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SPHERIC Grand Challenge Working Group

SPH Numerical Development Working Group


Damien Violeau
Rade Vignjevic

Purpose of this Group


Today SPH is considered as a promising method but still suffers from a lack of broad recognition from the scientific community as a serious candidate to become tomorrow's numerical tool. One of the main reason of this is that SPH still has unknown properties, and many questions remain unanswered on a purely theoretical ground. Although recent progress have been done, a huge amount of work remains to be done.

Convergence, numerical stability, boundary conditions, kernel properties, time marching, existence and properties of solutions, make a short list of the key issues which should be addressed in order to make SPH a mature method. In order to progress in the knowledge of the abovementioned problems, SPHERIC has started to build a working Group on SPH numerical development, named the SPHERIC Grand Challenge Working Group (GCWG).

Several Grand Challenges (GCs) are defined by the SPHERIC Steering Committee:

GC#1: Convergence, consistency and stability
Leaders: J.J. Monaghan, D. Violeau and R. Vignjevic

GC#2: Boundary conditions
Leaders: A. Souto-Iglesias

GC#3: Adaptivity
Leaders: B.D. Rogers and R. Vacondio

GC#4: Coupling to other models
Leaders: S. Marrone, C. Altomare and D. Le Touzé

GC#5: Applicability to industry
Leaders: J-C. Marongiu and M. De Leffe

Ideally, the GCWG should clarify the most important problems remaining in theses GCs, list the most significant publications on each topic (see below), keep aware of the state-of-the-art and identify active research teams and foster cooperation through a living network. Sharing knowledge and clarifying the needs will be our main motivation. So far, no clear agenda has been proposed, since the GCWG is under construction. It is open to any volunteer. All suggestions are welcome.

PhD and postdoc fellows are much welcome in this Group. Their contributions to the improvement of SPH will be of great help, and the Group aims at fostering their cooperation with other institutes.

What can YOU do?

  • Contribute to the GC sections below by adding references (contact:

  • Contribute to the GCs with your own work (if you do so, please inform the corresponding GC leaders)

  • Take advantage of the SPHERIC community and Workshops to share knowledge

  • Propose publications to be nominated for the GC Award

  • Propose new GCs


The Joe Monaghan Prize award has been initiated by SPHERIC to recognize the contribution of papers to these Grand Challenges.

Reference paper


Vacondio, R., Altomare, C., De Leffe, M., Hu, X., Le Touzé, D., Lind, S., Marongiu, J-C., Marrone, S., Rogers, B. D., Souto-Iglesias, A.,
Grand challenges for Smoothed Particle Hydrodynamics numerical schemes. Computational Particle Mechanics (2020).

GC#1: Convergence, consistency and stability


Joe Monaghan
Damien Violeau
Rade Vignjevic

  • zero-energy modes

  • time-stepping

  • particle pairing

  • tensile instability

  • etc.


Below is a (non-exhaustive) list of relevant key publications:


Hicks, D.L., Swegle, J.W., Attaway, S.W. (1993), SPH: Instabilities, wall heating, and conservative smoothing, Proc. workshop on advances in smooth particle hydrodynamics, Los Alamos National Laboratory Report #LA-UR-93-4375, pp. 223–256.


Dyka, C.T. (1994), Addressing tension instability in SPH methods, NRL Report NRLlMR/6384.

Morris, J.P.A. (1994), A study of the stability properties of SPH, Department of Mathematics, Monash University, Clayton Victoria, Australia, Report #94/22.


Wen, Y., Hicks, D.L., Swegle, J.W. (1994), Stabilizing SPH with Conservative Smoothing, Sandia Report #SAND94–1932.


Balsara, D.S. (1995), Von Neumann Stability analysis of smoothed particle hydrodynamics-suggestions for optimal algorithms, J. Comput. Phys. 121:357–372.


Morris J.P. (1996), A study of the stability properties of Smooth Particle Hydrodynamics, Publ. Astron. Soc. Aust., 13:97-102.


Randles, P.W., Liberski, L.D. (1996), Smoothed Particle Hydrodynamics: some recent improvements and applications, Comput. Methods Appl. Mech. Engrg. 139:375–408.


Dyka, C.T., Randles, P.W., Ingel, R.P. (1997), Stress points for tension instability in SPH, Int. J. Num. Meth. Eng. 40:2325–2341.


