Monaghan, Joseph J.

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Article, Published VersionMonaghan, Joseph J.A brief history of SPH in hydraulicsHydrolinkVerfügbar unter/Available at: https://hdl.handle.net/20.500.11970/109287Vorgeschlagene Zitierweise/Suggested citation:Monaghan, Joseph J. (2015): A brief history of SPH in hydraulics. In: Hydrolink 2015/3.Madrid: International Association for Hydro-Environment Engineering and Research (IAHR).S. 74-75. https://iahr.oss-accelerate.aliyuncs.com/library/HydroLink/HydroLink2015_03_SPH_in_Hydraulics.pdf.Standardnutzungsbedingungen/Terms of Use:Die Dokumente in HENRY stehen unter der Creative Commons Lizenz CC BY 4.0, sofern keine abweichendenNutzungsbedingungen getroffen wurden. Damit ist sowohl die kommerzielle Nutzung als auch das Teilen, dieWeiterbearbeitung und Speicherung erlaubt. Das Verwenden und das Bearbeiten stehen unter der Bedingung derNamensnennung. Im Einzelfall kann eine restriktivere Lizenz gelten; dann gelten abweichend von den obigenNutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte.Documents in HENRY are made available under the Creative Commons License CC BY 4.0, if no other license isapplicable. Under CC BY 4.0 commercial use and sharing, remixing, transforming, and building upon the materialof the work is permitted. In some cases a different, more restrictive license may apply; if applicable the terms ofthe restrictive license will be binding.The first description of Smoothed ParticleHydrodynamics (SPH) was published in 1977 byJoe Monaghan and Bob Gingold, and independ-ently by Leon Lucy. The method originated in thedesire to simulate the formation of binary starsystems. These systems are characterised byflows with complicated geometry and very largevariations in density. None of these character-istics could be handled with the finite differencemethods that were then available. The basis ofSPH was the assignment of the properties of thesystem to particles with fixed mass. By usinginterpolation modelled on the kernel method thatstatisticians used to estimate probabilitydensities, it was possible to estimate derivativeof quantities, such as the pressure and temper-ature that were known at the particles.Gravitational forces could be calculated bysumming over the particles, though a straight-forward summation was soon replaced by moresophisticated tree-code algorithms. In this waythe forces acting on the particles were calcu-lated and the motion of the particles followed.These particles represented elements of fluidand their stream lines and acceleration wereestimates of the same quantities for the fluid.The methods were extended to deal withthermodynamic effects in gas dynamics, and todeal with the shock waves that are very commonin astrophysical simulations. An attractive featureof SPH was that the resolution could be allowedto vary in space and time, although the correctway to include this in the algorithms was notknown for 25 years. Another attractive featurewas that the algorithms were simple, but verycomplicated problems could be simulatedeasily.The application of SPH to liquid problems beganin 1993. I had an interest in Archaeology andattended a seminar on the demise of theMinoans. The speaker pointed out that there wasconsiderable evidence that the Minoan civili-74 hydrolink number 3/2015A BRIEF HISTORY OF SPH IN HYDRAULICS BY JOSEPH J. MONAGHANsation on Crete had been badly disrupted at thetime of the eruption of a massive volcano onThera (Santorini), and some investigatorsthought the volcanic eruption had producedtsunamis that destroyed the coastal towns ofCrete. I was intrigued by this and asked anarchaeologist, Peter Bicknell (an old friend, whoworked with us on this problem), if the archaeol-ogists would be interested in a fluid dynamicistcalculating whether tsunamis would have beenproduced, and then what damage they mightcause. He said they would be, and he referredto the fluid dynamics simulations as  “the hardevidence” that was all too rare in Archaeology.At this time I had never simulated any problemin liquid dynamics but I was convinced thatwaves breaking on the Cretan coast could besimulated using SPH. It seemed to me toodifficult to treat a liquid as incompressible and