“Variational stokes: a unified pressure-viscosity solver for accurate viscous liquids” by Larionov, Batty and Bridson
Conference:
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Title:
- Variational stokes: a unified pressure-viscosity solver for accurate viscous liquids
Session/Category Title: Fluids II
Presenter(s)/Author(s):
Moderator(s):
Abstract:
We propose a novel unsteady Stokes solver for coupled viscous and pressure forces in grid-based liquid animation which yields greater accuracy and visual realism than previously achieved. Modern fluid simulators treat viscosity and pressure in separate solver stages, which reduces accuracy and yields incorrect free surface behavior. Our proposed implicit variational formulation of the Stokes problem leads to a symmetric positive definite linear system that gives properly coupled forces, provides unconditional stability, and treats difficult boundary conditions naturally through simple volume weights. Surface tension and moving solid boundaries are also easily incorporated. Qualitatively, we show that our method recovers the characteristic rope coiling instability of viscous liquids and preserves fine surface details, while previous grid-based schemes do not. Quantitatively, we demonstrate that our method is convergent through grid refinement studies on analytical problems in two dimensions. We conclude by offering practical guidelines for choosing an appropriate viscous solver, based on the scenario to be animated and the computational costs of different methods.
References:
1. Luiz Fernando de Souza Andrade, Marcos Sandim, Fabiano Petronetto, Paulo Pagliosa, and Afonso Paiva. 2015. Particle-based fluids for viscous jet buckling. Computers and Graphics 52 (2015), 106–115. Google ScholarDigital Library
2. Basile Audoly, Nicolas Clauvelin, Pierre-Thomas Brun, Miklos Bergou, Eitan Grinspun, and Max Wardetzky. 2012. A discrete geometric approach for simulating the dynamics of thin viscous threads. (2012).Google Scholar
3. David Baraff. 1996. Linear-time dynamics using Lagrange multipliers. In SIGGRAPH. 137–146. Google ScholarDigital Library
4. G. K. Batchelor. 1967. An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
5. Christopher Batty, Florence Bertails, and Robert Bridson. 2007. A fast variational framework for accurate solid-fluid coupling. ACM Trans. Graph. (SIGGRAPH) 26, 3 (2007), 100. http://portal.acm.org/citation.cfm?id=1276502Google ScholarDigital Library
6. Christopher Batty and Robert Bridson. 2008. Accurate viscous free surfaces for buckling, coiling, and rotating liquids. In Symposium on Computer Animation. 219–228. http://portal.acm.org/citation.cfm?id=1632624Google ScholarDigital Library
7. Christopher Batty and Ben Houston. 2011. A simple finite volume method for adaptive viscous liquids. In Symposium on Computer Animation. 111–118. Google ScholarDigital Library
8. Christopher Batty, Andres Uribe, Basile Audoly, and Eitan Grinspun. 2012. Discrete viscous sheets. ACM Trans. Graph. (SIGGRAPH) 31, 4 (2012), 113.Google ScholarDigital Library
9. Jan Bender and Dan Koschier. 2016. Divergence-Free SPH for Incompressible and Viscous Fluids. IEEE TVCG 99 (2016).Google Scholar
10. Michele Benzi, Gene H. Golub, and Jorg Liesen. 2005. Numerical solution of saddle point problems. Acta Numerica 14 (2005), 1–37. Google ScholarCross Ref
11. Miklos Bergou, Basile Audoly, Etienne Vouga, Max Wardetzky, and Eitan Grinspun. 2010. Discrete viscous threads. ACM Trans. Graph. (SIGGRAPH) 29, 4 (2010), 116.Google ScholarDigital Library
12. Andrea Bonito, Marco Picasso, and Manuel Laso. 2006. Numerical simulation of 3D viscoelastic flows with free surfaces. J. Comp. Phys. 215, 2 (2006), 691–716. Google ScholarDigital Library
13. Robert Bridson. 2015. Fluid simulation for computer graphics, 2nd edition. A. K. Peters, Ltd.Google Scholar
