Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
skip to main content
research-article

PySPH: A Python-based Framework for Smoothed Particle Hydrodynamics

Published: 28 September 2021 Publication History

Abstract

PySPH is an open-source, Python-based, framework for particle methods in general and Smoothed Particle Hydrodynamics (SPH) in particular. PySPH allows a user to define a complete SPH simulation using pure Python. High-performance code is generated from this high-level Python code and executed on either multiple cores, or on GPUs, seamlessly. It also supports distributed execution using MPI. PySPH supports a wide variety of SPH schemes and formulations. These include, incompressible and compressible fluid flow, elastic dynamics, rigid body dynamics, shallow water equations, and other problems. PySPH supports a variety of boundary conditions including mirror, periodic, solid wall, and inlet/outlet boundary conditions. The package is written to facilitate reuse and reproducibility. This article discusses the overall design of PySPH and demonstrates many of its features. Several example results are shown to demonstrate the range of features that PySPH provides.

References

[1]
L. B. Lucy. 1977. A numerical approach to testing the fission hypothesis. The Astronomical Journal 82, 12 (1977), 1013–1024.
[2]
R. A. Gingold and J. J. Monaghan. 1977. Smoothed particle hydrodynamics: Theory and application to non-spherical stars. Monthly Notices of the Royal Astronomical Society 181, 3 (1977), 375–389.
[3]
Alejandro J. C. Crespo, José M. Domínguez, Benedict D. Rogers, Moncho Gómez-Gesteira, S. Longshaw, R. Canelas, Renato Vacondio, A. Barreiro, and O. García-Feal. 2015. DualSPHysics: Open-source parallel CFD solver based on Smoothed Particle Hydrodynamics. Computer Physics Communications 187 (2015), 204–216.
[4]
Volker Springel, Rüdiger Pakmor, Oliver Zier, and Martin Reinecke. 2021. Simulating cosmic structure formation with the GADGET-4 code. Monthly Notices of the Royal Astronomical Society 506, 2 (2021), 2871–2949.
[5]
Jose L. Cercos-Pita. 2015. AQUAgpusph, a new free 3D SPH solver accelerated with OpenCL. Computer Physics Communications 192 (2015), 295–312.
[6]
Daniel J. Price, James Wurster, Terrence S. Tricco, Chris Nixon, Stéven Toupin, Alex Pettitt, Conrad Chan, Daniel Mentiplay, Guillaume Laibe, Simon Glover, Clare Dobbs, Rebecca Nealon, David Liptai, Hauke Worpel, Clément Bonnerot, Giovanni Dipierro, Giulia Ballabio, Enrico Ragusa, Christoph Federrath, Roberto Iaconi, Thomas Reichardt, Duncan Forgan, Mark Hutchison, Thomas Constantino, Ben Ayliffe, Kieran Hirsh, and Giuseppe Lodato.2018. PHANTOM: A smoothed particle hydrodynamics and magnetohydrodynamics code for astrophysics. Publications of the Astronomical Society of Australia 35 (2018), e031.
[7]
Dan Koschier, Jan Bender, Barbara Solenthaler, and Matthias Teschner. 2019. Smoothed particle hydrodynamics techniques for the physics based simulation of fluids and solids. In Proceedings of the Eurographics 2019 - Tutorials, Wenzel Jakob and Enrico Puppo (Eds.). The Eurographics Association.
[8]
