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Predictive-corrective incompressible SPH
Open accessAbstract
We present a novel, incompressible fluid simulation method based on the Lagrangian Smoothed Particle Hydrodynamics (SPH) model. In our method, incompressibility is enforced by using a prediction-correction scheme to determine the particle pressures. For this, the information about density fluctuations is actively propagated through the fluid and pressure values are updated until the targeted density is satisfied. With this approach, we avoid the computational expenses of solving a pressure Poisson equation, while still being able to use large time steps in the simulation. The achieved results show that our predictive-corrective incompressible SPH (PCISPH) method clearly outperforms the commonly used weakly compressible SPH (WCSPH) model by more than an order of magnitude while the computations are in good agreement with the WCSPH results.
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Citations
Cites
An Introduction to Fluid Dynamics
Batchelor, G. K. (2000) · doi:10.1017/cbo9780511800955 · Cited by 12,360
Smoothed Particle Hydrodynamics
Monaghan, J. J. (1992) · Annual Review of Astronomy and Astrophysics · doi:10.1146/annurev.astro.30.1.543 · Cited by 5,183
Smoothed particle hydrodynamics
Monaghan, J. J. (2005) · Reports on Progress in Physics · doi:10.1088/0034-4885/68/8/r01 · Cited by 2,770
On the Partial Difference Equations of Mathematical Physics
Courant, R., Friedrichs, K. O., & Lewy, H. (1967) · IBM Journal of Research and Development · doi:10.1147/rd.112.0215 · Cited by 2,513
On the Partial Difference Equations of Mathematical Physics
Courant, R., Friedrichs, K. O., & Lewy, H. (2002) · Birkhäuser Boston eBooks · doi:10.1007/978-1-4612-2080-0_6 · Cited by 1,353
Particle-Based Fluid Simulation for Interactive Applications
Müller, M., Charypar, D., & Groß, M. H. (2003) · doi:10.2312/sca03/154-159 · Cited by 1,000
Cummins, S. J., & Rudman, M. J. (1999) · Journal of Computational Physics · doi:10.1006/jcph.1999.6246 · Cited by 902
Zhu, Y., & Bridson, R. (2005) · ACM Transactions on Graphics · doi:10.1145/1073204.1073298 · Cited by 654
Proceedings of Eurographics 79
Bramer, B. (1980) · Advances in Engineering Software (1978) · doi:10.1016/0141-1195(80)90022-4 · Cited by 631
Animation and rendering of complex water surfaces
Enright, D. P., Marschner, S. R., & Fedkiw, R. P. (2002) · ACM SIGGRAPH Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH) · doi:10.1145/566570.566645 · Cited by 524
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Items 301–358 of 358
Gerszewski, D. J. (2014) · PhDT · doi:10.26053/0h-z6gb-rk00
Adaptive Particle Splitting Based on Turbulence Energy for Fluid Simulations on GPUs
ArnoInWoldeLubke, Fujisawa, M., Taketomi, T., Goshiro, Y., Miyazaki, J., & Kato, H. (2013) · Computer-Aided Design
An Adaptive FLIP-Levelset Hybrid Method for Efficient Fluid Simulation
임재광, Hong, J., & 김봉준 (2013) · Journal of the Korea Computer Graphics Society · doi:10.15701/kcgs.2013.19.3.1
Coupled simulation of grid-based fluid and mass-spring based deformation/fracture
김봉준, Hong, J., & 임재광 (2014) · Journal of the Korea Computer Graphics Society · doi:10.15701/kcgs.2014.20.4.9
Real-Time Visual Effects Programming
Kim, C., Kim, S.-J., Kim, S. K., & Kang, S.-J. (2015) · Gaming media and social effects · doi:10.1007/978-981-287-487-0_6
Simulation of Tsunami Impact upon Coastline
Spathis-Papadiotis, A., & Μουστάκας, Κ. (2016) · Lecture notes in computer science · doi:10.1007/978-3-319-40621-3_1
A Survey on Fluid Physical Simulation Technology Based on SPH Method
Shao, X., Liu, Y., Zhao, M., & Jing, X. (2016)
Particle-Based Two-Way Coupling of Fluids and Solids
Yang, X., Gu, H., & Feng-ju, K. (2016) · Communications in computer and information science · doi:10.1007/978-981-10-2669-0_13
Reconstructing flicker-free surfaces in hybrid particle-grid water simulation
Kim, J., Kim, C., & Lee, J. (2016) · Journal of Visualization · doi:10.1007/s12650-016-0400-8
A new Potential-based SPH Method
