Abstract
We present a new framework to simulate moving interfaces in viscous incompressible two phase flows. The goal is to achieve both conservation of the fluid volume and a detailed reconstruction of the fluid surface. To these ends, we incorporate sub-grid refinement of the level set with the volume-of-fluid method. In the context of this refined level set grid we propose the algorithms needed for the coupling of the level set and the volume-of-fluid, which include techniques for computing volume, redistancing the level set, and handling surface tension. We report the experimental results produced with the proposed method via simulations of the two phase fluid phenomena such as air-cushioning and deforming large bubbles.
Supporting Information
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References
- [AIA*12] Akinci N., Ihmsen M., Akinci G., Solenthaler B., Teschner M.: Versatile rigid-fluid coupling for incompressible SPH. ACM Trans. Graph. 31, 4 (July 2012), 62:1–62:8. 2.
- [APKG07] Adams B., Pauly M., Keiser R., Guibas L. J.: Adaptively sampled particle fluids. ACM Trans. Graph. 26, 3 (2007), 48. 2.
- [AT11]
Ando R.,
Tsuruno R.: A particle-based method for preserving fluid sheets. In
Proceedings of the 2011 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (2011), ACM, pp.
7–16. 3.
10.1145/2019406.2019408 Google Scholar
- [BB12] Boyd L., Bridson R.: MultiFLIP for energetic two-phase fluid simulation. ACM Trans. Graph. 31, 2 (Apr 2012), 16:1–16:12. 3.
- [BBB10] Brochu T., Batty C., Bridson R.: Matching fluid simulation elements to surface geometry and topology. ACM Trans. Graph. 29 (July 2010), 47:1–47:9. 3.
- [BCG89] Bell J., Colella P., Glaz H.: A second-order projection method for the incompressible Navier-Stokes equations. J. Comp. Phys. 85 (1989), 257–283. 4.
- [BGOS06] Bargteil A. W., Goktekin T. G., O'brien J. F., Strain J. A.: A semi-Lagrangian contouring method for fluid simulation. ACM Trans. Graph. 25, 1 (2006), 19–38. 3.
- [BKZ92] Brackbill J. U., Kothe D. B., Zemach C.: A continuum method for modeling surface tension. J. Comp. Phys. 100 (1992), 335–354. 6.
- [BT07]
Becker M.,
Teschner M.: Weakly compressible SPH for free surface flows. In
Proceedings of the 2007 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (2007), Eurographics Association, pp.
209–217. 2.
10.3917/ridp.781.0209 Google Scholar
- [Cho67]
Chorin A. J.: A numerical method for solving incomressible viscous flow problems.
J. Comp. Phys.
2 (1967), 12–26. 2.
10.1016/0021-9991(67)90037-X Google Scholar
- [CM11]
Chentanez N.,
Müller M.: A multigrid fluid pressure solver handling separating solid boundary conditions. In
Proceedings of the 2011 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (2011), ACM, pp.
83–90. 7.
10.1145/2019406.2019418 Google Scholar
- [CM12] Chentanez N., Müller M.: Mass-conserving eulerian liquid simulation. In Proceedings of the ACM SIGGRAPHEurographics Symposium on Computer Animation (2012), Eurographics Association, pp. 245–254. 2.
- COQ06 Cecil T. C., Osher S. J., Qian J.: Simplex free adaptive tree fast sweeping and evolution methods for solving level set equations in arbitrary dimension. J. Comp. Phys. 213 (2006), 458–473. 6.
- [CPPK07] Cleary P. W., Pyo S. H., Prakash M., Koo B. K.: Bubbling and frothing liquids. ACM Trans. Graph. 26, 3 (2007), 97. 2.
- [DP09] Desjardins O., Pitsch H.: A spectrally refined interface approach for simulating multiphase flows. J. Comput. Phys. 228, 5 (2009), 1658–1677. 4, 5, 7.
- [ED08] Eisemann E., Décoret X.: Single-pass GPU solid voxelization and applications. In Proceedings of graphics interface 2008 (2008), pp. 78–80. 5.