Idecided to explore the possibility that slightlycompressible fluids could give a good approxi-SPH[SMOOTHED PARTICLE HYDRODYNAMICS]IN HYDRAULICS DualSPHsics team75hydrolink number 3/2015IAHRmation to liquids like water. Incidentally, water isslightly compressible, but with a speed of soundof around 1500 m/s and this was too high forthe simulation of a fluid on a macroscopic scaleof 10 or 20 km. I therefore gave the fluid anartificial equation of state that was large enoughto guarantee, in most cases, that the fluctua-tions in the density were small. For me smallwas ∼ 1%, and this could be achieved byensuring the speed of sound was a factor 10greater than the impact speeds in the fluiddynamics problems we might consider. Apartfrom that, I used the same algorithm that I usedfor gas dynamics, with the exception that theastrophysicists calculated the density by asummation over the SPH particles while I foundthat, for liquids, it was better to integrate thecontinuity equation. The resulting algorithm wasapplied to a dam breaking over a triangularobstacle, a bore, and the generation of wavessurging up a beach (Monaghan 1994). Theresolution was poor but the main features of theflow were correct to within 10%. To end this storywe set up a laboratory and studied wavesproduced by moving bodies and we received agrant for a team to core likely areas on the coastof Crete for evidence of marine inundation. Thework was exciting but the results were meagre.Following this we began extending SPH to awider class of problems including wavesbreaking on beaches, and waves produced byrigid bodies sliding down ramps (Monaghanand Kos 1999, 2000). This was taken up andapplied successfully by Colagrossi and Landrini(2003) and later by Landrini et al. (2007)). Goodexamples of the application of SPH to problemsinvolving liquids is the work on oil spill over andunder booms (Violeau et al. 2007) and sloshing(Souto-Inglesias et al. 2006). It was alsoimmediately clear that SPH could be easily usedto simulate problems involving two or morefluids (Monaghan et. al. 1999) as in thesimulation of flow into a stratified fluid. Duringthe same period we got interested in thefracture mechanics of materials largely becausewe wanted to consider geological fractures likethose produced by magma beneath volcanoes(Gray and Monaghan 2004). Now we aresimulating fracture produced by boat hullshitting water. Fracture was the focus of the workof Willy Benz who used SPH very successfully tomodel the impact of asteroids (Benz andAsphaug 1994). When we started we had noknowledge of fracture mechanics, but I was alsosure that few (if any) people could simulate thefractures seen in practice. I can still rememberbeing in the Monash library and looking at theJoe Monaghan is Emeritus Professor ofApplied Mathematics in the School ofMathematical Sciences, at MonashUniversity, Australia. He is the author ofnumerous papers concerned with thedevelopment of SPH and its application toastrophysical problems, the motion ofliquids and gases, elasticity and fracture,and the dynamics of  dusty liquids andgases. several shelves of books on fracture andconvincing myself that most of them were eitherwrong or described methods that could not beused for complicated fracture problems. I stillthink I was right.Progress has been made in a number of areas(for a review see Monaghan 2012). The first ofthese is in modelling surface tension and multi-phase problems (Adami et al. 2010), the mostimportant of which is the combination of air andwater as in a breaking wave (Grenier et al. 2009,Monaghan and Raffiee 2013). The mass of theair is negligible but its pressure isn't and thatmakes air important. The second is the study ofthe accuracy of SPH algorithms near bound-aries (see for example Macia et al. 2011) whichshows that improvements can be made usingan appropriate mapping of the velocity field ofthe fluid onto ghost particles in the boundary.The third is improvements in the modelling ofboundaries (for example Adami et al. 2012 andLeroy et al. 2014). Adami et al. (2012) use ghostparticles with a pressure and velocity interpo-lated from the fluid particles. The density ofthese particles is then calculated from thepressure using the equation of state. Leroy et al.