Hicks D.L., Liebrock L.M. (1999), SPH Hydrocodes Can Be Stabilized with Shape-Shifting, Comput. Math. Appl. 38:1-16.


Monaghan J.J. (2000), SPH without a Tensile Instability, J. Comput. Phys. 159:290-311.


Belytschko, T., Xiao, S. (2002), Stability analysis of particle methods with corrected derivatives, Comput. Math. Appl. 43:329–350.


Vignjevic, R., Reveles, J., Campbell, J. (2006), SPH in a total Lagrangian formalism, Comput. Meth. Eng. Science 14(3):181–198.


García-Senz, D., Cabezón, R. M., Escartín, J. A. (2012), Improving smoothed particle hydrodynamics with an integral approach to calculating gradients, Astronomy & Astrophysics, 538:13.


Dehnen W., Aly H. (2012), Improving convergence in smoothed particle hydrodynamics simulations without pairing instability, Mon. Not. R. Astron. Soc. 425:1068-1082.


Violeau, D., Leroy, A. (2014), On the maximum time step in weakly compressible SPH, J. Comput. Phys. 256:388-415.


Imoto, Y. (2018), Unique solvability and stability analysis for incompressible smoothed particle hydrodynamics method, Comput. Part. Mech.


Franz, T., Wendland, H. (2018), Convergence of the Smoothed Particle Hydrodynamics Method for a Specific Barotropic Fluid Flow: Constructive Kernel Theory, SIAM J. Math. Anal., 50(5):4752-4784.


Collé, A., Limido, J., Vila, J.-P. (2019), An accurate multi-regime SPH scheme for barotropic flows, J. Comput. Phys. 388:561-600

Duan, G., Matsunaga, T., Koshizuka, S., et  al. (2022),  New  insights  into  error  accumulation  due  to  biased  particle  distribution  in  semi-implicit particle  methods,  Comput.  Methods  Appl.  Mech.  Engrg.  388 

Imoto, Y. (2022) Difference between smoothed particle hydrodynamics and moving particle semi-implicit operators,  Comput.  Methods  Appl.  Mech.  Engrg.  395

GC#2: Boundary conditions


Antonio Souto Iglesias


In order to close the fluid dynamics equations (Euler and Navier-Stokes, both compressible or incompressible) initial (ICs) and boundary conditions (BCs) are necessary. They can be classified as:

  1. solid boundaries (free slip, no slip, pressure normal derivative)

  2. free surface,

  3. inlet/oulet,

  4. initial conditions,

  5. coupling with other models.


To include these boundaries in an SPH simulation, researchers use various techniques depending on the type of condition considered. Let’s try to summarize the most relevant references. This list is of course open to discussion and is also a living one, since new relevant references can be incorporated. It is relevant to mention that in the most important SPH review papers, [Monaghan, 2012, 2005a, Gomez- Gesteira et al., 2010], there are already specific review sections on BCs. There are some key issues that remain to be addressed:

  1. How to include BCs without loosing intrinsic SPH conservation properties?

  2. How to include BCs consistently?

  3. How to include solid wall BCs for real geometries with complex shapes (2D, 3D)?

  4. How to provide an initial distribution of particles which avoids the onset of shocks once the time-integration starts?

  5. How to treat back flows when implementing inlet/oulet boundary conditions?

  6. etc.


The references follow:


A. Amicarelli, G. Agate, and R. Guandalini. A 3D Fully Lagrangian Smoothed Particle Hydrodynamics model with both volume and surface discrete elements. International Journal for Numerical Methods in Engineering, 95:419–450, 2013. URL


S. Attaway, M. Heinstein, and J. Swegle. Coupling of smooth particle hydrodynamics with the finite element method. Nuclear Engineering and Design, 150 (2–3):199–205, 1994. URL


F. Bierbrauer, P. Bollada, and T. Phillips. A consistent reflected image particle approach to the treatment of boundary conditions in smoothed particle hydrodynamics. Computer Methods in Applied Mechanics and Engineering, 198(41-44): 3400 – 3410, 2009. URL


A. Colagrossi and M. Landrini. Numerical simulation of interfacial flows by smoothed particle hydrodynamics. J. Comp. Phys., 191:448–475, 2003. URL


A. Colagrossi, G. Colicchio, and D. Le Touzé. Enforcing boundary conditions in SPH applications involving bodies with right angles. 2007.