M. S. Shadloo, G. Oger, and D. Le Touze. 2016. Smoothed particle hydrodynamics method for fluid flows, toward industrial applications: Motivations, current state, and challenges. Computers & Fluids 136 (September 2016), 11–34.
[9]
Philip F. Hopkins. 2015. A new class of accurate, mesh-free hydrodynamic simulation methods. Monthly Notices of the Royal Astronomical Society 450, 1 (2015), 53–110.
[10]
Giuseppe Bilotta, Alexis Hérault, Annalisa Cappello, Gaetana Ganci, and Ciro Del Negro. 2016. GPUSPH: A Smoothed Particle Hydrodynamics model for the thermal and rheological evolution of lava flows. Geological Society, London, Special Publications 426, 1 (2016), 387–408.
[11]
Andrea Amicarelli, Sauro Manenti, Raffaele Albano, Giordano Agate, Marco Paggi, Laura Longoni, Domenica Mirauda, Latifa Ziane, Giacomo Viccione, Sara Todeschini, Aurelia Sole, Lara Martina Baldini, Davide Brambilla, Monica Papini, Mohamed Cherif Khellaf, Bonaventura Tagliafierro, Luca Sarno, and Guido Pirovano.2020. SPHERA v. 9.0. 0: A computational fluid dynamics research code, based on the smoothed particle hydrodynamics mesh-less method. Computer Physics Communications 250, (2020), 107157.
[12]
J. Michael Owen et al. 2011–. SPHERAL++. (2011–). Retrieved on 28th December, 2020 from https://github.com/LLNL/spheral.
[13]
Chi Zhang, Massoud Rezavand, Yujie Zhu, Yongchuan Yu, Dong Wu, Wenbin Zhang, Shuoguo Zhang, Jianhang Wang, and Xiangyu Hu. 2020. SPHinXsys: An open-source meshless, multi-resolution and multi-physics library. Software Impacts 6 (2020), 100033.
[14]
L. Prechelt. 2000. An empirical comparison of seven programming languages. Computer 33, 10 (Oct. 2000), 23–29.
[15]
Jan Gmys, Tiago Carneiro, Nouredine Melab, El-Ghazali Talbi, and Daniel Tuyttens. 2020. A comparative study of high-productivity high-performance programming languages for parallel metaheuristics. Swarm and Evolutionary Computation 57 (Sept. 2020), 100720.
[16]
Guido van Rossum and Fred L. Drake. 1991–. The Python Programming Language. (1991–). Retrieved August 12, 2019 from http://www.python.org/.
[17]
Jefferey M. Perkel. 2015. Pickup Python. Nature 5187537 (February 2015), 125–126.
[18]
Philip Guo. 2014. Python is Now the Most Popular Introductory Teaching Language at Top U.S. Universities. (2014). Retrieved December 24, 2020 from http://goo.gl/iYc1qt.
[19]
Peter A. Cundall and Otto D. L. Strack. 1979. A discrete numerical model for granular assemblies. geotechnique 29, 1 (1979), 47–65.
[20]
Wing Kam Liu, Sukky Jun, and Yi Fei Zhang. 1995. Reproducing kernel particle methods. International Journal for Numerical Methods in Fluids 20, 8–9 (1995), 1081–1106.
[21]
Gary A. Dilts. 1999. Moving-least-squares-particle hydrodynamics—I. Consistency and stability. International Journal for Numerical Methods in Engineering 44, 8 (1999), 1115–1155. 3.0.CO;2-L
[22]
Vinh Phu Nguyen, Timon Rabczuk, Stéphane Bordas, and Marc Duflot. 2008. Meshless methods: A review and computer implementation aspects. Mathematics and Computers in Simulation 79, 3 (2008), 763–813.
[23]
Prabhu Ramachandran. 2016. PySPH: A reproducible and high-performance framework for smoothed particle hydrodynamics. In Proceedings of the 15th Python in Science Conference, Sebastian Benthall and Scott Rostrup (Eds.). 127–135.
