Consistency and errors in Smoothed Particle Hydrodynamics using several approaches in a 2D pipe
DOI:
https://doi.org/10.31349/RevMexFis.71.020602Keywords:
Smoothed Particle Hydrodynamics, consistency, error measuresAbstract
Smoothed Particle Hydrodynamics (SPH) has become a promising tool for the simulation of fluids. Although too much research has been addressed to improve the method over the years, a comparison of the errors and consistency evolution when trying different approaches are still necessary to define the best scheme for practical applications. Here, a two-dimensional Poiseuille flow test benchmark is employed to enforce comparisons when varying the kernel, the definition of the sound speed in
the pressure term, the viscosity and the Reynolds number.
References
L. B. Lucy, A numerical approach to the testing of the fission hypothesis. The Astronomical Journal 82 (1977) 1013, https://doi.org/10.1086/112164
R. Gingold, J. Monaghan, Smoothed particle hydrodynamics theory and application to non-spherical stars. Monthly Notices of the Royal Astronomical Society 181 (1977) 375, https://doi.org/10.1093/mnras/181.3.375
D.d. Padova, L. Calvo, P. Carbone, D. Maraglino, M. Mossa, Comparison between the Lagrangian and Eulerian Approach for Simulating Regular and Solitary Waves Propagation, Breaking and Run- Up. Applied Sciences 11 (2021) 1, doi: https://doi.org/10.3390/app11209421
C. Alvarado-Rodríguez, L. Díaz-Damacillo, E. Plaza, L. Sigalotti, Smoothed Particle Hydrodynamics Simulations of Porous Medium Flow Using Ergun’s Fixed- Bed Equation. Water 15 (2023) 1, doi: https://doi.org/10.3390/w15132358
R. Burden, D. Faires, Numerical Analysus. USA: BROOKS COLE. 2010. ISBN 13: 978-0-538-73351-9
C. A. Dutra-Filho, Smoothed Particle Hydrodynamics. Fundamentals and Basic Applications in Continuum Mechanicsd. Springer Cham. (2019)
F. Rasio, Particle Methods in Astrophysical Fluid Dynamics. Progress of Theoretical Physics Supplement 138 (2000) 609, https://doi.org/10.1143/PTPS.138.609
R. Gabbasov, L. Sigalotti, F. Cruz, J. Klapp, and J. Ramirez Velasquez, Consistent SPH Simulations of Protostellar Collapse and Fragmentation. The Astrophysical Journal 835 (2017) 25, https://doi.org/10.3847/1538-4357/aa5655
J. Read, T. Hayfield, O. Agertz, Resolving mixing in smoothed particle hydrodynamics. Monthly Notices of the Royal Astronomical Society 405 (2010) 1513, https://doi.org/10.1111/j.1365-2966.2010.16577.x
Q. Zhu, L. Hernquist, and Y. Li Numerical convergence in smoothed particle hydrodynamics. The Astrophysical Journal 800 (2015) 6, https://doi.org/10.1088/0004-637X/800/1/6
L. Sigalotti, J. Klapp, O. Rendon, C. Vargas, F. Peña-Polo, On the kernel and particle consistency in smoothed particle hydrodynamics. Applied Numerical Mathematics 108 (2016) 242, https://doi.org/10.1016/j.apnum.2016.05.007
L. Sigalotti O. Rendon J. Klapp C. Vargas and F. Cruz, A new insight into the consistency of the SPH interpolation formula. Applied Mathematics and Computation 356 (2019) 50, https://doi.org/10.1016/j.amc.2019.03.018
D. Violeau and T. Fonty, Calculating the smoothing error in SPH. Computers and Fluids 191 (2019) 104240, https://doi.org/10.1016/j.compfluid.2019.104240
L. Landau, and E. Lifshitz Fluid Mechanics. (Oxford: Pergamon Press. 1987). ISBN 0-08-033933-6
J. Klapp, Sigalotti LDG, Alvarado-Rodríguez CE, Rendon O, Dıaz-Damacillo L. Approximately consistent SPH simulations of the anisotropic dispersion of a contaminant plume. Computational Particle Mechanics 9 (2022) 987, https://doi.org/10.1007/s40571-022-00461-1
G. Batchelor, An Introduction to Fluid Dynamics. Cambridge: (Cambridge University Press. 1967)
J. Morris, P. Fox, and Y. Zhu, Modeling Low Reynolds Number Incompressible Flows Using SPH. Journal of computational physics 136 (1997) 214, https://doi.org/10.1006/jcph.1997.5776
A. Tartakovsky et al., Smoothed particle hydrodynamics and its applications for multiphase flow and reactive transport in porous media. Computational Geoscience 20 (2015) 807, https://doi.org/10.1007/s10596-015-9468-9
J. Monaghan, Smoothed particle hydrodynamics. Reports on Progress in Physics 68 (2005) 1703, https://doi.org/10.1088/0034-4885/68/8/R01
A. Colagrossi, and M. Landrini, Numerical simulation of interfacial flows by smoothedparticle hydrodynamics. Journal of computational physics 191 (2003) 448, https://doi.org/10.1016/S0021-9991(03)00324-3
J. Monaghan and R. Gingold, Shock Simulation by the Particle Method SPH. Journal of Computational Physics 52 (1983) 374, https://doi.org/10.org/10.1016/0021-9991(83)90036-0
E. Lo, and S. Shao, Simulation of near-shore solitary wave mechanics by an incompressible SPH method. Applied Ocean Research 24 (2002) 275, https://doi.org/10.1016/S0141-1187(03)00002-6