A. Colagrossi, M. Antuono, and D. L. Touz´e. Theoretical considerations on the free-surface role in the Smoothed-particle-hydrodynamics model. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 79(5):056701, 2009. URL


A. Colagrossi, M. Antuono, A. Souto-Iglesias, and D. Le Touzé. Theoretical analysis and numerical verification of the consistency of viscous smoothed-particlehydrodynamics formulations in simulating free-surface flows. Physical Review E, 84:26705+, 2011. URL


A. Colagrossi, B. Bouscasse, M. Antuono, and S. Marrone. Particle packing algorithm for SPH schemes. Computer Physics Communications, 183(2):1641–1683, 2012. URL


M. De Leffe, D. Le Touz´e, and B. Alessandrini. Normal flux method at the boundary for SPH. In 4th SPHERIC, pages 149–156, May 2009


M. De Leffe, D. Le Touz´e, and B. Alessandrini. A modified no-slip condition in weakly-compressible SPH. In 6th ERCOFTAC SPHERIC workshop on SPH applications, pages 291–297, 2011


A. English, J.M. Domínguez, R. Vacondio, A.J.C. Crespo, P.K. Stansby, S.J. Lind, L. Chiapponi, M. Gómez-Gesteira. 2021. Modified dynamic boundary conditions (mDBC) for general purpose smoothed particle hydrodynamics (SPH): application to tank sloshing, dam break and fish pass problems. Computational Particle Mechanics. URL

I. Federico, S. Marrone, A. Colagrossi, F. Aristodemo, and M. Antuono. Simulating 2D open-channel flows through an SPH model. European Journal of Mechanics- B/Fluids, 34:35–46, 2012. URL


J. Feldman and J. Bonet. Dynamic refinement and boundary contact forces in SPH with applications in fluid flow problems. International Journal for Numerical Methods in Engineering, 72(3):295–324, 2007. URL


M. Ferrand, D. R. Laurence, B. D. Rogers, D. Violeau, and C. Kassiotis. Unified semi-analytical wall boundary conditions for inviscid, laminar or turbulent flows in the meshless SPH method. International Journal for Numerical Methods in Fluids, 71(4):446–472, 2013. URL


G. Fourey, D. Le Touzé, B. Alessandrini, and G. Oger. SPH-FEM coupling to simulate fluid-structure interactions with complex free-surface flows. In 5th ERCOFTAC SPHERIC workshop on SPH applications, 2010.


M. Gomez-Gesteira, B. D. Rogers, R. A. Dalrymple, and A. J. C. Crespo. State-of-the-art of classical SPH for free-surface flows. Journal of Hydraulic Research, 48(S1):6–27, 2010. URL


M. Ihmsen, J. Bader, G. Akinci, and M. Teschner. Animation of air bubbles with SPH. In GRAPP, 2011


C. Kassiotis, R. B.D., M. Ferrand, D. Violeau, S. B. K., and M. Benoit. Strong coupling between 2d sph and 1d finite difference


Sh. Khorasanizade, J. M. M. Sousa. An innovative open boundary treatment for incompressible SPH. Int. J. Num. Meth. Fluids,

Boussinesq solvers. In 6th ERCOFTAC SPHERIC workshop on SPH applications, 2011.


E. S. Lee, C. Moulinec, R. Xu, D. Violeau, D. Laurence, and P. Stansby. Comparisons of weakly compressible and truly incompressible algorithms for the SPH mesh free particle method. Journal of Computational Physics, 227(18):8417– 8436, 9/10 2008. URL


L. Lobovsky and P. H. L. Groenenboom. Remarks on FSI simulations using SPH. In 4th ERCOFTAC SPHERIC workshop on SPH applications, pages 378–383, May 2009.


F. Macía, M. Antuono, L. M. González, and A. Colagrossi. Theoretical analysis of the no-slip boundary condition enforcement in SPH methods. Progress of Theoretical Physics, 125(6):1091–1121, 2011. URL


F. Macía, L. M. González, J. L. Cercos-Pita, and A. Souto-Iglesias. A boundary integral SPH formulation. Consistency and applications to ISPH and WCSPH. Progress of Theoretical Physics, 128(3), Sept. 2012a. URL


F. Macía, J. M. Sánchez, A. Souto-Iglesias, and L. M. González. WCSPH viscosity diffusion processes in vortex flows. International

Journal for Numerical Methods in Fluids, 69(3):509–533, May 2012b. URL


O. Mahmood, C. Kassiotis, D. Violeau, B. Rogers, and M. Ferrand. Absorbing inlet/outlet boundary conditions for SPH 2-D turbulent free-surface flows. 2012. ISBN 88-7617-003-0


