“Thin-film smoothed particle hydrodynamics fluid” by Wang, Deng, Kong, Prasad, Xiong, et al. …

We propose a particle-based method to simulate thin-film fluid that jointly facilitates aggressive surface deformation and vigorous tangential flows. We build our dynamics model from the surface tension driven Navier-Stokes equation with the dimensionality reduced using the asymptotic lubrication theory and customize a set of differential operators based on the weakly compressible Smoothed Particle Hydrodynamics (SPH) for evolving pointset surfaces. The key insight is that the compressible nature of SPH, which is unfavorable in its typical usage, is helpful in our application to co-evolve the thickness, calculate the surface tension, and enforce the fluid incompressibility on a thin film. In this way, we are able to two-way couple the surface deformation with the in-plane flows in a physically based manner. We can simulate complex vortical swirls, fingering effects due to Rayleigh-Taylor instability, capillary waves, Newton’s interference fringes, and the Marangoni effect on liberally deforming surfaces by presenting both realistic visual results and numerical validations. The particle-based nature of our system also enables it to conveniently handle topology changes and codimension transitions, allowing us to marry the thin-film simulation with a wide gamut of 3D phenomena, such as pinch-off of unstable catenoids, dripping under gravity, merging of droplets, as well as bubble rupture.

1. Mridul Aanjaneya, Saket Patkar, and Ronald Fedkiw. 2013. A monolithic mass tracking formulation for bubbles in incompressible flow. J. Comput. Phys. 247 (2013), 17–61.Google ScholarCross Ref
2. Nadir Akinci, Gizem Akinci, and Matthias Teschner. 2013. Versatile surface tension and adhesion for SPH fluids. ACM Transactions on Graphics (TOG) 32, 6 (2013), 1–8.Google ScholarDigital Library
3. A Albadawi, DB Donoghue, AJ Robinson, DB Murray, and YMC Delauré. 2013. Influence of surface tension implementation in volume of fluid and coupled volume of fluid with level set methods for bubble growth and detachment. International Journal of Multiphase Flow 53 (2013), 11–28.Google ScholarCross Ref
4. Ryoichi Ando and Reiji Tsuruno. 2011. A particle-based method for preserving fluid sheets. In Proceedings of the 2011 ACM SIGGRAPH/Eurographics symposium on computer animation. 7–16.Google ScholarDigital Library
5. Stefan Auer, Colin B Macdonald, Marc Treib, Jens Schneider, and Rüdiger Westermann. 2012. Real-time fluid effects on surfaces using the closest point method. In Computer Graphics Forum, Vol. 31. Wiley Online Library, 1909–1923.Google Scholar
6. Stefan Auer and Rüdiger Westermann. 2013. A Semi-Lagrangian Closest Point Method for Deforming Surfaces. In Computer Graphics Forum, Vol. 32. Wiley Online Library, 207–214.Google Scholar
7. Omri Azencot, Orestis Vantzos, Max Wardetzky, Martin Rumpf, and Mirela Ben-Chen. 2015a. Functional thin films on surfaces. In Proceedings of the 14th ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 137–146.Google ScholarDigital Library
8. Omri Azencot, Orestis Vantzos, Max Wardetzky, Martin Rumpf, and Mirela Ben-Chen. 2015b. Functional thin films on surfaces. In Proceedings of the 14th ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 137–146.Google ScholarDigital Library
9. Omri Azencot, Steffen Weißmann, Maks Ovsjanikov, Max Wardetzky, and Mirela BenChen. 2014. Functional fluids on surfaces. In Computer Graphics Forum, Vol. 33. Wiley Online Library, 237–246.Google Scholar
10. Stefan Band, Christoph Gissler, Markus Ihmsen, Jens Cornelis, Andreas Peer, and Matthias Teschner. 2018. Pressure boundaries for implicit incompressible SPH. ACM Transactions on Graphics (TOG) 37, 2 (2018), 1–11.Google ScholarDigital Library