[24]
Nils Meyer, Oleg Saburow, Martin Hohberg, Andrew N. Hrymak, Frank Henning, and Luise Kärger. 2020. Parameter identification of fiber orientation models based on direct fiber simulation with smoothed particle hydrodynamics. Journal of Composites Science 4, 2 (June 2020), 77.
[25]
Erin Arai, Alexandre Tartakovsky, R. Glynn Holt, Sheryl Grace, and Emily Ryan. 2020. Comparison of surface tension generation methods in smoothed particle hydrodynamics for dynamic systems. Computers & Fluids 203 (May 2020), 104540.
[26]
Ling Li, Luming Shen, Giang D. Nguyen, Abbas El-Zein, and Federico Maggi. 2018. A smoothed particle hydrodynamics framework for modelling multiphase interactions at meso-scale. Computational Mechanics 62, 5 (Nov. 2018), 1071–1085.
[27]
Yanyao Bao, Ling Li, Luming Shen, Chengwang Lei, and Yixiang Gan. 2019. Modified smoothed particle hydrodynamics approach for modelling dynamic contact angle hysteresis. Acta Mechanica Sinica 35, 3 (June 2019), 472–485.
[28]
Damien Violeau. 2012. Fluid mechanics and the SPH method: theory and applications (1st ed ed.). Oxford University Press. OCLC: ocn776772541.
[29]
J. J. Monaghan. 1992. Smoothed particle hydrodynamics. Annual Review of Astronomy and Astrophysics 30, 1 (1992), 543–574. arXiv:https://doi.org/10.1146/annurev.aa.30.090192.002551
[30]
J. J. Monaghan. 2005. Smoothed particle hydrodynamics. Reports on Progress in Physics 68 (2005), 1703–1759.
[31]
Moncho Gomez-Gesteria, Benedict D. Rogers, Robert. A Dalrymple, and Alex J. C. Crespo. 2010. State-of-the-art classical SPH for free-surface flows. Journal of Hydraulic Research 84 (2010), 6–27.
[32]
L. Hernquist and N. Katz. 1989. TREESPH - A unification of SPH with the hierarchical tree method. Astrophysical Journal Supplement Series 70 (1989), 419–446.
[33]
Volker Springel. 2005. The cosmological simulation code GADGET-2. Monthly Notices of the Royal Astronomical Society 364 (2005), 1105–1134.
[34]
J. M. Dominguez, A. J. C. Crespo, M. Gomez-Gesteira, and J. C. Marongiu. 2011. Neighbour lists in smoothed particle hydrodynamics. International Journal for Numerical Methods in Fluids 67, 12 (2011), 2026–2042.
[35]
G. Morton. 1966. A Computer Oriented Geodetic Data Base and a New Technique in File Sequencing. IBM, Ottawa.
[36]
J. J. Monaghan. 1994. Simulating free surface flows with SPH. Journal of Computational Physics 110, 2 (1994), 399–406.
[37]
J. P. Hughes and D. I. Graham. 2010. Comparison of incompressible and weakly-compressible SPH models for free-surface water flows. Journal of Hydraulic Research 48, sup 1 (2010), 105–117.
[38]
J. J. Monaghan. 2000. SPH without a tensile instability. Journal of Computational Physics 159, 2 (2000), 290–311.
[39]
S. Marrone, M. Antuono, A. Colagrossi, G. Colicchio, D. Le Touzé, and G. Graziani. 2011. -SPH model for simulating violent impact flows. Computer Methods in Applied Mechanics and Engineering 200, 13–16 (March 2011), 1526–1542.
[40]
S. Adami, X. Y. Hu, and N. A. Adams. 2013. A transport-velocity formulation for smoothed particle hydrodynamics. Journal of Computational Physics 241 (May 2013), 292–307.
[41]