J. C. Marongiu, F. Leboeuf, and E. Parkinson. A new treatment of solid boundaries for the SPH method. In ”SPHERIC - Smoothed Particle Hydrodynamics European Research Interest Community”., pages 165+, 2007


S. Marrone, A. Colagrossi, M. Antuono, G. Colicchio, and G. Graziani. An accurate SPH modeling of viscous flows around bodies at low and moderate reynolds numbers. Journal of Computational Physics, 245(0):456 – 475, 2013. URL


J. Monaghan. Smoothed particle hydrodynamics and its diverse applications. Annual Review of Fluid Mechanics, 44(1):323–346, 2012. URL


J. Monaghan and J. Kajtar. SPH particle boundary forces for arbitrary boundaries. Computer Physics Communications, 180(10):1811 – 1820, 2009. URL


J. Monaghan and A. Kos. Solitary waves on a Cretan beach. J. Waterway, Port, Coastal, and Ocean Eng., 125(3):145, 1999. URL


J. J. Monaghan. Smoothed particle hydrodynamics. Reports on Progress in Physics, 68:1703–1759, 2005a. URL


J. J. Monaghan. Smoothed Particle Hydrodynamic simulations of shear flow. Monthly Notices of the Royal Astronomical Society, 365:199–213, 2005b. URL


J. Simpson and M. Wood. Classical kinetic theory simulations using smoothed particle hydrodynamics. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics, 54(2):2077–2083, 1996. URL


A. Souto-Iglesias, L. Delorme, L. Pérez-Rojas, and S. Abril-Pérez. Liquid moment amplitude assessment in sloshing type problems with smooth particle hydrodynamics. Ocean Engineering, 33(11-12):1462–1484, 8 2006. URL


A. Souto-Iglesias, F. Macía, L. M. González, and J. L. Cercos-Pita. On the consistency of MPS. Computer Physics Communications, 184(3):732–745, 2013. URL

A. Tafuni, J. M. , R. Vacondio, and A.J.C. Crespo. A versatile algorithm for the treatment of open boundary conditions in Smoothed particle hydrodynamics GPU models. Computer Methods in Applied Mechanics and Engineering, 342:604-624, 2018.

Q. Yang, V. Jones, and L. McCue. Free-surface flow interactions with deformable structures using an SPH-FEM model. Ocean Engineering, 55(0): 136–147, 2012.

GC#3: Adaptivity


Benedict Rogers 
Renato Vacondio


In classical Eulerian computational models, adaptive structured or unstructured grids have been used successfully for a long time to provide variable resolution and to simulate multiscale flows while retaining computational efficiency. Many engineering applications that are ideal for SPH are still using uniformly sized particles. This is inherently inefficient and unattractive to industry.


In meshfree numerical schemes there have been some early attempts to introduce variable resolution by either remeshing, and particle insertion/removal techniques, e.g. Børve et al. (2001, 2005), Lastiwka et al. (2005). Recently within the SPH formalism, dynamic particle refinement which conserves mass and momentum has been developed and applied to both the shallow water equations and the Navier-Stokes equations in 2-D (Feldman and Bonet 2007), (Vacondio et al. 2013a&b) which has built on the theoretical work of Bonet and Rodríguez-Paz (2005) who proposed a momentum-conservative weakly compressible formulation which takes into account variable smoothing length. This has been applied first to particle splitting, and then for the first time by Vacondio et al. (2013) for particle coalescing/merging to provide a truly dynamic resolution scheme that can vary in time and space. This was both variationally consistent and ensures momentum conservation in the presence of particles with different smoothing length.

Providing adaptivity within SPH is a new issue. There are some key issues that remain to be addressed:

  • Should adaptivity be performed in nested blocks or continuous variation?

  • How can it be implemented efficiently?