11. Christopher Batty, Andres Uribe, Basile Audoly, and Eitan Grinspun. 2012. Discrete viscous sheets. ACM Transactions on Graphics (TOG) 31, 4 (2012), 1–7.Google ScholarDigital Library
12. Markus Becker and Matthias Teschner. 2007. Weakly compressible SPH for free surface flows. In Proceedings of the 2007 ACM SIGGRAPH/Eurographics symposium on Computer animation. 209–217.Google ScholarDigital Library
13. Laurent Belcour and Pascal Barla. 2017. A practical extension to microfacet theory for the modeling of varying iridescence. ACM Transactions on Graphics (TOG) 36, 4 (2017), 1–14.Google ScholarDigital Library
14. Mikhail Belkin and Partha Niyogi. 2008. Towards a theoretical foundation for Laplacian-based manifold methods. J. Comput. System Sci. 74, 8 (2008), 1289–1308.Google ScholarDigital Library
15. Mikhail Belkin, Jian Sun, and Yusu Wang. 2009. Constructing Laplace operator from point clouds in R d. In Proceedings of the twentieth annual ACM-SIAM symposium on Discrete algorithms. Society for Industrial and Applied Mathematics, 1031–1040.Google ScholarDigital Library
16. Jan Bender and Dan Koschier. 2016. Divergence-free SPH for incompressible and viscous fluids. IEEE Transactions on Visualization and Computer Graphics 23, 3 (2016), 1193–1206.Google ScholarDigital Library
17. Miklós Bergou, Basile Audoly, Etienne Vouga, Max Wardetzky, and Eitan Grinspun. 2010. Discrete viscous threads. ACM Transactions on graphics (TOG) 29, 4 (2010), 1–10.Google Scholar
18. Robert Bridson. 2015. Fluid simulation for computer graphics. CRC press.Google ScholarDigital Library
19. L. Brookshaw. 1985. A Method of Calculating Radiative Heat Diffusion in Particle Simulations. Publications of the Astronomical Society of Australia 6, 2 (1985), 207–210.Google ScholarCross Ref
20. Ka Chun Cheung, Leevan Ling, and Steven J Ruuth. 2015. A localized meshless method for diffusion on folded surfaces. J. Comput. Phys. 297 (2015), 194–206.Google ScholarDigital Library
21. Jean-Marc Chomaz. 2001. The dynamics of a viscous soap film with soluble surfactant. Journal of Fluid Mechanics 442 (2001), 387–409.Google ScholarCross Ref
22. Jens Cornelis, Markus Ihmsen, Andreas Peer, and Matthias Teschner. 2014. IISPH-FLIP for incompressible fluids. In Computer Graphics Forum, Vol. 33. Wiley Online Library, 255–262.Google Scholar
23. Y Couder, JM Chomaz, and M Rabaud. 1989. On the hydrodynamics of soap films. Physica D: Nonlinear Phenomena 37, 1-3 (1989), 384–405.Google ScholarDigital Library
24. Fang Da, Christopher Batty, Chris Wojtan, and Eitan Grinspun. 2015. Double bubbles sans toil and trouble: Discrete circulation-preserving vortex sheets for soap films and foams. ACM Transactions on Graphics (TOG) 34, 4 (2015), 1–9.Google ScholarDigital Library
25. C Gaulon, C Derec, T Combriat, P Marmottant, and F Elias. 2017. Sound and Vision: Visualization of music with a soap film, and the physics behind it. (2017).Google Scholar
26. Robert A Gingold and Joseph 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.Google Scholar
27. Christoph Gissler, Andreas Henne, Stefan Band, Andreas Peer, and Matthias Teschner. 2020. An implicit compressible SPH solver for snow simulation. ACM Transactions on Graphics (TOG) 39, 4 (2020), 36–1.Google ScholarDigital Library
28. Christoph Gissler, Andreas Peer, Stefan Band, Jan Bender, and Matthias Teschner. 2019. Interlinked SPH pressure solvers for strong fluid-rigid coupling. ACM Transactions on Graphics (TOG) 38, 1 (2019), 1–13.Google ScholarDigital Library
29. Andrew Glassner. 2000. Soap bubbles: part 2. IEEE Annals of the History of Computing 20, 06 (2000), 99–109.Google ScholarDigital Library
30. David J Hill and Ronald D Henderson. 2016. Efficient fluid simulation on the surface of a sphere. ACM Transactions on Graphics (TOG) 35, 2 (2016), 1–9.Google ScholarDigital Library
