Abstract
The SPH method (smoothed-particle hydrodynamics) is a numerical meshless, particle and lagrangian method. It is used in a lot of fields of engineering and science such as solids mechanics, hydraulics, and astrophysics. The medium is represented, thanks to a set of particles which interact with each other. Nowadays, the SPH method is still under development but is able to deal with a wide range of problems in hydraulics. This article focuses especially on open channel quasi-incompressible flows. While implementing a SPH code, a programmer can face up some difficulties such as the neighbors search, the boundary conditions, the speed of sound, or the initialization of the particles. We have drawn some unexpected conclusions concerning the compressibility of the fluid and the way the particles are initialized. This paper presents also a list of test cases that can be performed in order to validate an SPH code. It includes: (a) a tank of still water, (b) a spinning tank, and (c) a dam break on a dry bed. These test cases allowed us to highlight some undesired effects. Finally, a new test case is developed. It is based on new experimental results of a flow on a spillway. For this test case, open boundaries have been implemented. The results presented in this paper are based on a 3-D code implemented during a master thesis.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Canor, T., & Denoël, V. (2013). Transient Fokker-Planck-Kolmogorov equation solved with smoothed particle hydrodynamics method. International Journal for Numerical Methods in Engineering, 94(6), 535–553.
Crespo, A. J. C., Gómez-Gesteira, M., & Dalrymple, R. A. (2007). Boundary conditions generated by dynamic particles in SPH methods. Computers, Materials and Continua, 5(3), 173–184.
Dalrymple, R. A., & Knio, O. (2001). SPH modelling of water waves. Sweden: ASCE.
Dymond, J. H., & Malhotra, R. (1988). The Tait equation: 100 years on. International Journal of Thermophysics, 9(6), 941–951.
Ferrand, M., et al. (2013). 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.
Gingold, R. A., & Monaghan, J. J. (1977). Smoothed particle hydrodynamics-theory and application to non-spherical stars. Monthly Notices of the Royal Astronomical Society, 181, 375–389.
Goffin, L. (2013). Development of a didactic SPH model. Liege: University of Liege (ULg).
Gomez-Gesteira, M., et al. (2012). SPHysics—development of a free-surface fluid solver—Part 2: Efficiency and test cases. Computers and Geosciences, 48, 300–307.
Gomez-Gesteira, M., et al. (2012). SPHysics—development of a free-surface fluid solver—Part 1: Theory and formulations. Computers and Geosciences, 48, 289–299.
Gomez-Gesteira, M., et al. (2010). State-of-the-art of classical SPH for free-surface flows. Journal of Hydraulic Research, 48(1), 6–27.
Hager, W., & Schleiss, A. (2009). Traité de Génie Civil, Volume 15—Constructions Hydrauliques—Ecoulements Stationnaires. Switzerland: PPUR-Presses Polytechniques Romandes.
Jánosi, I. M., et al. (2004). Turbulent drag reduction in dam-break flows. Experiments in Fluids, 37(2), 219–229.
Johnson, G. R., Stryk, R. A., & Beissel, S. R. (1996). SPH for high velocity impact computations. Computer Methods in Applied Mechanics and Engineering, 139(1), 347–373.
Koshizuka, S., & Oka, Y. (1996). Moving-particle semi-implicit method for fragmentation of incompressible fluid. Nuclear Science and Engineering, 123(3), 421–434.
Lastiwka, M., Basa, M., & Quinlan, N. J. (2009). Permeable and non-reflecting boundary conditions in SPH. International Journal for Numerical Methods in Fluids, 61(7), 709–724.
Lind, S. J., et al. (2012). Incompressible smoothed particle hydrodynamics for free-surface flows: A generalised diffusion-based algorithm for stability and validations for impulsive flows and propagating waves. Journal of Computational Physics, 231(4), 1499–1523.
Liu, G. (2003). Mesh free methods: moving beyond the finite element method. New York: CRC Press.
Liu, G. G.-R., & Liu, M. (2003). Smoothed particle hydrodynamics: a meshfree particle method. Singapore: World Scientific.
Lodomez, M. (2014). Determining the characteristics of a free jet in 2-D by the SPH method. Liege: University of Liege (ULg).
Lucy, L. B. (1977). A numerical approach to the testing of the fission hypothesis. The astronomical journal, 82, 1013–1024.
Monaghan, J. J. (1988). An introduction to SPH. Computer Physics Communications, 48(1), 89–96.
Monaghan, J. J. (1994). Simulating Free Surface Flows with SPH. Journal of Computational Physics, 110(2), 399–406.
Monaghan, J. J., & Kos, A. (1999). Solitary waves on a cretan beach. Journal of Waterway, Port, Coastal and Ocean Engineering, 125(3), 145–154.
Monaghan, J. J., & Lattanzio, J. C. (1985). A refined particle method for astrophysical problems. Astronomy and Astrophysics, 149, 135–143.
Nelson, R. P., & Papaloizou, J. C. (1994). Variable smoothing lengths and energy conservation in smoothed particle hydrodynamics. arXiv preprint astro-ph/9406053.
Randles, P. W., & Libersky, L. D. (1996). Smoothed particle hydrodynamics: Some recent improvements and applications. Computer Methods in Applied Mechanics and Engineering, 139(1–4), 375–408.
Violeau, D. (2009). Dissipative forces for Lagrangian models in computational fluid dynamics and application to smoothed-particle hydrodynamics. Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, 80(3).
Violeau, D. (2012). Fluid Mechanics and the SPH method: theory and applications. Oxford: Oxford University Press.
Violeau, D., & Leroy, A. (2014). On the maximum time step in weakly compressible SPH. Journal of Computational Physics, 256, 388–415.
Aknowledgments
The authors are grateful for the data provided and the fruitful discussions with Dr. Yann Peltier.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer Science+Business Media Singapore
About this chapter
Cite this chapter
Goffin, L., Erpicum, S., Dewals, B.J., Pirotton, M., Archambeau, P. (2016). Validation and Test Cases for a Free Surface SPH Model. In: Gourbesville, P., Cunge, J., Caignaert, G. (eds) Advances in Hydroinformatics. Springer Water. Springer, Singapore. https://doi.org/10.1007/978-981-287-615-7_12
Download citation
DOI: https://doi.org/10.1007/978-981-287-615-7_12
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-287-614-0
Online ISBN: 978-981-287-615-7
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)