  • How does adaptivity interact with the other grand challenges: Convergence, Stability and Boundary Conditions

The references follow:

J. Bonet, M.X. Rodríguez-Paz (2005), Hamiltonian formulation of the variable-h SPH equations, Journal of Computational Physics, 209 (2) pp. 541–558

S. Børve, M. Omang, J. Trulsen (2001), Regularized smoothed particle hydrodynamics: a new approach to simulating magnetohydrodynamic shocks, The Astrophysical Journal, 561 (1), p. 82

S. Børve, M. Omang, J. Trulsen (2005), Regularized smoothed particle hydrodynamics with improved multi-resolution handling, Journal of Computational Physics, 208 (1), pp. 345–367

J. Feldman, J. Bonet (2007), Dynamic refinement and boundary contact forces in SPH with applications in fluid flow problems, International journal for numerical methods in engineering, 72 (3) (2007), pp. 295–324

M. Lastiwka, N. Quinland, M. Basa (2005), Adaptive particle distribution for smoothed particle hydrodynamics, International Journal for Numerical Methods in Fluids, 47(10–11), pp. 1403–1409,

R. Vacondio, B.D. Rogers, P.K. Stansby (2012), Accurate particle splitting for smoothed particle hydrodynamics in shallow water with shock capturing, International Journal for Numerical Methods in Fluids, 69(8), pp. 1377–1410,

R. Vacondio, B.D. Rogers, P.K. Stansby, P. Mignosa, J. Feldman (2013a), Variable resolution for SPH: A dynamic particle coalescing and splitting scheme, Computer Methods in Applied Mechanics and Engineering, 256, April, pp. 132–148,

R. Vacondio, B.D. Rogers, P.K. Stansby, P. Mignosa (2013b), Shallow water SPH for flooding with dynamic particle coalescing and splitting, Advances in Water Resources, 58, August pp. 10–23

F. Spreng, D. Schnabel, A. Mueller, P. Eberhard (2014), A local adaptive discretization algorithm for Smoothed Particle Hydrodynamics, Computational Particle Mechanics, 1, 131–145,

D.A. Barcarolo, D. Le Touzé, G. Oger, F. de Vuyst (2014) Adaptive particle refinement and derefinement applied to the smoothed particle hydrodynamics method, Journal of Computational Physics, 273, 640–657,

Y. R. López, D. Roose, C. R. Morfa, (2013) Dynamic particle refinement in SPH: application to free surface flow and non-cohesive soil simulations, Computational Mechanics, Comput Mech (2013) 51:731–741

Sh. Khorasanizade, J. M. M. Sousa, (2015) Dynamic flow-based particle splitting in smoothed particle hydrodynamics, Computational Mechanics, International Journal Numerical Methods in Engineering, online

GC#4: Coupling to other models


Salvatore Marrone
Corrado Altomare
David Le Touzé


SPH method is naturally able to resolve multi-mechanics problems and include different physical models in its meshless formalism. As other Lagrangian meshless methods, SPH is very accurate and efficient when dealing with moving boundaries and complex interfaces, which are generally addressed with difficulties by conventional numerical methods (e.g., FVM, FEM). However, for problems where the latter methods are currently used and well established SPH is generally less effective and results more costly for the same level of attained accuracy. In several contexts, it can be much more efficient to couple an SPH-based solver to a different numerical solver, in order to enhance the capabilities of both models within their specific application fields. In this way, a wider range of problems is efficiently addressed. 

The coupling algorithm and the related implementation complexity can largely vary depending on several aspects:

●     One-way (offline) or two-way coupling;
●     Heterogeneity of the modelled physics (e.g. potential flow/Navier-Stokes, fluid/solid, compressible/incompressible, etc.);
●     Lagrangian or Eulerian approach adopted in the method coupled to SPH;
●     Discrete coupling interfaces between solvers (mesh/meshless, sharp interface/blending region, etc.);
●     Time stepping and stability of the coupled algorithm (e.g. explicit/implicit time integration, multiple time step);
●     Efficiency of the coupled solver with respect to the single ones;
●     Preservation of conservative quantities by the coupling.

Below is a (non-exhaustive) list of relevant key public:

Chiron, L., Marrone, S., Di Mascio, A., & Le Touzé, D. (2018). Coupled SPH–FV method with net vorticity and mass transfer. Journal of Computational Physics, 364, 111-136. 


Attaway, S. W., Heinstein, M. W., & Swegle, J. W. (1994). Coupling of smooth particle hydrodynamics with the finite element method. Nuclear engineering and design, 150(2-3), 199-205.

Li, Z., Leduc, J., Nunez-Ramirez, J., Combescure, A., & Marongiu, J. C. (2015). A non-intrusive partitioned approach to couple smoothed particle hydrodynamics and finite element methods for transient fluid-structure interaction problems with large interface motion. Computational Mechanics, 55(4), 697-718.