Chi. Zhang, Xiangyu Y. T. Hu, and Nikolaus A. Adams. 2017. A generalized transport-velocity formulation for smoothed particle hydrodynamics. Journal of Computational Physics 337 (2017), 216–232.
[42]
Prabhu Ramachandran and Kunal Puri. 2019. Entropically damped artificial compressibility for SPH. Computers and Fluids 179, 30 (January 2019), 579–594.
[43]
Prabhu Ramachandran, Abhinav Muta, and Mokkapati Ramakrishna. 2021. Dual-Time smoothed particle hydrodynamics for incompressible fluid simulation. Computers & Fluids227 (15 September 2021), 105031.
[44]
Joseph P. Morris. 2000. Simulating surface tension with smoothed particle hydrodynamics. International Journal for Numerical Methods in Fluids 33, 3 (2000), 333–353. -7
[45]
S. Adami, X. Y. Hu, and N. A. Adams. 2010. A new surface-tension formulation for multi-phase SPH using a reproducing divergence approximation. Journal of Computational Physics 229, 13 (2010), 5011–5021.
[46]
S. J. Cummins and M. Rudman. 1999. An SPH projection method. Journal of Computational Physics 152, 2 (1999), 584–607.
[47]
Markus Ihmsen, Jens Cornelis, Barbara Solenthaler, Christopher Horvath, and Matthias Teschner. 2014. Implicit Incompressible SPH. IEEE Transactions on Visualization and Computer Graphics 20, 3 (2014), 426–435.
[48]
Abhinav Muta, Prabhu Ramachandran, and Pawan Negi. An efficient, open source, iterative ISPH scheme. Computer Physics Communications 255 (2020) 107283.
[49]
Shu-ichiro Inutsuka. 2002. Reformulation of smoothed particle hydrodynamics with riemann solver. Journal of Computational Physics 179, 1 (2002), 238–267.
[50]
Kunal Puri and Prabhu Ramachandran. 2014. Approximate Riemann solvers for the Godunov SPH. Journal of Computational Physics 270 (2014), 432–458.
[51]
Leonardo Di G. Sigalotti, Hender López, Arnaldo Donoso, Eloy Sira, and Jaime Klapp. 2006. A shock-capturing SPH scheme based on adaptive kernel estimation. Journal of Computational Physics 212, 1 (2006), 124–149.
[52]
Daniel J. Price. 2012. Smoothed particle hydrodynamics and magnetohydrodynamics. Journal of Computational Physics 231, 3 (2012), 759–794.
[53]
Nicholas Frontiere, Cody D. Raskin, and J. Michael Owen. 2017. CRKSPH - A conservative reproducing kernel smoothed particle hydrodynamics scheme. Journal of Computational Physics 332, 1 (March 2017), 160–209.
[54]
J. P. Gray, J. J. Monaghan, and R. P. Swift. 2001. SPH elastic dynamics. Computer Methods in Applied Mechanics and Engineering 190, 49 (2001), 6641–6662.
[55]
Nadir Akinci, Markus Ihmsen, Gizem Akinci, Barbara Solenthaler, and Matthias Teschner. 2012. Versatile rigid-fluid coupling for incompressible SPH. ACM Transactions on Graphics 31, 4 (July 2012), Article 62, 8 pages.
[56]
R. Vacondio, B. D. Rogers, P. K. Stansby, and P. Mignosa. 2013. Shallow water SPH for flooding with dynamic particle coalescing and splitting. Advances in Water Resources 58 (2013), 10–23.
[57]
R. Vacondio, B. D. Rogers, and 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 (2012), 1377–1410.
[58]
Miguel Rodriguez-Paz and Javier Bonet. 2005. A corrected smooth particle hydrodynamics formulation of the shallow-water equations. Computers & Structures 83, 17 (2005), 1396–1410.
[59]
