–12. [Google Scholar] [CrossRef]

**Figure 1.**Rheological models for non-cohesive sediment erosion with bed load transport and for dense granular flows. I

_{2}: second invariant of the rate of deformation tensor; μ

_{app}: apparent viscosity.

**Figure 2.**Snapshots of incompressible smoothed particle hydrodynamics (ISPH) calculated equilibrium scouring pit with different overflow depth: (

**a**) η = 3.3 cm; (

**b**) η = 4.7 cm, and (

**c**) η = 6.0 cm.

**Figure 3.**ISPH computed sediment bed scouring process: (

**a**) snapshots of ISPH calculated vorticity in the scouring pit; (

**b**) Snapshots of the ISPH calculated scouring pit.

**Figure 4.**Frames of the 2D smoothed particle hydrodynamics (SPH) simulation of the rainfall induced shallow landslide occurred on April 2009 at Recoaro, Oltrepò Pavese (Northern Italy). (

**a**) Velocity field; (

**b**) Density field.

**Figure 6.**Demonstrative test case for the meshless SPH method applied to a 3D erosional dam-break flood on complex topography [8]. (

**a**) 3D view. (

**b**) Top view. Digital elevation model (grey, with a black vertex triangulation), liquid SPH particles (blue), mixture SPH particles (brown).

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Manenti, S.; Wang, D.; Domínguez, J.M.; Li, S.; Amicarelli, A.; Albano, R. SPH Modeling of Water-Related Natural Hazards. *Water* **2019**, *11*, 1875.
https://doi.org/10.3390/w11091875

**AMA Style**

Manenti S, Wang D, Domínguez JM, Li S, Amicarelli A, Albano R. SPH Modeling of Water-Related Natural Hazards. *Water*. 2019; 11(9):1875.
https://doi.org/10.3390/w11091875

**Chicago/Turabian Style**

Manenti, Sauro, Dong Wang, José M. Domínguez, Shaowu Li, Andrea Amicarelli, and Raffaele Albano. 2019. "SPH Modeling of Water-Related Natural Hazards" *Water* 11, no. 9: 1875.
https://doi.org/10.3390/w11091875