Yang, X., Liu, M., Peng, S., & Huang, C. (2016). Numerical modeling of dam-break flow impacting on flexible structures using an improved SPH–EBG method. Coastal Engineering, 108, 56-64.

Long, T., Hu, D., Yang, G., & Wan, D. (2016). A particle-element contact algorithm incorporated into the coupling methods of FEM-ISPH and FEM-WCSPH for FSI problems. Ocean Engineering, 123, 154-163.

Fourey, G., Hermange, C. L. T. D., Le Touzé, D., & Oger, G. (2017). An efficient FSI coupling strategy between Smoothed Particle Hydrodynamics and Finite Element methods. Computer Physics Communications, 217, 66-81.

Siemann, M. H., & Langrand, B. (2017). Coupled fluid-structure computational methods for aircraft ditching simulations: Comparison of ALE-FE and SPH-FE approaches. Computers & Structures, 188, 95-108.

Ren, B., Jin, Z., Gao, R., Wang, Y. X., & Xu, Z. L. (2013). SPH-DEM modeling of the hydraulic stability of 2D blocks on a slope. Journal of Waterway, Port, Coastal, and Ocean Engineering, 140(6), 04014022.

Canelas, R. B., Crespo, A. J., Domínguez, J. M., Ferreira, R. M., & Gómez-Gesteira, M. (2016). SPH–DCDEM model for arbitrary geometries in free surface solid–fluid flows. Computer Physics Communications, 202, 131-140.

Canelas, R. B., Domínguez, J. M., Crespo, A. J. C., Gómez-Gesteira, M., & Ferreira, R. M. L. (2017). Resolved simulation of a granular-fluid flow with a coupled SPH-DCDEM model. Journal of Hydraulic Engineering, 143(9), 06017012.

Canelas, R.B., Brito, M., Feal, O.G., Domínguez, J.M., Crespo, A.J.C., 2018. Extending DualSPHysics with a Differential Variational Inequality: modeling fluid-mechanism interaction, Applied Ocean Research, Volume 76, 2018, 88-97.

Markauskas, D., Kruggel-Emden, H., Sivanesapillai, R., & Steeb, H. (2017). Comparative study on mesh-based and mesh-less coupled CFD-DEM methods to model particle-laden flow. Powder Technology, 305, 78-88.

Robinson, M., Ramaioli, M., & Luding, S. (2014). Fluid–particle flow simulations using two-way-coupled mesoscale SPH–DEM and validation. International journal of multiphase flow, 59, 121-134.

Altomare, C., Domínguez, J. M., Crespo, A. J. C., Suzuki, T., Caceres, I., & Gómez-Gesteira, M. (2016). Hybridization of the wave propagation model SWASH and the meshfree particle method SPH for real coastal applications. Coastal Engineering Journal, 57(4), 1550024-1.

Altomare, C., Tagliafierro, B., Dominguez, J. M., Suzuki, T., & Viccione, G. (2018). Improved relaxation zone method in SPH-based model for coastal engineering applications. Applied Ocean Research, 81, 15-33.

Oger, G., Le Touzé, D., Ducrozet, G., Candelier, J., & Guilcher, P. M. (2014). A Coupled SPH-Spectral Method for the Simulation of Wave Train Impacts on a FPSO. In ASME 2014 33rd International Conference on Ocean, Offshore and Arctic Engineering (pp. V002T08A088-V002T08A088). American Society of Mechanical Engineers.

Verbrugghe, T., Domínguez, J. M., Crespo, A. J., Altomare, C., Stratigaki, V., Troch, P., & Kortenhaus, A. (2018). Coupling methodology for smoothed particle hydrodynamics modelling of non-linear wave-structure interactions. Coastal Engineering, 138, 184-198.

Serván-Camas, B., Cercos-Pita, J. L., Colom-Cobb, J., García-Espinosa, J., & Souto-Iglesias, A. (2016). Time domain simulation of coupled sloshing–seakeeping problems by SPH–FEM coupling. Ocean Engineering, 123, 383-396.

Bulian, G., & Cercos-Pita, J. L. (2018). Co-simulation of ship motions and sloshing in tanks. Ocean Engineering, 152, 353-376.

Marrone, S., Di Mascio, A., & Le Touzé, D. (2016). Coupling of Smoothed Particle Hydrodynamics with Finite Volume method for free-surface flows. Journal of Computational Physics, 310, 161-180.