- [EMF02] Enright D., Marschner S., Fedkiw R.: Animation and rendering of complex water surfaces. ACM Trans. Graph. 21, 3 (2002), 736–744. 2, 3.
- [HK10]
Heo N.,
Ko H.-S.: Detail-preserving fully-Eulerian interface tracking framework.
ACM Trans. Graph.
29 (December 2010), 176:1–176:8. 2, 4, 5.
10.1145/1882261.1866198 Google Scholar
- [HLYK08] Hong J.-M., Lee H.-Y., Yoon J.-C., Kim C.-H.: Bubbles alive. ACM Trans. Graph. 27, 3 (2008), 1–4. 3.
- [HN81] Hirt C. W., Nichols B. D.: Volume of fluid(VOF) method for the dynamics of free boundaries. J. Comp. Phys. 39 (1981), 201–225. 2.
- [IAAT12] Ihmsen M., Akinci N., Akinci G., Teschner M.: Unified spray, foam and air bubbles for particle-based fluids. The Visual Computer 28, 6–8 (June 2012), 669–677. 2.
- [Jak10] Jakob W.: Mitsuba renderer, 2010. http://www.mitsubarenderer.org. 7.
- [KLL*07]
Kim B.,
Liu Y.,
Llamas I.,
Jiao X.,
Rossignac J.: Simulation of bubbles in foam with the volume control method.
ACM Trans. Graph.
26, 3 (2007), 98. 2.
10.1145/1276377.1276500 Google Scholar
- [KPNS10] Kang N., Park J., Noh J., Shin S. Y.: A hybrid approach to multiple fluid simulation using volume fractions. Computer Graphics Forum 29 (2010), 685–694. 2.
- [KSK09] Kim D., Song O.-y., Ko H.-S.: Stretching and wiggling liquids. ACM Trans. Graph. 28, 5 (2009), 1–7. 2.
- [KSK10] Kim D., Song O.-y., Ko H.-S.: A practical simulation of dispersed bubble flow. ACM Trans. Graph. 29 (July 2010), 70:1–70:5. 3.
- [LCPF12] Lentine M., Cong M., Patkar S., Fedkiw R.: Simulating free surface flow with very large time steps. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation (2012), Eurographics Association, pp. 107–116. 2.
- [LGF04] Losasso F., Gibou F., Fedkiw R.: Simulating water and smoke with an octree data structure. ACM Trans. Graph. 23, 3 (2004), 457–462. 2, 4.
- [LGF11] Lentine M., Grétarsson J. T., Fedkiw R.: An unconditionally stable fully conservative semi-Lagrangian method. J. Comp. Phys. 230 (2011), 2857–2879. 2.
- [LTKF08] Losasso F., Talton J., Kwatra N., Fedkiw R.: Two-way coupled SPH and particle level set fluid simulation. IEEE Transactions on Visualization and Computer Graphics 14, 4 (2008), 797–804. 3.
- [MÖ9]
Müller M.: Fast and robust tracking of fluid surfaces. In
Proceedings of the 2009 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (2009), ACM, pp.
237–245. 3.
10.1145/1599470.1599501 Google Scholar
- [MCG03] Müller M., Charypar D., Gross M.: Particle-based fluid simulation for interactive applications. In Proceedings of the 2003 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (2003), pp. 154–159. 2.
- [MG07] Min C., Gibou F.: A second order accurate level set method on non-graded adaptive Cartesian grids. J. Comput. Phys. 225 (July 2007), 300–321. 4.
- [MG08] Min C., Gibou F.: Robust second-order accurate discretizations of the multi-dimensional Heaviside and Dirac delta functions. J. Comp. Phys. 227 (2008), 9686–9695. 5.
- [Min10] Min C.: On reinitializing level set functions. J. Comp. Phys. 229 (2010), 2764–2772. 6.
- [MMS09] Mihalef V., Metaxas D., Sussman M.: Simulation of two-phase flow with sub-scale droplet and bubble effects. Comput. Graph. Forum 28, 2 (2009), 229–238. 3.
- [MMTD07] Mullen P., McKenzie A., Tong Y., Desbrun M.: A variational approach to Eulerian geometry processing. ACM Trans. Graph. 26, 3 (2007), 66. 2.