31. Jeong-Mo Hong and Chang-Hun Kim. 2003. Animation of bubbles in liquid. In Computer Graphics Forum, Vol. 22. Wiley Online Library, 253–262.Google Scholar
32. Jeong-Mo Hong and Chang-Hun Kim. 2005. Discontinuous fluids. ACM Transactions on Graphics (TOG) 24, 3 (2005), 915–920.Google ScholarDigital Library
33. Libo Huang, Torsten Hädrich, and Dominik L Michels. 2019. On the accurate large-scale simulation of ferrofluids. ACM Transactions on Graphics (TOG) 38, 4 (2019), 1–15.Google ScholarDigital Library
34. Weizhen Huang, Julian Iseringhausen, Tom Kneiphof, Ziyin Qu, Chenfanfu Jiang, and Matthias B. Hullin. 2020. Chemomechanical Simulation of Soap Film Flow on Spherical Bubbles. ACM Transactions on Graphics 39, 4 (2020).Google ScholarDigital Library
35. Markus Ihmsen, Jens Cornelis, Barbara Solenthaler, Christopher Horvath, and Matthias Teschner. 2013. Implicit incompressible SPH. IEEE transactions on visualization and computer graphics 20, 3 (2013), 426–435.Google Scholar
36. Sadashige Ishida, Peter Synak, Fumiya Narita, Toshiya Hachisuka, and Chris Wojtan. 2020. A Model for Soap Film Dynamics with Evolving Thickness. ACM Transactions on Graphics 39, 4 (2020), 31:1–31:11.Google ScholarDigital Library
37. Sadashige Ishida, Masafumi Yamamoto, Ryoichi Ando, and Toshiya Hachisuka. 2017. A hyperbolic geometric flow for evolving films and foams. ACM Transactions on Graphics (TOG) 36, 6 (2017), 1–11.Google ScholarDigital Library
38. Kei Iwasaki, Keichi Matsuzawa, and Tomoyuki Nishita. 2004. Real-time rendering of soap bubbles taking into account light interference. In Proceedings Computer Graphics International, 2004. IEEE, 344–348.Google ScholarDigital Library
39. Dariusz Jaszkowski and Janusz Rzeszut. 2003. Interference colours of soap bubbles. The Visual Computer 19, 4 (2003), 252–270.Google ScholarDigital Library
40. Min Jiang, Yahan Zhou, Rui Wang, Richard Southern, and Jian Jun Zhang. 2015. Blue noise sampling using an SPH-based method. ACM Transactions on Graphics (TOG) 34, 6 (2015), 1–11.Google ScholarDigital Library
41. Myungjoo Kang, Barry Merriman, and Stanley Osher. 2008. Numerical simulations for the motion of soap bubbles using level set methods. Computers & fluids 37, 5 (2008), 524–535.Google Scholar
42. Richard Keiser, Bart Adams, Philip Dutré, Leonidas J Guibas, and Mark Pauly. 2006. Multiresolution particle-based fluids. Technical Report/ETH Zurich, Department of Computer Science 520 (2006).Google Scholar
43. Namjung Kim, SaeWoon Oh, and Kyoungju Park. 2015. Giant soap bubble creation model. Computer Animation and Virtual Worlds 26, 3-4 (2015), 445–455.Google ScholarDigital Library
44. Theodore Kim, Jerry Tessendorf, and Nils Thuerey. 2013. Closest point turbulence for liquid surfaces. ACM Transactions on Graphics (TOG) 32, 2 (2013), 15.Google ScholarDigital Library
45. M. Kness. 2008. ColorPy-A Python package for handling physical descriptions of color and light spectra. (2008).Google Scholar
46. Dan Koschier, Jan Bender, Barbara Solenthaler, and Matthias Teschner. 2019. Smoothed Particle Hydrodynamics Techniques for the Physics Based Simulation of Fluids and Solids. In Eurographics 2019 – Tutorials, Wenzel Jakob and Enrico Puppo (Eds.). The Eurographics Association.Google Scholar
47. Rongjie Lai, Jiang Liang, and Hongkai Zhao. 2013. A local mesh method for solving PDEs on point clouds. Inverse Problems & Imaging 7, 3 (2013).Google Scholar
48. Peter Lancaster and Kes Salkauskas. 1981. Surfaces generated by moving least squares methods. Mathematics of computation 37, 155 (1981), 141–158.Google Scholar
49. David Levin. 1998. The approximation power of moving least-squares. Mathematics of computation 67, 224 (1998), 1517–1531.Google Scholar