Napoli, E., De Marchis, M., Gianguzzi, C., Milici, B., & Monteleone, A. (2016). A coupled finite volume–smoothed particle hydrodynamics method for incompressible flows. Computer Methods in Applied Mechanics and Engineering, 310, 674-693.

Fernandez-Gutierrez, D., Souto-Iglesias, A., & Zohdi, T. I. (2018). A hybrid Lagrangian Voronoi–SPH scheme. Computational Particle Mechanics, 5(3), 345-354.

Kumar, P., Yang, Q., Jones, V., & McCue-Weil, L. (2015). Coupled SPH-FVM simulation within the OpenFOAM framework. Procedia IUTAM, 18, 76-84.

GC#5: Applicability to industry


Jean-Christophe Marongiu
Matthieu De Leffe


Even though the SPH method is getting more popular in the research community, there are several important aspects to be considered to foster its diffusion and adoption among industry:

Pre-processing: the creation of a suitable initial condition can be a delicate task, especially regarding the initial distribution of particles. It is usually possible to use existing tools and file formats to manipulate discretized surfaces of solid objects, often in the form of triangulated surfaces  (STL, PLY, VTK), describing solid wall boundary conditions. “Particle meshers” are however required to cover the initial fluid domain (volume) with particles. Traditional meshing tools are not suitable because the initial configuration of particles should minimize integration errors for the numerical scheme employed in the solver. As an illustration, most SPH practitioners make use of an isotropic SPH kernel function with uniform smoothing length. In that case the initial particle distribution should be made of equidistant particle centers. Some numerical treatments of boundary conditions also require the filling of a specific region outside the boundary with particles. The so-called particle packing algorithm (Colagrossi et al., 2012) has brought a convenient way to optimally arrange position of particles. The burden of creating the particles in an empty arbitrarily shaped volume is usually treated in complex workflows involving several steps. Turnaround time should be kept as short as possible.


Post-processing: the traditional visualization tools are not well suited for the visualization of results from particle methods. It is necessary to be able to visualize several hundred million particles. Moreover, in order to visualize the free surface or the interfaces between fluids, it is necessary to carry out a reconstruction of the interface, compatible with the new techniques of automatic refinement. Similarly, making slice in the computational domain or plotting the trajectory of particles should be made possible. Many advanced processing still rely on a projection of particles data onto a grid. Development of post-processing tools natively using particle data should be encouraged.

Ratio computational cost vs precision: in industry, the ratio cost vs precision is the first criterion of choice for numerical methods. In order to reduce this ratio it is possible to tackle either the cost or the precision. o   For a calculation of several hundred million particles, the calculation costs could be thousands of euros, with a turnaround time of several days or several weeks. In order to make the SPH method compatible with the time constraints in the industry, the calculation costs as well as the restitution time must be significantly reduced. o   The cost of a simulation also includes pre- and post-processing steps. o    The traditional SPH method has more or less a precision of order one. Techniques for increasing the order must be developed and applicable to real case, while maintaining a reasonable turnaround time.

Robustness and ease of use: to achieve a stable and precise simulation, several numerical parameters (choice of kernel function, size of support, artificial viscosity, CFL, ICT, XSPH ...) may be adjusted. These parameters are case dependent. For a non-expert CFD engineer to achieve an SPH simulation, generalist methods with a minimum of parameters (eg Riemann solvers instead of artificial viscosity, adaptive particle refinement) should be developed and encouraged. Indicators helping is assessing the quality of a simulation result (local / global error estimates, convergence) would provide non-specialists with some confidence in their decisions. Graphical User Interfaces are also a standard in CFD packages available on the market. Traditional CFD users are getting used to run their complete workflows from a single interface. 

Reputation: Decision making in industry may not always receive the time and efforts it deserves, but also alternatives showing minimized risks are often favored. Publications showing technical progress of the method with respect to other Grand Challenges and well validated applications in diverse real life fields should be encouraged and well-advertised.  


The references follow:


M.S. Shadloo, G. Oger, D. Le Touzé, Smoothed particle hydrodynamics method for fluid flows, towards industrial applications: Motivations, current state, and challenges, In Computers & Fluids, Volume 136, 2016, Pages 11-34, ISSN 0045-7930,

Andrea Colagrossi, B. Bouscasse, M. Antuono, S. Marrone, Particle packing algorithm for SPH schemes, In Computer Physics Communications, Volume 183, Issue 8, 2012, Pages 1641-1653, ISSN 0010-4655,

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