14. Pierre-Thomas Brun, Neil Ribe, and Basile Audoly. 2012. A numerical investigation of the fluid-mechanical sewing machine. Phys. Fluids 24, 4 (2012), 043102.Google ScholarCross Ref
15. Mark Carlson, Peter J. Mucha, R. Van Horn, and Greg Turk. 2002. Melting and flowing. In Symposium on Computer Animation. 167–174. Google ScholarDigital Library
16. Pascal Clausen, Martin Wicke, Jonathan Richard Shewchuk, and James F. O’Brien. 2013. Simulating liquids and solid-liquid interactions with Lagrangian meshes. ACM Trans. Graph. 32, 2 (2013), 17. Google ScholarDigital Library
17. M. S. Darwish, J. R. Whiteman, and M. J. Bevis. 1992. Numerical modelling of viscoelastic liquids using a finite-volume method. Journal of Non-Newtonian Fluid Mechanics 45, 3 (1992), 311–337. Google ScholarCross Ref
18. Gilles Daviet and Florence Bertails-Descoubes. 2016. A semi-implicit material point method for the continuum simulation of granular materials. ACM Trans. Graph. (SIGGRAPH) (2016).Google Scholar
19. Mathieu Desbrun and Marie-Paule Gascuel. 1996. Smoothed particles: a new paradigm for animating highly deformable bodies. In Eurographics Workshop on Computer Animation and Simulation. 61–76. Google ScholarCross Ref
20. Howard Elman. 2002. Preconditioners for saddle point problems arising in computational fluid dynamics. Applied Numerical Mathematics 43, 1–2 (2002), 75–89.Google ScholarDigital Library
21. Doug Enright, Duc Nguyen, Frédéric Gibou, and Ron Fedkiw. 2003. Using the particle level set method and a second order accurate pressure boundary condition for free surface flows. In Proceedings of the 4th ASME-JSME Joint Fluids Engineering Conference. ASME, 337–342. Google ScholarCross Ref
22. Kenny Erleben, Marek Misztal, and Andreas Baerentzen. 2011. Mathematical foundation of the optimization-based fluid animation method. In Symposium on Computer Animation. 101–110. Google ScholarDigital Library
23. Henrik Fält and Doug Roble. 2003. Fluids with extreme viscosity. In SIGGRAPH Sketches. 1. Google ScholarDigital Library
24. Nick Foster and Dimitris Metaxas. 1996. Realistic animation of liquids. Graphical Models and Image Processing 58, 5 (1996), 471–483. http://portal.acm.org/citation.cfm?id=244315 Google ScholarDigital Library
25. Theodore F. Gast, Craig Schroeder, Alexey Stomakhin, Chenfanfu Jiang, and Joseph M. Teran. 2015. Optimization integrator for large time steps. IEEE TVCG 21, 10 (2015), 1103–1115. Google ScholarDigital Library
26. Tolga G. Goktekin, Adam W. Bargteil, and James F. O’Brien. 2004. A method for animating viscoelastic fluids. ACM Trans. Graph. (SIGGRAPH) 23, 3 (aug 2004), 463–468. Google ScholarDigital Library
27. Rony Goldenthal, David Harmon, Raanan Fattal, Michel Bercovier, and Eitan Grinspun. 2007. Efficient simulation of inextensible cloth. ACM Trans. Graph. (SIGGRAPH) 26, 3 (2007), 49.Google ScholarDigital Library
28. Jeong-Mo Hong and Chang-Hun Kim. 2005. Discontinuous fluids. ACM Trans. Graph. (SIGGRAPH) 24, 3 (jul 2005), 915–920. Google ScholarDigital Library
29. Chenfanfu Jiang, Craig Schroeder, Andrew Selle, Joseph Teran, and Alexey Stomakhin. 2015. The affine particle-in-cell method. ACM Trans. Graph. (SIGGRAPH) 34, 4 (2015), 51.Google ScholarDigital Library
30. Nahyup Kang, Jinho Park, Junyong Noh, and Sung Yong Shin. 2010. A hybrid approach to multiple fluid simulation using volume fractions. Computer Graphics Forum (Eurographics) 29, 2 (2010), 685–694.Google ScholarCross Ref
31. Gergely Klar, Theodore Gast, Andre Pradhana, Chuyuan Fu, Craig Schroeder, Chenfanfu Jiang, and Joseph Teran. 2016. Drucker-Prager elastoplasticity for sand animation. ACM Trans. Graph. (SIGGRAPH) (2016).Google Scholar
32. Benjamin Lalanne, Lucia Rueda Villegas, Sebastian Tanguy, and Frederic Risso. 2015. On the computation of viscous terms for incompressible two-phase flows with Level Set/Ghost Fluid Method. J. Comput. Phys. 301 (2015), 289–307. Google ScholarDigital Library
