Abstract
Smoothed-Particle Hydrodynamics (SPH) has drawn a great deal of attention in recent years to model various phenomena in engineering and science. SPH is a Lagrangian model in which moving particles represent the fluid body during simulation. Therefore, the initial distribution of particles may affect the model results along with the simulation, and a good initial condition can minimize numerical errors or increase the computational efficiency. Since SPH model particle distributions need a flow pattern, the dam break flow as a classic benchmark SPH problem is selected in this study, and the best initial particle distribution for this case has to be found. Different results, including the mean density of particles, hydrostatic and dynamic pressures and surge front position, are considered the main model results for the adequacy of different initial particle distributions to be discussed. All models are verified at first by simulating different test cases and comparing the results with analytical and experimental data. Acceptable agreements between these data show the model’s capability in well predicting the dam break flows. Then, the effects of initial particle distribution on the results are investigated by considering five different particle distributions. For this purpose, Body-Centered Cubic (BCC), Simple Cubic (SC), Greedy, Voronoi Tessellation and Fibonacci algorithms for particle distributions have been modeled. To get reliable conclusions, these distributions have been utilized in models with different kernel functions as well as with different particle spacings. Based on the results, irregular arrangements such as Greedy distribution perform better than regular SC and BCC distributions in modeling dam-break flow. In addition, both Voronoi and Fibonacci distributions perform almost the same with a moderate level of accuracy. Regarding mentioned arrangements, the main outcome of this study, is that the initial particle distribution is an important issue in SPH models, which clearly affects the results.
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References
Akbari H (2018) Evaluatoin of incompressible and compressible SPH methods in modeling dam break flows. International Journal of Coastal and Offshore Engineering 2(1):45–57, DOI: https://doi.org/10.29252/ijcoe.2.1.45
Akbari H (2019) An improved particle shifting technique for incompressible smoothed particle hydrodynamics methods. International Journal for Numerical Methods in Fluids, DOI: https://doi.org/10.1002/fld.4737
Akbari H, Pooyarad A (2020) Wave force on protected submarine pipelines over porous and impermeable beds using SPH numerical model. Applied Ocean Research 98:102118, DOI: https://doi.org/10.1016/j.apor.2020.102118
Arth A, Donnert J, Steinwandel U, Böss L, Halbesma T, Pütz M, Hubber D, Dolag K (2019) WVTICs — SPH initial conditions for everyone. ArXiv Vol. abs, DOI: https://doi.org/10.48550/arXiv.1907.11250
Brown DK (2013) Institute for electronics and nanotechnology, Georgia Institute of Technology
Chaniotis AK, Poulikakos D, Koumoutsakos P (2003) Remeshed smoothed particle hydrodynamics for the simulation of viscous and heat conducting flows. Journal of Computational Physics 182:67–90, DOI: https://doi.org/10.1006/jcph.2002.7152
Chanson H (2005) Analytical solution of dam break wave with flow resistance: Application to tsunami surges — UQ espace. Proceedings of the 31st IAHR Biennial Congress, 31st IAHR Congress 2005: Water Engineering for the Future, Choices and Challenges, Korea Water Resources Association
Cleary PW, Monaghan JJ (1999) Conduction modelling using smoothed particle hydrodynamics. Journal of Computational Physics 148(1): 227–264, DOI: https://doi.org/10.1006/jcph.1998.6118
Colagrossi A, Landrini M (2003) Numerical simulation of interfacial flows by smoothed particle hydrodynamics. Journal of Computational Physics 191(2):448–475, DOI: https://doi.org/10.1016/S0021-9991(03)00324-3
Cormen TH, Leiserson CE, Rivest RL, Stein C (2009) Introduction to Algorithms, Third Edition, 3rd Ed., The MIT Press
Cummins SJ, Rudman M (1999) An SPH projection method. Journal of Computational Physics 152(2):584–607, DOI: https://doi.org/10.1006/jcph.1999.6246
De Marchi S, Schaback R, Wendland H (2005) Near-optimal data-independent point locations for radial basis function interpolation. Advances in Computational Mathematics 23(3):317–330, DOI: https://doi.org/10.1007/s10444-004-1829-1
Di Mascio A, Marrone S, Colagrossi A, Chiron L, Le Touzé D (2021) SPH-FV coupling algorithm for solving multi-scale three-dimensional free-surface flows. Applied Ocean Research 115:102846, DOI: https://doi.org/10.1016/j.apor.2021.102846
Diehl S, Rockefeller G, Fryer CL, Riethmiller D, Statler TS (2015) Generating optimal initial conditions for smoothed particle hydrodynamics simulations. Publications of the Astronomical Society of Australia 32, DOI: https://doi.org/10.1017/pasa.2015.50
Flow Science Inc. (2018) FLOW-3D® Version 12.0 Users Manual. Flow Science, Inc.