Ata. Riadh and Azzeddine. Soulaïmani. 2005. A stabilized SPH method for inviscid shallow water flows. International Journal for Numerical Methods in Fluids 47, 2 (2005), 139–159.
[60]
J. Bonet and T.-S. L. Lok. 1999. Variational and momentum preservation aspects of Smooth Particle Hydrodynamic formulations. Computer Methods in Applied Mechanics and Engineering 180, 1 (1999), 97–115.
[61]
Rui Xu, Peter Stansby, and Dominique Laurence. 2009. Accuracy and stability in incompressible SPH based on the projection method and a new approach. Journal of Computational Physics 228, 18 (2009), 6703–6725.
[62]
Alex Skillen, Steven Lind, Peter K. Stansby, and Benedict D. Rogers. 2013. Incompressible smoothed particle hydrodynamics with reduced temporal noise and generalised Fickian smoothing applied to body–water slam and efficient wave–body interaction. Computer Methods in Applied Mechanics and Engineering 265 (2013), 163–173.
[63]
S. Adami, X. Y. Hu, and N. A. Adams. 2012. A generalized wall boundary condition for smoothed particle hydrodynamics. Journal of Computational Physics 231, 21 (Aug. 2012), 7057–7075.
[64]
I. Federico, S. Marrone, A. Colagrossi, F. Aristodemo, and M. Antuono. 2012. Simulating 2D open-channel flows through an SPH model. European Journal of Mechanics - B/Fluids 34 (2012), 35–46.
[65]
Pawan Negi, Prabhu Ramachandran, and Asmelash Haftu. 2020. An improved non-reflecting outlet boundary condition for weakly-compressible SPH. Computer Methods in Applied Mechanics and Engineering 367 (2020), 113119.
[66]
Martin Lastiwka, Mihai Basa, and Nathan J. Quinlan. 2009. Permeable and non-reflecting boundary conditions in SPH. International Journal for Numerical Methods in Fluids 61, 7 (2009), 709–724.
[67]
A. Tafuni, J. M. Domínguez, R. Vacondio, and A. J. C. Crespo. 2018. A versatile algorithm for the treatment of of open boundary conditions in smoothed particle hydrodynamics GPU models. Computer methods in applied mechanical engineering 342 (2018), 604–624.
[68]
Travis Oliphant. 2006. Guide to NumPy. CreateSpace Independent Publishing Platform, North Charleston, SC
[69]
Aditya Bhosale and Prabhu Ramachandran. 2020. Compyle: a Python package for parallel computing. In Proceedings of the 19th Python in Science Conference, Meghann Agarwal, Chris Calloway, Dillon Niederhut, and David Shupe (Eds.). 32–39.
[70]
Erik Boman, Karen Devine, Lee Ann Fisk, Robert Heaphy, Bruce Hendrickson, Vitus Leung, Courtenay Vaughan, Umit Catalyurek, Doruk Bozdag, and William Mitchell. 1999. Zoltan home page. (1999). Retrieved August 12, 2019 from http://www.cs.sandia.gov/Zoltan.
[71]
E. G. Boman, U. V. Catalyurek, C. Chevalier, and K. D. Devine. 2012. The Zoltan and Isorropia Parallel Toolkits for Combinatorial Scientific Computing: Partitioning, Ordering, and Coloring. Scientific Programming 20, 2 (2012), 129–150.
[72]
Kunal Puri, Prabhu Ramachandran, and Pushkar Godbole. 2013. Load balancing strategies for SPH. In Proceedings of the 2013 National Conference on Parallel Computing Technologies. IEEE.
[73]
Prabhu Ramachandran and Gaël Varoquaux. 2011. Mayavi: 3D Visualization of Scientific Data. Computing in Science and Engineering 13, 2 (2011), 40–51.