(2014) use analytical methods. The fourthimprovement is the extension of SPH algorithmsto three dimensions. It is ironic that the appli-cation of SPH to astrophysics always usedalgorithms for three dimensions whereas all theearly SPH applications to fluids were for 2D. It isone of the pleasures of using SPH that the codefor three dimensions is as easy to write as onefor two dimensions. However, in the case ofnearly incompressible flow, the time steps aresmall, and the computations in 3D were tootime consuming. The situation has nowchanged with progress being driven by newhardware. Looking back 10 years, we can seethat the astrophysicists were using between 105to 109 SPH particles for their simulations. Thesesimulations required parallel processing units,and there is publicly available software for astro-physical gas dynamics (Gadget) pioneered byVolker Springel. In the last 2 years there havebeen increasing applications of GPUs (GraphicsProcessing Units) to SPH problems relevant toEngineering problems (Hérault et al. 2010), andpublic software (SPHysics) due to Ben Rogersand Tony Dalrymple and their colleagues is nowavailable. This hardware allows ∼ 106 SPHparticles to be used in hydraulic computations.Finally, it is worth remembering, that SPH iswidely used for special effects in movies whereits ability to model violent impact with water isappreciated.REFERENCESS. Adami, X.Y. Hu, N. A. Adams, A generalized wall boundarycondition for SPH, J. Computat. Phys. 231, 7057-7075, (2012).S. Adami, X.Y. Hu, N. A. Adams, A new surface tension formulation formulti-phase SPH. J. Computat. Phys., 229, 5011-5021, (2012).W. Benz and E.Asphaug, Impact simulation with fracture: 1. Methodsand tests, Icarus, 107, 98-116, (1994).J.P. Gray and J. J. Monaghan, Numerical modelling of stress fieldsand fracture around magma chambers, J. Volcanology andGeothermal Research, 135, 259-283, (2004).N. Grenier, M. Antuono, A. Colagrossi, and D, le Touz e, AnHamiltonian interface SPH formulation for multi-fluid and freesurface flows, J. Comptat. Phys. 228, 8380-8393, (2009).R.A. Gingold and J. J. Monaghan, Smoothed particle hydrodynamics:theory and applications to non spherical stars, Mon. Not. Roy. Astr.Soc. 181, 375-389, (1977).A. Hérault, G. Bilotta, and R. A. Dalrymple, SPH on GPU with CUDA,J. of Hydraulic Res., 48(s1), 74-79, (2010).M. Landrini, A. Colagrossi, M. Greco, M. P. Tulin, Gridless simulationofsplashing processes and near-shore bore propagation, J. FluidMech., 591,183-213, (2007).A. Leroy, D. Violeau, M. Ferrand, and C. Kassiotis , Unified semi-analytical wall boundary conditions for 2D incompressible SPH, J.Computat. Phys. 261, 106-129, (2014).L.B. Lucy, A numerical approach to the testing of the fissionhypothesis, The Astron. J. 82(12), 1013-1024, (1977).F. Macia, M. Antuono, L.M.Gonzalez, A. Colagrossi, Theoreticalanalysis of the no-slip boundary condition enforcement in SPHmethods, Prog. Theor. Phys., 124(6), 1091-1121. (2011).J. J. Monaghan, Simulating free surface flows with SPH, J. Computat.Phys., 110, 399-405, (1994).J. J. Monaghan, SPH and its diverse applications, Ann. Rev. FluidMech., 44, 323-346, (2012).J. J. Monaghan and A. Kos. Solitary waves on a Cretan beach, J.Waterways Ports, Coastal and Ocean engineering, 125, 145-154,(1999).J.J. Monaghan, R.F. Cas, A. Kos, M. Hallworth, Gravity currentsdescending a ramp in a stratified tank. J. Fluid Mech. 379, 39-69,(1999).J. J. Monaghan and A. Kos, Scott Russell's wave generator, Phys. ofFluids, 12(3), 622-630, (2000).J.J. Monaghan and Ashkan Raffiee, A simple SPH algorithm for multi-fluid flow with high density ratio, Int. J. for Num. Methods in Fluids,71(5), 537-561, (2013).A. Souto-Inglesias, L. Delorme, L. Perez-Rojas, and S. Abril-Perez.Smoothed particle hydrodynamics simulation of a tuned liquiddamper (TLD) with angular motion, Ocean Eng. 33(11-12), 1462-1484, (2006).D. Violeau, C. Buvat, K. Abed-Merain, and E. de Nanteuil, Numericalmodeling of book and oil spill, Coastal Eng., 54, 895-913, (2007).SPH[SMOOTHED PARTICLE HYDRODYNAMICS]IN HYDRAULICS 

A brief history of SPH in hydraulics

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A brief history of SPH in hydraulics

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