Fu L, Ji Z (2019) An optimal particle setup method with centroidal voronoi particle dynamics. Computer Physics Communications 234:72–92, DOI: https://doi.org/10.1016/j.cpc.2018.08.002
Gesteira MG, Rogers BD, Dalrymple RA, Crespo AJC, Narayanaswamy M (2010) User guide for the SPHysics code
Gomez-Gesteira M, Rogers BD, Dalrymple RA, Crespo AJC (2010) State-of-the-art of classical SPH for free-surface flows. Journal of Hydraulic Research 48(sup1):6–27, DOI: https://doi.org/10.1080/00221686.2010.9641242
Hirt CW, Nichols BD (1981) Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics 39(1):201–225, DOI: https://doi.org/10.1016/0021-9991(81)90145-5
Hu C, Kashiwagi M (2004) A CIP-based method for numerical simulations of violent free-surface flows. SpringerLink 9:143–157, DOI: https://doi.org/10.1007/s00773-004-0180-z
Hu T, Wang S, Zhang G, Sun Z, Zhou B (2019) Numerical simulations of sloshing flows with an elastic baffle using a SPH-SPIM coupled method. Applied Ocean Research 93:101950, DOI: https://doi.org/10.1016/j.apor.2019.101950
Kang JM (2008) Voronoi diagram. Encyclopedia of GIS, Shekhar, S. and Xiong, H. eds., Springer US, Boston, MA 1232–1235
Koumoutsakos P (1997) Inviscid axisymmetrization of an elliptical vortex. Journal of Computational Physics 138(2):821–857, DOI: https://doi.org/10.1006/jcph.1997.5749
Lejeune Dirichlet G (1850) Über die reduction der positiven quadratischen formen mit drei unbestimmten ganzen Zahlen. Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal) 1850(40): 209–227, DOI: https://doi.org/10.1515/crll.1850.40.209
Lind SJ, Stansby PK, Rogers BD (2016) Fixed and moored bodies in steep and breaking waves using SPH with the Froude-Krylov approximation. Journal of Ocean Engineering and Marine Energy 2(3):331–354, DOI: https://doi.org/10.1007/s40722-016-0056-4
Lind SJ, Xu R, Stansby PK, Rogers BD (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, DOI: https://doi.org/10.1016/j.jcp.2011.10.027
Liu GR, Liu MB (2003) Smoothed particle hydrodynamics: A meshfree particle method, DOI: https://doi.org/10.1142/5340
Lucy LB (1977) A numerical approach to the testing of the fission hypothesis. The Astronomical Journal 82:1013–1024, DOI: https://doi.org/10.1086/112164
Luo M, Khayyer A, Lin P (2021) Particle methods in ocean and coastal engineering. Applied Ocean Research 114:102734, DOI: https://doi.org/10.1016/j.apor.2021.102734
Ma QW, Zhou Y, Yan S (2016) A review on approaches to solving Poisson’s equation in projection-based meshless methods for modelling strongly nonlinear water waves. Journal of Ocean Engineering and Marine Energy 2(3):279–299, DOI: https://doi.org/10.1007/s40722-016-0063-5
Martin JC, Moyce WJ, Penney WG, Price AT, Thornhill CK (1952) An experimental study of the collapse of liquid columns on a rigid horizontal plane. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences 244(882): 312–324, DOI: https://doi.org/10.1098/rsta.1952.0006
Monaghan JJ (1992) Smoothed particle hydrodynamics. Annual Review of Astronomy and Astrophysics 30(1):543–574, DOI: https://doi.org/10.1146/annurev.aa.30.090192.002551