[74]
Thomas Kluyver, Benjamin Ragan-Kelley, Fernando Pérez, Brian Granger, Matthias Bussonnier, Jonathan Frederic, Kyle Kelley, Jessica Hamrick, Jason Grout, Sylvain Corlay, Paul Ivanov, Damián Avila, Safia Abdalla, and Carol Willing. 2016. Jupyter Notebooks – a publishing format for reproducible computational workflows. In Proceedings of the Positioning and Power in Academic Publishing: Players, Agents and Agendas, F. Loizides and B. Schmidt (Eds.). IOS Press, 87–90.
[75]
Matthias Bussonnier, Jessica Forde, Jeremy Freeman, Brian Granger, Tim Head, Chris Holdgraf, Kyle Kelley, Gladys Nalvarte, Andrew Osheroff, M Pacer, Yuvi Panda, Fernando Perez, Benjamin Ragan-Kelley, and Carol Willing. 2018. Binder 2.0 - Reproducible, interactive, sharable environments for science at scale. In Proceedings of the 17th Python in Science Conference, Fatih Akici, David Lippa, Dillon Niederhut, and M Pacer (Eds.). 113–120.
[76]
Stefan Behnel, Robert Bradshaw, Craig Citro, Lisandro Dalcin, Dag Sverre Seljebotn, and Kurt Smith. 2011. Cython: The Best of Both Worlds. Computing in Science and Engineering 13, 2 (March 2011), 31–39.
[77]
Andreas Klöckner, Nicolas Pinto, Yunsup Lee, Bryan Catanzaro, Paul Ivanov, and Ahmed Fasih. 2012. PyCUDA and PyOpenCL: A Scripting-based Approach to GPU Run-time Code Generation. Parallel Computing 38, 3 (March 2012), 157–174.
[78]
Mike Bayer et al. 2006–. Mako Templates. (2006–). Retrieved on 17th August, 2019 from https://www.makotemplates.org/.
[79]
Prabhu Ramachandran, Aditya Bhosale, and Rahul Govind. 2018–. ComPyle: execute a subset of Python on HPC platforms. (2018–). Retrieved December 25, 2020 from https://github.com/pypr/compyle.
[80]
Kunal Puri and Prabhu Ramachandran. 2013–. PyZoltan: a Python wrapper for the Zoltan library. (2013–). Retrieved 25th December, 2020 from https://github.com/pypr/pyzoltan.
[81]
Prabhu Ramachandran. 2018. automan: A Python-Based Automation Framework for Numerical Computing. Computing in Science & Engineering 20, 5 (Sep./Oct. 2018), 81–97.
[82]
U. Ghia, K. N. Ghia, and C. T. Shin. 1982. High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. Journal of Computational Physics 48, 3 (1982), 387–411.
[83]
Brant E. Robertson, Andrey V. Kravtsov, Nickolay Y. Gnedin, Tom Abel, and Douglas H. Rudd. 2010. Computational Eulerian hydrodynamics and Galilean invariance. Monthly Notices of the Royal Astronomical Society 401, 4 (Jan. 2010), 2463–2476.
[84]
Stefan Luding. 2008. Introduction to discrete element methods: basic of contact force models and how to perform the micro-macro transition to continuum theory. European journal of environmental and civil engineering 12, 7–8 (2008), 785–826.
[85]
Dan Terpstra, Heike Jagode, Haihang You, and Jack Dongarra. 2010. Collecting Performance Data with PAPI-C. In Proceedings of the Tools for High Performance Computing 2009, Matthias S. Müller, Michael M. Resch, Alexander Schulz, and Wolfgang E. Nagel (Eds.). Springer, Berlin, 157–173.
[86]
Endong Wang, Qing Zhang, Bo Shen, Guangyong Zhang, Xiaowei Lu, Qing Wu, and Yajuan Wang. 2014. Intel Math Kernel Library. High-Performance Computing on the Intel, Springer, Cham. 167–188.