33. David I. W. Levin, Joshua Litven, Garret L. Jones, Shinjiro Sueda, and Dinesh K. Pai. 2011. Eulerian solid simulation with contact. ACM Trans. Graph. (SIGGRAPH) (2011).Google Scholar
34. Frank Losasso, Tamar Shinar, Andrew Selle, and Ronald Fedkiw. 2006. Multiple interacting liquids. ACM Trans. Graph. (SIGGRAPH) 25, 3 (2006), 812–819. Google ScholarDigital Library
35. Sebastian Martin, Bernhard Thomaszewski, Eitan Grinspun, and Markus Gross. 2011. Example-based elastic materials. ACM Trans. Graph. (SIGGRAPH) 30, 4 (2011), 72.Google ScholarDigital Library
36. Chohong Min and Frédéric Gibou. 2007. Geometric integration over irregular domains with application to level-set methods. J. Comp. Phys. 226, 2 (oct 2007), 1432–1443. Google ScholarDigital Library
37. Marek Misztal, Robert Bridson, Kenny Erleben, Andreas Baerentzen, and Francois Anton. 2010. Optimization-based fluid simulation on unstructured meshes. In VRIPHYS.Google Scholar
38. Marek Misztal, Kenny Erleben, Adam W. Bargteil, B. Bunch Christensen, Andreas Baerentzen, and Robert Bridson. 2012. Multiphase flow of immiscible fluids on unstructured moving meshes. In Symposium on Computer Animation. Eurographics Association, Lausanne, Switzerland, 97–106.Google Scholar
39. G. Mompean and M. Deville. 1997. Unsteady finite volume simulation of Oldroyd-B fluid through a three-dimensional planar contraction. Journal of Non-Newtonian Fluid Mechanics 72, 2–3 (oct 1997), 253–279. Google ScholarCross Ref
40. Patrick Mullen, Keenan Crane, Dmitry Pavlov, Yiying Tong, and Mathieu Desbrun. 2009. Energy-preserving integrators for fluid animation. ACM Trans. Graph. (SIGGRAPH) 28, 3 (2009), 38. http://portal.acm.org/citation.cfm?id=1531326.1531344Google ScholarDigital Library
41. Rahul Narain, Abhinav Golas, and Ming C. Lin. 2010. Free-flowing granular materials with two-way solid coupling. ACM Trans. Graph. (SIGGRAPH Asia) 29, 6 (2010), 173.Google ScholarDigital Library
42. Rahul Narain, Jason Sewall, Mark Carlson, and Ming C. Lin. 2008. Fast animation of turbulence using energy transport and procedural synthesis. ACM Trans. Graph. (SIGGRAPH Asia) 27, 5 (2008), 166. http://portal.acm.org/citation.cfm?id=1457515.1409119Google ScholarDigital Library
43. Yen Ting Ng, Chohong Min, and Frédéric Gibou. 2009. An efficient fluid-solid coupling algorithm for single-phase flows. J. Comp. Phys. 228, 23 (2009), 8807–8829. Google ScholarDigital Library
44. Michael B. Nielsen and Brian B. Christensen. 2010. Improved variational guiding of smoke animations. Computer Graphics Forum (Eurographics) 29, 2 (2010), 705–712.Google ScholarCross Ref
45. Cassio M. Oishi, Murilo F. Tomé, José A. Cuminato, and Sean McKee. 2008. An implicit technique for solving 3D low Reynolds number moving free surface flows. J. Comp. Phys. 227, 16 (2008), 7446–7468. Google ScholarDigital Library
46. Andreas Peer, Markus Ihmsen, Jens Cornelis, and Matthias Teschner. 2015. An implicit viscosity formulation for SPH fluids. ACM Trans. Graph. (SIGGRAPH) 34, 4 (2015), 114.Google ScholarDigital Library
47. Andreas Peer and Matthias Teschner. 2016. Prescribed velocity gradients for highly viscous SPH fluids with vorticity diffusion. IEEE TVCG (2016).Google Scholar
48. 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 Symposium on Computer Animation. 157–163. Google ScholarDigital Library
49. Nick Rasmussen, Doug Enright, Duc Nguyen, Sebastian Marino, N. Sumner, Willi Geiger, Samir Hoon, and Ron Fedkiw. 2004. Directable photorealistic liquids. In Symposium on Computer Animation. 193–202. Google ScholarDigital Library
50. Neil Ribe, Mehdi Habibi, and Daniel Bonn. 2012. Liquid rope coiling. Annual review of fluid mechanics 44 (2012), 249–266. Google ScholarCross Ref
51. Avi Robinson-Mosher, R. Elliot English, and Ronald Fedkiw. 2009. Accurate tangential velocities for solid fluid coupling. In Symposium on Computer Animation. 227–236. http://portal.acm.org/citation.cfm?id=1599470.1599500Google ScholarDigital Library