Monaghan JJ (1994) Simulating free surface flows with SPH. Journal of Computational Physics 110(2):399–406, DOI: https://doi.org/10.1006/jcph.1994.1034
Morris JP, Fox PJ, Zhu Y (1997) Modeling low reynolds number incompressible flows using SPH. Journal of Computational Physics 136(1):214–226, DOI: https://doi.org/10.1006/jcph.1997.5776
Okahci N, Hirota A, Izawa S, Fukunishi Y, Higuchi H (2001) SPH simulation of pulsating pipe flow at a junction. Proceedings of the 1st International Symposium on Advanced Fluid Information 388–391
Sasani Babak A, Akbari H (2019) Numerical study of wave run-up and overtopping considering bed roughness using SPH-GPU. Coastal Engineering Journal 61(4):502–519, DOI: https://doi.org/10.1080/21664250.2019.1647961
Siemann MH, Ritt SA (2019) Novel particle distributions for SPH bird-strike simulations. Computer Methods in Applied Mechanics and Engineering 343:746–766, DOI: https://doi.org/10.1016/j.cma.2018.08.044
Vela Vela L, Sanchez R Geiger J (2018) ALARIC: An algorithm for constructing arbitrarily complex initial density distributions with low particle noise for SPH/SPMHD applications. Computer Physics Communications 224:186–197, DOI: https://doi.org/10.1016/j.cpc.2017.10.017
Voronoi G (1908) Nouvelles applications des paramètres continus à la théorie des formes quadratiques. Premier mémoire. Sur quelques propriétés des formes quadratiques positives parfaites. Journal Für Die Reine und Angewandte Mathematik (Crelles Journal) 1908(133): 97–102, DOI: https://doi.org/10.1515/crll.1908.133.97
Xu R, Stansby P, Laurence D (2009) Accuracy and stability in incompressible SPH (ISPH) based on the projection method and a new approach. Journal of Computational Physics 228(18):6703–6725, DOI: https://doi.org/10.1016/j.jcp.2009.05.032
Yeylaghi S, Moa B, Oshkai P, Buckham B, Crawford C (2017) ISPH modelling for hydrodynamic applications using a new MPI-based parallel approach. Journal of Ocean Engineering and Marine Energy 3(1):35–50, DOI: https://doi.org/10.1007/s40722-016-0070-6
Young J, Alcântara I, Teixeira-Dias F, Ooi J, Mill F (2015) Regular or random: A discussion on SPH initial particle distribution. Proceedings of the 4th International Conference on Particle-Based Methods — Fundamentals and Applications, PARTICLES 2015, International Center for Numerical Methods in Engineering 1105–1116
Zhang AM, Ming FR, Wang SP (2013) Coupled SPHS-BEM method for transient fluid-structure interaction and applications in underwater impacts. Applied Ocean Research 43:223–233, DOI: https://doi.org/10.1016/j.apor.2013.10.002
Zhang ZL, Khalid MSU, Long T, Liu MB, Shu C (2021) Improved element-particle coupling strategy with δ-SPH and particle shifting for modeling sloshing with rigid or deformable structures. Applied Ocean Research 114:102774, DOI: https://doi.org/10.1016/j.apor.2021.102774
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Pourlak, M., Akbari, H. & Jabbari, E. Importance of Initial Particle Distribution in Modeling Dam Break Analysis with SPH. KSCE J Civ Eng 27, 218–232 (2023). https://doi.org/10.1007/s12205-022-0304-1
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DOI: https://doi.org/10.1007/s12205-022-0304-1