Perea, J. J., & Cordero, J. M. (2016) · Eurographics · doi:10.2312/ceig.20161315
Rigid Body Sampling and Individual Time Stepping for Rigid-Fluid Coupling of Fluid Simulation
Wang, X., Ban, X., Zhang, Y., & Liu, X. (2017) · Scientific Programming · doi:10.1155/2017/8502691
An Optical Flow using SVD for Video based Fluid Animation
An, H.-A., & Park, J. (2015) · International Journal of Multimedia and Ubiquitous Engineering · doi:10.14257/ijmue.2015.10.9.38
Physics-Based Fluid-Solid Interaction of Ocean Simulation Using SPH
Yu, Y., Hu, M., Li, F., & Zhao, Y. (2016) · International Conference on Virtual Reality and Visualization · doi:10.1109/icvrv.2016.60
The Non-Newtonian Fluid Simulation Based on Predictive-Corrective Incompressible SPH
Zhang, Y., Ban, X., Wang, X., & Liu, X. (2016) · International Conference on Virtual Reality and Visualization · doi:10.1109/icvrv.2016.20
Modeling and data assimilation for improved ultrasound measurement of blood velocity fields
Grønli, T. (2017) · BIBSYS Brage (BIBSYS (Norway))
Sümengen, S. (2013) · Sabanci University
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Kanetsuki, Y., & Nakata, S. (2017) · Communications in computer and information science · doi:10.1007/978-981-10-6502-6_30
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Chayanurak, N., & Watcharopas, C. (2018) · International Joint Conference on Computer Science and Software Engineering · doi:10.1109/jcsse.2018.8457371
Realistic Simulation of Incompressible Fluids with Arbitrarily Shaped Boundaries
Nie, X. B., Chen, L., Zhou, C., & Qiu, H. (2015) · International Journal of Multimedia and Ubiquitous Engineering · doi:10.14257/ijmue.2015.10.6.22
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Quan, H., Wang, N., Li, J., & Wang, C. (2019) · Multimedia Systems · doi:10.1007/s00530-019-00612-0
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Li, H., Ren, H., & Fan, X. (2019) · 3D Research · doi:10.1007/s13319-019-0225-z
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Gac, P. T. L., Darles, E., Louis, P., & Aveneau, L. (2019) · IntechOpen eBooks · doi:10.5772/intechopen.86619
Palyanov, A. Y., & Palyanova, N. V. (2019) · International Multi-Conference on Engineering, Computer and Information Sciences (SIBIRCON) · doi:10.1109/sibircon48586.2019.8958238
Particle based modeling and simulation of natural phenomena
Bayraktar, S. (2010) · Bilkent University Institutional Repository (Bilkent University)
Takahashi, T. (2020) · Carolina Digital Repository (University of North Carolina at Chapel Hill) · doi:10.17615/3ddw-rh95
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Verma, K., & Wille, R. (2021) · Springer eBooks · doi:10.1007/978-3-030-71625-7_10
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Liu, W., Yu, Z., Meng, Y., Wang, G., & Liu, X. (2022) · Lecture notes in computer science · doi:10.1007/978-3-030-93571-9_8
Coutinho, M. G. (2012) · Simulation foundations, methods and applications · doi:10.1007/978-1-4471-4417-5_3
Smoothed Particle Hydrodynamics-Based Viscous Deformable Object Modelling
Kim, J., Ruggiero, F., Lippiello, V., & Siciliano, B. (2022) · Springer tracts in advanced robotics · doi:10.1007/978-3-030-93290-9_3
(2010) · Elsevier eBooks · doi:10.1016/b978-0-12-374903-1.00015-3
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Zhao, Y., Ren, R., Dib, H. N., McGraw, T., & Chen, Y. (2022) · ASCE International Conference on Computing in Civil Engineering (i3CE) · doi:10.1061/9780784483893.145
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Xu, Y., Wang, X., Ban, X., Wang, J., Song, C., & Wang, Y. (2022) · Journal of Computer-Aided Design & Computer Graphics · doi:10.3724/sp.j.1089.2022.19190
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Keller, M. (2022) · Logos Verlag Berlin eBooks · doi:10.30819/5582
Sun, Z., Dou, L.-Y., Mu, Z., Tan, S., Zong, Z., Djidjeli, K., & Zhang, G. (2023) · Journal of Marine Science and Engineering · doi:10.3390/jmse11112183
Schmidt, M., & Savoye, Y. (2024) · Encyclopedia of Computer Graphics and Games · doi:10.1007/978-3-031-23161-2_55
