A moving eulerian-lagrangian particle method for thin film and foam simulation

Abstract

We present the Moving Eulerian-Lagrangian Particles (MELP), a novel mesh-free method for simulating incompressible fluid on thin films and foams. Employing a bi-layer particle structure, MELP jointly simulates detailed, vigorous flow and large surface deformation at high stability and efficiency. In addition, we design multi-MELP: a mechanism that facilitates the physically-based interaction between multiple MELP systems, to simulate bubble clusters and foams with non-manifold topological evolution. We showcase the efficacy of our method with a broad range of challenging thin film phenomena, including the Rayleigh-Taylor instability across double-bubbles, foam fragmentation with rim surface tension, recovery of the Plateau borders, Newton black films, as well as cyclones on bubble clusters.

References

1. Keith C Afas. 2018. Extending the Calculus of Moving Surfaces to Higher Orders. arXiv preprint arXiv:1806.02335 (2018).
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.
3. 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.
4. John WM Bush and Alexander E Hasha. 2004. On the collision of laminar jets: fluid chains and fishbones. Journal of fluid mechanics 511 (2004), 285--310.
5. Jingyu Chen, Victoria Kala, Alan Marquez-Razon, Elias Gueidon, David A. B. Hyde, and Joseph Teran. 2021. A Momentum-Conserving Implicit Material Point Method for Surface Tension with Contact Angles and Spatial Gradients. ACM TOG 40, 4 (2021), 1--16.
6. Jean-Marc Chomaz. 2001. The dynamics of a viscous soap film with soluble surfactant. Journal of Fluid Mechanics 442 (2001), 387--409.
7. Jonathan M Cohen, Sarah Tariq, and Simon Green. 2010. Interactive fluid-particle simulation using translating Eulerian grids. In Proceedings of the 2010 ACM SIGGRAPH symposium on Interactive 3D Graphics and Games. 15--22.
8. Sylvie Cohen-Addad, Reinhard Höhler, and Olivier Pitois. 2013. Flow in foams and flowing foams. Annual Review of Fluid Mechanics 45 (2013), 241--267.
9. Y Couder, JM Chomaz, and M Rabaud. 1989. On the hydrodynamics of soap films. Physica D: Nonlinear Phenomena 37, 1--3 (1989), 384--405.
10. 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.
11. Fang Da, David Hahn, Christopher Batty, Chris Wojtan, and Eitan Grinspun. 2016. Surface-only liquids. ACM Transactions on Graphics (TOG) 35, 4 (2016), 1--12.
12. R Elliot English, Linhai Qiu, Yue Yu, and Ronald Fedkiw. 2013. An adaptive discretization of incompressible flow using a multitude of moving Cartesian grids. J. Comput. Phys. 254 (2013), 107--154.
13. Robert Finn. 1999. Capillary surface interfaces. Notices of the AMS 46, 7 (1999), 770--781.
14. Frederic Gibou, Ronald Fedkiw, and Stanley Osher. 2018. A review of level-set methods and some recent applications. J. Comput. Phys. 353 (2018), 82--109.
15. Andrew Glassner. 2000. Soap bubbles. 1. IEEE Computer Graphics and Applications 20, 5 (2000), 76--84.
16. Michael Grinfeld and Pavel Grinfeld. 2017. Modeling of Stability of Electrostatic and Magnetostatic Systems. Technical Report. US Army Research Laboratory Aberdeen Proving Ground United States.
17. Pavel Grinfeld. 2009. Shape optimization and electron bubbles. Numerical Functional Analysis and Optimization 30, 7--8 (2009), 689--710.
18. P Grinfeld. 2010a. Hamiltonian dynamic equations for fluid films. Studies in Applied Mathematics 125, 3 (2010), 223--264.
19. Pavel Grinfeld. 2010b. Variable thickness model for fluid films under large displacement. Physical review letters 105, 13 (2010), 137802.
20. Pavel Grinfeld. 2010c. Viscous equations of fluid film dynamics. Computers Materials and Continua 19, 3 (2010), 239.
21. Pavel Grinfeld. 2013. Introduction to tensor analysis and the calculus of moving surfaces. Springer.
22. Pavel Grinfeld et al. 2009. Exact nonlinear equations for fluid films and proper adaptations of conservation theorems from classical hydrodynamics. Journal of Geometry and Symmetry in Physics 16 (2009), 1--21.
23. Pavel Grinfeld et al. 2012. A better calculus of moving surfaces. Journal of Geometry and Symmetry in Physics 26 (2012), 61--69.
24. 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.
25. Cyrill W Hirt, Anthony A Amsden, and JL Cook. 1974. An arbitrary Lagrangian-Eulerian computing method for all flow speeds. Journal of computational physics 14, 3 (1974), 227--253.
26. 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). }
27. David A. B. Hyde, Steven W. Gagniere, Alan Marquez-Razon, and Joseph Teran. 2020. An Implicit Updated Lagrangian Formulation for Liquids with Large Surface Energy. ACM TOG 39, 4 (2020).
28. 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.
29. 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, Article 31 (2020), 31:1--31:11 pages. }
30. 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.
31. 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.