G. Liu, M. Liu, Smoothed Particle Hydrodynamics: A Meshfree Particle Method. Singapore: (World Scientific. 2003)
J. Monaghan, Smoothed particle hydrodynamics. Annual Review of Astronomy and Astrophysics 30 (1992) 543, https://doi.org/10.1146/annurev.aa.30.090192.002551
D. Price, Smoothed particle hydrodynamics and magnetohydrodynamics. Journal of Computational Physics 231 (2012) 759, https://doi.org/10.1016/j.jcp.2010.12.011
S. Nugent and H. Posch Liquid drops and surface tension with smoothed particle applied mechanics. Physical Review E 62 (2000) 4968, https://doi.org/10.1103/Phys-RevE.62.4968
L. Sigalotti, J. Klapp, E. Sira, Y. Melean, and A. Hasmy, SPH simulations of time-dependent Poiseuille flow at low Reynolds numbers. Journal of Computational Physics 191 (2003) 622, https://doi.org/10.1016/S0021-9991(03) 00343-7
Y. Melean, L. Sigalotti, and A. Hasmy, On the SPH tensile instability in forming viscous liquid drops. Computer Physics Communications 157 (2004) 191, https://doi.org/10.1016/j.comphy.2003.11.002
F. Jiang M. Oliveira, and A. Sousa, Mesoscale SPH modeling of fluid flow in isotropic porous media. Computer Physics Communications 176 (2007) 471, https://doi.org/10.1016/j.cpc.2006.12.003
P. Kunz et al., Study of multi-phase flow in porous media: Comparison of SPH simulations with micro-model experiments. Transport in Porous Media 114 (2015) 581, https://doi.org/10.1007/s11242-015-0599-1
R. Canelas, A. Crespo, J. Dominguez, R. Ferreira, and M. Gomez- Gesteira, SPH-DCDEM model for arbitrary geometries in free surface solid-fluid flows. Computer Physics Communications 202 (2016) 131, https://doi.org/10.1016/j.cpc.2016.01.006
E. Plaza et al., Efficiency of particle search methods in smoothed particle hydrodynamics: a comparative study (part I). Progress in Computational Fluid Dynamics 21 (2021) 1, https://doi.org/10.1504/PCFD.2021.112625
W. Dehnen and H. Aly, Improving convergence in smoothed particle hydrodynamics simulations without pairing instability. Monthly Notices of the Royal Astronomical Society, 425 (2012) 1068, https://doi.org/10.1111/j.1365-2966.2012.21439.x
H. Wendland, Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree. Advances in Computational Mathematics 4 (1995) 389, https://doi.org/10.1007/BF02123482
K. Urbanowicz, A. Bergant, M. Stosiak, A. Deptuła, M. Karpenko, Navier-Stokes Solutions for Accelerating Pipe Flow - A Review of Analytical Models. Energies, 16 (2023) 1, https://doi.org/10.3390/en16031407
A. Chorin, A numerical method for solving incompressible viscous flow problems. Journal of Computational Physics, 2 (1967) 12, https://doi.org/10.1016/0021-9991(67)90037-X
C. Alvarado-Rodríguez, J. Klapp, L. Sigalotti, J. Domínguez, d. lE. Cruz-Sanchez, Nonreflecting outlet boundary conditions for incompressible flows using SPH. Computers and Fluids 159 (2017) 177, https://doi.org/10.1016/j.compfluid.2017.09.020
J. Monaghan, J. Lanttazio, A refined particle method for astrophysical problems. Astronomy and astrophysics 149 (1985) 135
L. Libersky, A. Petschek, T. Carney, J. Hipp, and F. Allahdadi High Strain Lagrangian Hydrodynamics: A Three- Dimensional SPH Code for Dynamic Material Response. Advances in Computational Mathematics, 109 (1993) 67, https://doi.org/10.1006/jcph.1993.1199
J. Monaghan, Simulating free surface flows with SPH. Journal of Computational Physics, 110 (1994) 399, https://doi.org/10.1006/jcph.1994.1034
S. Liu, I. Nistor, M. Mohammadian, Evaluation of the Solid Boundary Treatment Methods in SPH. International Journal of Ocean and Coastal Engineering 1 (2018) 1, https://doi.org/10.1142/S252980701840002X
P. Randles, L. Libersky, SPH Modeling of Solid Boundaries Through a SemiAnalytic Approach. Computer Methods in Applied Mechanics and Engineering 139 (1996) 375, https://doi.org/10.1016/S0045-7825(96)01090-0
A. Monaco, S. Manenti, M. Gallati,and S. Sibilla, Agate G, Guandalini R. SPH Modeling of Solid Boundaries Through a SemiAnalytic Approach. Engineering Applications of Computational Fluid Mechanics 5 (2011) 1, https://doi.org/10.1080/19942060.2011.11015348
H. Takeda, S. Miyama, M. Sekiya, Numerical Simulation of Viscous Flow by Smoothed Particle Hydrodynamics. Progress of Theoretical Physics 92 (1994) 939, https://doi.org/10.1143/ptp/92.5.939
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 E. Plaza, E. Santacruz, D. Aguila, R. Cobos, W. Angulo, L. Di G Sigalotti, J. Klapp
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors retain copyright and grant the Revista Mexicana de Física right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