50. MB Liu and GR Liu. 2010. Smoothed particle hydrodynamics (SPH): an overview and recent developments. Archives of computational methods in engineering 17, 1 (2010), 25–76.Google Scholar
51. Frank Losasso, Jerry Talton, Nipun Kwatra, and Ronald Fedkiw. 2008. Two-way coupled SPH and particle level set fluid simulation. IEEE Transactions on Visualization and Computer Graphics 14, 4 (2008), 797–804.Google ScholarDigital Library
52. Joe J Monaghan. 1992. Smoothed particle hydrodynamics. Annual review of astronomy and astrophysics 30, 1 (1992), 543–574.Google Scholar
53. Joseph J Monaghan and John C Lattanzio. 1985. A refined particle method for astro-physical problems. Astronomy and astrophysics 149 (1985), 135–143.Google Scholar
54. Dieter Morgenroth, Stefan Reinhardt, Daniel Weiskopf, and Bernhard Eberhardt. 2020. Efficient 2D simulation on moving 3D surfaces. In Computer Graphics Forum, Vol. 39. Wiley Online Library, 27–38.Google Scholar
55. Joseph P Morris, Patrick J Fox, and Yi Zhu. 1997. Modeling low Reynolds number incompressible flows using SPH. J. Comput. Phys. 136, 1 (1997), 214–226.Google ScholarDigital Library
56. Matthias Müller, David Charypar, and Markus H Gross. 2003. Particle-based fluid simulation for interactive applications.. In Symposium on Computer animation. 154–159.Google Scholar
57. Metin Muradoglu and Gretar Tryggvason. 2008. A front-tracking method for computation of interfacial flows with soluble surfactants. J. Comput. Phys. 227, 4 (2008), 2238–2262.Google ScholarDigital Library
58. Andrew Nealen. 2004. An as-short-as-possible introduction to the least squares, weighted least squares and moving least squares methods for scattered data approximation and interpolation. URL: http://www.nealen.com/projects 130, 150 (2004), 25.Google Scholar
59. Xingyu Ni, Bo Zhu, Bin Wang, and Baoquan Chen. 2020. A level-set method for magnetic substance simulation. ACM Transactions on Graphics (TOG) 39, 4 (2020), 29–1.Google ScholarDigital Library
60. M Omang, Steinar Børve, and Jan Trulsen. 2006. SPH in spherical and cylindrical coordinates. J. Comput. Phys. 213, 1 (2006), 391–412.Google ScholarDigital Library
61. Saket Patkar, Mridul Aanjaneya, Dmitriy Karpman, and Ronald Fedkiw. 2013. A hybrid Lagrangian-Eulerian formulation for bubble generation and dynamics. In Proceedings of the 12th ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 105–114.Google ScholarDigital Library
62. Andreas Peer, Christoph Gissler, Stefan Band, and Matthias Teschner. 2018. An implicit SPH formulation for incompressible linearly elastic solids. In Computer Graphics Forum, Vol. 37. Wiley Online Library, 135–148.Google Scholar
63. Andreas Peer, Markus Ihmsen, Jens Cornelis, and Matthias Teschner. 2015. An implicit viscosity formulation for SPH fluids. ACM Transactions on Graphics (TOG) 34, 4 (2015), 1–10.Google ScholarDigital Library
64. Fabiano Petronetto, Afonso Paiva, Elias S Helou, DE Stewart, and Luis Gustavo Nonato. 2013. Mesh-Free Discrete Laplace-Beltrami Operator. In Computer Graphics Forum, Vol. 32. Wiley Online Library, 214–226.Google Scholar
65. Daniel J Price. 2012. Smoothed particle hydrodynamics and magnetohydrodynamics. J. Comput. Phys. 231, 3 (2012), 759–794.Google ScholarDigital Library
66. Steven J Ruuth and Barry Merriman. 2008. A simple embedding method for solving partial differential equations on surfaces. J. Comput. Phys. 227, 3 (2008), 1943–1961.Google ScholarDigital Library
67. Robert Saye. 2014. High-order methods for computing distances to implicitly defined surfaces. Communications in Applied Mathematics and Computational Science 9, 1 (2014), 107–141.Google ScholarCross Ref
68. Robert I Saye and James A Sethian. 2013. Multiscale modeling of membrane rearrangement, drainage, and rupture in evolving foams. Science 340, 6133 (2013), 720–724.Google Scholar