52. Avi Robinson-Mosher, Craig Schroeder, and Ron Fedkiw. 2011. A symmetric positive definite formulation for monolithic fluid structure interaction. J. Comp. Phys. 230, 4 (2011), 1547–1566. http://physbam.stanford.edu/ Google ScholarDigital Library
53. Avi Robinson-Mosher, Tamar Shinar, Jon Gretarsson, Jonathan Su, and Ronald Fedkiw. 2008. Two-way coupling of fluids to rigid and deformable solids and shells. ACM Trans. Graph. (SIGGRAPH) 27, 3 (2008), 46. http://portal.acm.org/citation.cfm?id=1399504.1360645Google ScholarDigital Library
54. Allen Ruilova. 2007. Creating realistic CG honey. In SIGGRAPH Posters. 58.Google Scholar
55. Craig Schroeder, Alexey Stomakhin, Russel Howes, and Joseph M. Teran. 2014. A second order virtual node algorithm for NavierâĂŞStokes flow problems with interfacial forces and discontinuous material properties. J. Comp. Phys. 265 (2014), 221–245. Google ScholarDigital Library
56. Rajsekhar Setaluri, Mridul Aanjaneya, Sean Bauer, and Eftychios Sifakis. 2014. SPGrid: A sparse paged grid structure applied to adaptive smoke simulation. ACM Trans. Graph. (SIGGRAPH Asia) 33, 6 (2014), 205.Google ScholarDigital Library
57. Side Effects Software. 2016. Houdini. (2016).Google Scholar
58. Alexey Stomakhin, Craig Schroeder, Lawrence Chai, Joseph Teran, and Andrew Selle. 2013. A material point method for snow simulation. ACM Trans. Graph. (SIGGRAPH) 32, 4 (2013), 102.Google ScholarDigital Library
59. Alexey Stomakhin, Craig Schroeder, Chenfanfu Jiang, Lawrence Chai, Joseph Teran, and Andrew Selle. 2014. Augmented MPM for phase-change and varied materials. ACM Trans. Graph. (SIGGRAPH) 33, 4 (2014), 138.Google ScholarDigital Library
60. M. Sussman, K.M. Smith, M.Y. Hussaini, M. Ohta, and R. Zhi-Wei. 2007. A sharp interface method for incompressible two-phase flows. J. Comp. Phys. 221 (2007), 469–505. Google ScholarDigital Library
61. Tetsuya Takahashi, Yoshinori Dobashi, Issei Fujishiro, Tomoyuki Nishita, and Ming C. Lin. 2015. Implicit formulation for SPH-based viscous fluids. Computer Graphics Forum (Eurographics) 34, 2 (2015), 493–502.Google ScholarDigital Library
62. Murilo F. Tomé, L. Grossi, Antonio Castelo, José A. Cuminato, Norberto Mangiavacchi, Valdemir G. Ferreira, F. S. de Sousa, and Sean McKee. 2004. A numerical method for solving three-dimensional generalized Newtonian free surface flows. Journal of Non-Newtonian Fluid Mechanics 123, 2–3 (2004), 85–103.Google ScholarCross Ref
63. Murilo F. Tomé and Sean McKee. 1994. GENSMAC: A computational marker and cell method for free surface flows in general domains. J. Comp. Phys. 110, 1 (1994), 171–186. Google ScholarDigital Library
64. M F Tomé and Sean McKee. 1999. Numerical simulation of viscous flow: Buckling of planar jets. International Journal for Numerical Methods in Fluids 29, 6 (1999), 705–718.Google ScholarCross Ref
65. Maxime Tournier, Matthieu Nesme, Benjamin Gilles, and Francois Faure. 2015. Stable constrained dynamics. ACM Trans. Graph. (SIGGRAPH) 34, 4 (2015), 132.Google ScholarDigital Library
66. Mark Wiebe and Ben Houston. 2004. The Tar Monster: Creating a character with fluid simulation. In SIGGRAPH Sketches.Google Scholar
67. Yonghao Yue, Breannan Smith, Christopher Batty, Changxi Zheng, and Eitan Grinspun. 2015. Continuum foam: A material point method for shear-dependent flows. ACM Trans. Graph. (SIGGRAPH) 34, 5 (2015), 160.Google ScholarDigital Library
68. Xinxin Zhang and Robert Bridson. 2015. Restoring the missing vortices in advection-projection fluid solvers. ACM Trans. Graph. (SIGGRAPH) 34, 4 (2015), 52.Google ScholarDigital Library
69. Bo Zhu, Minjae Lee, Ed Quigley, and Ronald Fedkiw. 2015. Codimensional non-Newtonian fluids. ACM Trans. Graph. (SIGGRAPH) 34, 4 (2015), 115.Google ScholarDigital Library
70. Bo Zhu, Ed Quigley, Matthew Cong, Justin Solomon, and Ronald Fedkiw. 2014. Codimensional surface tension flow on simplicial complexes. ACM Trans. Graph. (SIGGRAPH) 33, 4 (2014), 111.Google ScholarDigital Library