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Sun, P., & Liu, P. X. (2024) · Physics of Fluids · doi:10.1063/5.0213889
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Sergeev, P., Kiselev, D., & Makarov, I. (2024) · IEEE International Conference on Intelligent Engineering Systems (INES) · doi:10.1109/ines63318.2024.10629094
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Zhu, T., Ren, H., Li, H., & Yang, X. (2024) · Journal of Marine Science and Engineering · doi:10.3390/jmse12091498
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Sun, Y., Zhou, F. J., & Dai, J. (2025) · Lecture notes in computer science · doi:10.1007/978-981-96-3679-2_7
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Yu, C., Zheng, S., Wang, N., Jin, M., & Chang, Y. (2025) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v39i15.33752
Mitani, J., Takayama, K., Dobashi, Y., Mukai, T., & Fujisawa, M. (2025) · Springer eBooks · doi:10.1007/978-981-96-2933-6_4
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Wu, Y., Wang, F., Sun, X., Liu, Z., Xiong, Z., Zhang, M., Zhao, B., & Zhou, T. (2025) · Mathematics · doi:10.3390/math13152439
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Farjami, S., Palyanov, A. Y., Zhang, H.-Y., Saccomanno, V., Merrison‐Hort, R., Ferrario, A., Borisyuk, R. M., Tabak, J., & Li, W. (2025) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2025.09.08.674955
Zhu, T., Ren, H., Tao, R., Wei, D., & Xie, P. (2025) · Scientific Reports · doi:10.1038/s41598-025-22144-6
Crude Oil Leakage Simulation Method Based on Physical Processes
Lian, Y., Xu, Z., Li, G., Ji, L., & Dong, S. (2023) · Journal of Computer-Aided Design & Computer Graphics · doi:10.3724/sp.j.1089.2023.19716
Stability and Detail Improvement Method for SPH Volume Maps Fluid-Solid Interaction
Zhao, J., Yuan, H., Xu, L., An, Y., Tang, C., & Lyu, M. (2023) · Journal of Computer-Aided Design & Computer Graphics · doi:10.3724/sp.j.1089.2023.19494
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Zou, C., & Li, X. (2025) · Computers · doi:10.3390/computers15010011
Dimension reduction for fluid simulation and animation
Paliard, C. (2024) · theses.fr (ABES) · doi:10.70675/2783e762z9bfaz4974z9483zf9e72247a775
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Che, Y. (2026) · theses.fr (ABES) · doi:10.70675/7c36bc77zbcf8z4d6ez988dzdd814ec9a952
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Čoko, U., Potisk, T., & Praprotnik, M. (2026) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2610567123
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Bender, J., Jeske, S. R., Böttcher, T., & Löschner, F. (2026) · Computer Graphics Forum · doi:10.1111/cgf.70559
Metadata
- Authors
- Solenthaler, B., & Pajarola, R.
- Affiliations
- University of Zurich (CH)
- Venue
- ACM Transactions on Graphics
- Published
- 2009-07-27
- Volume
- 28
- Issue
- 3
- Pages
- 1-6
- ISSN
- 0730-0301 (ISSN-L)
- 1557-7368
- OpenAlex
- W2045670663
- Cited by
- 362
- References
- 37
- Citations by year
- 2026: 6 · 2025: 12 · 2024: 9 · 2023: 9 · 2022: 14 · 2021: 25 · 2020: 28 · 2019: 25 · 2018: 28 · 2017: 25 · 2016: 32 · 2015: 31 · 2014: 32 · 2013: 32 · 2012: 19
- FWCI
- 18.12
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- ACM Transactions on Graphics (publishedVersion)
- Zurich Open Repository and Archive (University of Zurich) (acceptedVersion, other-oa)
- Zurich Open Repository and Archive (University of Zurich) (submittedVersion, other-oa)
- Zurich Open Repository and Archive (University of Zurich)
- Topics
- Physical Sciences › Engineering › Computational Mechanics › Fluid Dynamics Simulations and Interactions
- Physical Sciences › Computer Science › Computer Graphics and Computer-Aided Design › Computer Graphics and Visualization Techniques
- Physical Sciences › Engineering › Mechanics of Materials › Numerical methods in engineering
- Keywords
- incompressible fluid simulation, smoothed particle hydrodynamics, prediction-correction scheme, density fluctuations, large time steps, weakly compressible SPH
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