69. Hagit Schechter and Robert Bridson. 2012. Ghost SPH for animating water. ACM Transactions on Graphics (TOG) 31, 4 (2012), 1–8.Google ScholarDigital Library
70. Frank Schmidt. 2014. The laplace-beltrami-operator on riemannian manifolds. In Seminar Shape Analysis.Google Scholar
71. Andrew Selle, Nick Rasmussen, and Ronald Fedkiw. 2005. A vortex particle method for smoke, water and explosions. In ACM SIGGRAPH 2005 Papers. 910–914.Google ScholarDigital Library
72. Brian E Smits and Gary W Meyer. 1992. Newton’s colors: simulating interference phenomena in realistic image synthesis. In Photorealism in Computer Graphics. Springer, 185–194.Google Scholar
73. Barbara Solenthaler, Peter Bucher, Nuttapong Chentanez, Matthias Müller, and Markus Gross. 2011. SPH based shallow water simulation. (2011).Google Scholar
74. Barbara Solenthaler and Renato Pajarola. 2008. Density contrast SPH interfaces. (2008).Google Scholar
75. Barbara Solenthaler and Renato Pajarola. 2009. Predictive-corrective incompressible SPH. In ACM SIGGRAPH 2009 papers. 1–6.Google ScholarDigital Library
76. Jos Stam. 2003. Flows on surfaces of arbitrary topology. ACM Transactions On Graphics (TOG) 22, 3 (2003), 724–731.Google ScholarDigital Library
77. Alexandre M Tartakovsky and Paul Meakin. 2005. A smoothed particle hydrodynamics model for miscible flow in three-dimensional fractures and the two-dimensional Rayleigh-Taylor instability. J. Comput. Phys. 207, 2 (2005), 610–624.Google ScholarDigital Library
78. Sasan Tavakkol, Amir Reza Zarrati, and Mahdiyar Khanpour. 2017. Curvilinear smoothed particle hydrodynamics. International Journal for Numerical Methods in Fluids 83, 2 (2017), 115–131.Google ScholarCross Ref
79. Orestis Vantzos, Saar Raz, and Mirela Ben-Chen. 2018. Real-time viscous thin films. ACM Transactions on Graphics (TOG) 37, 6 (2018), 1–10.Google ScholarDigital Library
80. Hui Wang, Yongxu Jin, Anqi Luo, Xubo Yang, and Bo Zhu. 2020. Codimensional surface tension flow using moving-least-squares particles. ACM Transactions on Graphics (TOG) 39, 4 (2020), 42–1.Google ScholarDigital Library
81. Jian Jun Xu, Zhilin Li, John Lowengrub, and Hongkai Zhao. 2006. A level-set method for interfacial flows with surfactant. J. Comput. Phys. 212, 2 (2006), 590–616.Google ScholarDigital Library
82. Sheng Yang, Xiaowei He, Huamin Wang, Sheng Li, Guoping Wang, Enhua Wu, and Kun Zhou. 2016. Enriching SPH simulation by approximate capillary waves.. In Symposium on Computer Animation. 29–36.Google Scholar
83. Tao Yang, Jian Chang, Ming C Lin, Ralph R Martin, Jian J Zhang, and Shi-Min Hu. 2017a. A unified particle system framework for multi-phase, multi-material visual simulations. ACM Transactions on Graphics (TOG) 36, 6 (2017), 1–13.Google ScholarDigital Library
84. Tao Yang, Ralph R Martin, Ming C Lin, Jian Chang, and Shi-Min Hu. 2017b. Pairwise force SPH model for real-time multi-interaction applications. IEEE transactions on visualization and computer graphics 23, 10 (2017), 2235–2247.Google ScholarDigital Library
85. Jong-Chul Yoon, Hyeong Ryeol Kam, Jeong-Mo Hong, Shin Jin Kang, and Chang-Hun Kim. 2009. Procedural synthesis using vortex particle method for fluid simulation. In Computer Graphics Forum, Vol. 28. Wiley Online Library, 1853–1859.Google Scholar
86. Wen Zheng, Jun-Hai Yong, and Jean-Claude Paul. 2009. Simulation of bubbles. Graphical Models 71, 6 (2009), 229–239.Google ScholarDigital Library
87. Bo Zhu, Ed Quigley, Matthew Cong, Justin Solomon, and Ronald Fedkiw. 2014. Codimensional surface tension flow on simplicial complexes. ACM Transactions on Graphics (TOG) 33, 4 (2014), 1–11.Google ScholarDigital Library
88. Bo Zhu, Xubo Yang, and Ye Fan. 2010. Creating and preserving vortical details in sph fluid. In Computer Graphics Forum, Vol. 29. Wiley Online Library, 2207–2214.Google Scholar