32. Dariusz Jaszkowski and Janusz Rzeszut. 2003. Interference colours of soap bubbles. The Visual Computer 19, 4 (2003), 252--270.
33. Chenfanfu Jiang, Craig Schroeder, Andrew Selle, Joseph Teran, and Alexey Stomakhin. 2015. The affine particle-in-cell method. ACM Transactions on Graphics (TOG) 34, 4 (2015), 1--10.
34. M. Kness. 2008. ColorPy-A Python package for handling physical descriptions of color and light spectra. (2008).
35. Stephan A Koehler, Sascha Hilgenfeldt, and HA Stone. 2004. Foam drainage on the microscale: I. Modeling flow through single Plateau borders. Journal of colloid and interface science 276, 2 (2004), 420--438.
36. Petros Koumoutsakos. 2005. Multiscale flow simulations using particles. Annu. Rev. Fluid Mech. 37 (2005), 457--487.
37. Andrew M Kraynik, Douglas A Reinelt, and Frank van Swol. 2004. Structure of random foam. Physical Review Letters 93, 20 (2004), 208301.
38. David IW Levin, Joshua Litven, Garrett L Jones, Shinjiro Sueda, and Dinesh K Pai. 2011. Eulerian solid simulation with contact. ACM Transactions on Graphics (TOG) 30, 4 (2011), 1--10.
39. S.J. Lind, R. Xu, P.K. Stansby, and B.D. Rogers. 2012. Incompressible smoothed particle hydrodynamics for free-surface flows: A generalised diffusion-based algorithm for stability and validations for impulsive flows and propagating waves. J. Comput. Phys. 231, 4 (2012), 1499 -- 1523.
40. 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.
41. Daniel Ram, Theodore Gast, Chenfanfu Jiang, Craig Schroeder, Alexey Stomakhin, Joseph Teran, and Pirouz Kavehpour. 2015. A material point method for viscoelastic fluids, foams and sponges. In Proceedings of the 14th ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 157--163.
42. Milton J Rosen and Joy T Kunjappu. 2012. Surfactants and interfacial phenomena. John Wiley & Sons.
43. Amaresh Sahu, Yannick AD Omar, Roger A Sauer, and Kranthi K Mandadapu. 2020. Arbitrary Lagrangian-Eulerian finite element method for curved and deforming surfaces: I. General theory and application to fluid interfaces. J. Comput. Phys. 407 (2020), 109253.
44. 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.
45. Robert I Saye and James A Sethian. 2016. Multiscale modelling of evolving foams. J. Comput. Phys. 315 (2016), 273--301.
46. Hagit Schechter and Robert Bridson. 2012. Ghost SPH for animating water. ACM Transactions on Graphics (TOG) 31, 4 (2012), 1--8.
47. Nicholas Sharp and Keenan Crane. 2020. A Laplacian for Nonmanifold Triangle Meshes. Computer Graphics Forum (SGP) 39, 5 (2020).
48. 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.
49. Barbara Solenthaler. 2011. SPH Based Shallow Water Simulation. The Eurographics Association.
50. Alexey Stomakhin, Craig Schroeder, Lawrence Chai, Joseph Teran, and Andrew Selle. 2013. A material point method for snow simulation. ACM Transactions on Graphics (TOG) 32, 4 (2013), 1--10.
51. David V Svintradze. 2019. Shape dynamics of bouncing droplets. Scientific reports 9, 1 (2019), 1--10.
52. Gilberto L Thomas, Julio M Belmonte, François Graner, James A Glazier, and Rita MC de Almeida. 2015. 3D simulations of wet foam coarsening evidence a self similar growth regime. Colloids and Surfaces A: Physicochemical and Engineering Aspects 473 (2015), 109--114.
53. 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.
54. Mengdi Wang, Yitong Deng, Xiangxin Kong, Aditya H. Prasad, Shiying Xiong, and Bo Zhu. 2021. Thin-Film Smoothed Particle Hydrodynamics Fluid. ACM Trans. Graph. 40, 4, Article 110 (jul 2021), 16 pages.
55. Stephanie Wang and Albert Chern. 2021. Computing minimal surfaces with differential forms. ACM Transactions on Graphics (TOG) 40, 4 (2021), 1--14.
56. D Weaire and R Phelan. 1996. The physics of foam. Journal of Physics: Condensed Matter 8, 47 (1996), 9519.
57. J. Z. Wu, H. Y. Ma, and M. D. Zhou. 2006. Vorticity and Vortex Dynamics. Springer.
58. 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.
59. Bowen Yang, William Corse, Jiecong Lu, Joshuah Wolper, and Chen-Fanfu Jiang. 2019. Real-Time Fluid Simulation on the Surface of a Sphere. Proceedings of the ACM on Computer Graphics and Interactive Techniques 2, 1 (2019), 1--17.
60. Jiaping You and Yue Yang. 2020. Modelling of the turbulent burning velocity based on Lagrangian statistics of propagating surfaces. Journal of Fluid Mechanics 887 (2020).
61. Yonghao Yue, Breannan Smith, Christopher Batty, Changxi Zheng, and Eitan Grinspun. 2015. Continuum foam: A material point method for shear-dependent flows. ACM Transactions on Graphics (TOG) 34, 5 (2015), 1--20.
62. Y. L. Zhang, K. S. Yeo, B. C. Khoo, and C. Wang. 2001. 3D Jet Impact of Toroidal Bubbles. J. Comput. Phys. 166 (2001), 336--360.
63. Wen Zheng, Jun-Hai Yong, and Jean-Claude Paul. 2009. Simulation of bubbles. Graphical Models 71, 6 (2009), 229--239.
64. 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.
65. Y. Zhu and R. Bridson. 2005. Animating sand as a fluid. ACM Trans. Graph. (SIGGRAPH Proc.) 24, 3 (2005), 965--972.

Index Terms

• Computing methodologies

  • Modeling and simulation