Cited By

View all
  • (2024)A hybrid finite volume method and smoothed particle hydrodynamics approach for efficient and accurate blast simulationsFrontiers in Physics10.3389/fphy.2023.132529411Online publication date: 8-Jan-2024
  • (2024)Fault rupture propagation through stratified sand–clay deposits and engineered earth structures: a meshfree and critical-state modeling approachActa Geotechnica10.1007/s11440-024-02421-w19:12(7767-7798)Online publication date: 23-Oct-2024
  • (2024)A nonlocal kernel-based continuum damage model for compaction band formation in porous sedimentary rockComputational Mechanics10.1007/s00466-024-02540-xOnline publication date: 4-Oct-2024
  • Show More Cited By

Index Terms

  1. PySPH: A Python-based Framework for Smoothed Particle Hydrodynamics

      Recommendations

      Comments

      Information & Contributors

      Information

      Published In

      cover image ACM Transactions on Mathematical Software
      ACM Transactions on Mathematical Software  Volume 47, Issue 4
      December 2021
      242 pages
      ISSN:0098-3500
      EISSN:1557-7295
      DOI:10.1145/3485138
      Issue’s Table of Contents
      Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

      Publisher

      Association for Computing Machinery

      New York, NY, United States

      Publication History

      Published: 28 September 2021
      Accepted: 01 April 2021
      Revised: 01 December 2020
      Received: 01 December 2019
      Published in TOMS Volume 47, Issue 4

      Permissions

      Request permissions for this article.

      Check for updates

      Author Tags

      1. PySPH
      2. smoothed particle hydrodynamics
      3. open source
      4. Python
      5. GPU
      6. CPU

      Qualifiers

      • Research-article
      • Refereed

      Contributors

      Other Metrics

      Bibliometrics & Citations

      Bibliometrics

      Article Metrics

      • Downloads (Last 12 months)181
      • Downloads (Last 6 weeks)14
      Reflects downloads up to 12 Jan 2025

      Other Metrics

      Citations

      Cited By

      View all
      • (2024)A hybrid finite volume method and smoothed particle hydrodynamics approach for efficient and accurate blast simulationsFrontiers in Physics10.3389/fphy.2023.132529411Online publication date: 8-Jan-2024
      • (2024)Fault rupture propagation through stratified sand–clay deposits and engineered earth structures: a meshfree and critical-state modeling approachActa Geotechnica10.1007/s11440-024-02421-w19:12(7767-7798)Online publication date: 23-Oct-2024
      • (2024)A nonlocal kernel-based continuum damage model for compaction band formation in porous sedimentary rockComputational Mechanics10.1007/s00466-024-02540-xOnline publication date: 4-Oct-2024
      • (2024)An SPH framework for drained and undrained loading over large deformationsInternational Journal for Numerical and Analytical Methods in Geomechanics10.1002/nag.379048:12(3227-3257)Online publication date: 14-Jun-2024
      • (2023)Smoothed particle hydrodynamics method for free surface flow based on MPI parallel computingFrontiers in Physics10.3389/fphy.2023.114197211Online publication date: 20-Mar-2023
      • (2023)Application of Smoothed Particle Hydrodynamics (SPH) for the Simulation of Flow-Like Landslides on 3D TerrainsComputer Modeling in Engineering & Sciences10.32604/cmes.2022.022309135:1(357-376)Online publication date: 2023
      • (2023) Single and multiple walled CNTs-TiO 2 ternary hybrid nanofluid flow of Williamson fluid in an unsteady combined convective regime: An entropy analysis Numerical Heat Transfer, Part A: Applications10.1080/10407782.2023.217422284:10(1216-1237)Online publication date: 13-Mar-2023
      • (2023)SPHydro: Promoting smoothed particle hydrodynamics method toward extensive applications in ocean engineeringPhysics of Fluids10.1063/5.013378235:1Online publication date: 6-Jan-2023
      • (2023)Impact of impulsive motion on the Eyring-Powell nanofluid flow across a rotating sphere in MHD convective regime: Entropy analysisJournal of Magnetism and Magnetic Materials10.1016/j.jmmm.2023.170590571(170590)Online publication date: Apr-2023
      • (2023)A coupled smoothed particle hydrodynamics-finite volume approach for shock capturing in one-dimensionHeliyon10.1016/j.heliyon.2023.e179229:7(e17922)Online publication date: Jul-2023
      • Show More Cited By

      View Options

      Login options

      Full Access

      View options

      PDF

      View or Download as a PDF file.

      PDF

      eReader

      View online with eReader.

      eReader

      HTML Format

      View this article in HTML Format.

      HTML Format

      Media

      Figures

      Other

      Tables

      Share

      Share

      Share this Publication link

      Share on social media