- [Mon92] Monaghan J. J.: Smoothed particle hydrodynamics. Ann. Rev. Astron. Astrophys. 30 (1992), 543–74. 2.
- [MR06] Marchandise E., Remacle J.-F.: A stabilized finite element method using a discontinuous level set approach for solving two phase incompressible flows. J. Comput. Phys. 219, 2 (2006), 780–800. 6.
- [MST10] McAdams A., Sifakis E., Teran J.: A parallel multigrid poisson solver for fluids simulation on large grids. In Proceedings of the 2010 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (2010), Eurographics Association, pp. 65–74. 7.
- [MTB07] Ménard T., Tanguy S., Berlemont A.: Coupling level set/VOF/ghost fluid methods: Validation and application to 3D simulation of the primary break-up of a liquid jet. Journal of Multiphase Flow 33 (2007), 510–524. 5, 9.
- [MUM*06] Mihalef V., Unlusu B., Metaxas D., Sussman M., Hussaini M. Y.: Physics based boiling simulation. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation (2006), pp. 317–324. 2.
- [OS88] Osher S., Sethian J. A.: Fronts propagating with curvature-dependent speed: Algorithms based on hamilton-jacobi formulations. J. Comp. Phys. 79 (1988), 12–49. 2.
- [Pop03] Popinet S.: Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries. J. Comp. Phys. 228 (2003), 572–600. 2, 3, 4.
- [Pop09] Popinet S.: An accurate adaptive solver for surface-tension-driven interfacial flows. J. Comp. Phys. 228 (2009), 5838–5866. 7.
- [PTB*03] Premoze S., Tasdizen T., Bigler J., Lefohn A. E., Whitaker R. T.: Particle-based simulation of fluids. Comput. Graph. Forum 22, 3 (2003), 401–410. 2.
- [RK98] Rider W. J., Kothe D. B.: Reconstructing volume tracking. J. Comput. Phys. 141 (1998), 112–152. 2.
- [RS00] Russo G., Smereka P.: A remark on computing distance functions. J. Comput. Phys. 163 (September 2000), 51–67. 2.
- [SG11]
Solenthaler B.,
Gross M.: Two-scale particle simulation.
ACM Trans. Graph.
30 (August 2011), 81:1–81:8. 2.
10.1145/2010324.1964976 Google Scholar
- [SKK07] Song O.-Y., Kim D., Ko H.-S.: Derivative particles for simulating detailed movements of fluids. IEEE Transactions on Visualization and Computer Graphics 13, 4 (2007), 711–719. 2, 3.
- [SO09] Sussman M., Ohta M.: A stable and efficient method for treating surface tension in incompressible two-phase flow. SIAM J. Sci. Comput. 31, 4 (June 2009), 2447–2471. 8.
- [SP00] Sussman M., Puckett E. G.: A coupled level set and volume-of-fluid method for computing 3D and axisymmetric incompressible two-phase flows. J. Comp. Phys. 162 (2000), 301–337. 2.
- [SP09] Solenthaler B., Pajarola R.: Predictive-corrective incompressible SPH. ACM Trans. Graph. 28, 3 (2009), 1–6. 2.
- [SSO94] Sussman M., Smereka P., Osher S.: A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. 114, 1 (1994), 146–159. 2.
- [Sta99] Stam J.: Stable fluids. Computer Graphics (Proc. ACM SIGGRAPH '99) 33, Annual Conference Series (1999), 121–128. 2.
- [Sus11] Sussman M.: A method for overcoming the surface tension time step constraint in multiphase flows ii. Int. J. Numer. Meth. Fluids 68 (2011), 1343–1361. 8.
- [Tau95]
Taubin G.: A signal processing approach to fair surface design. In
Proceedings of the 22nd annual conference on Computer graphics and interactive techniques (1995), SIGGRAPH '95, ACM, pp.
351–358. 7, 8.
10.1145/218380.218473 Google Scholar
- [Tow09] Towers J. D.: Finite difference methods for approximating Heaviside functions. J. Comp. Phys. 228 (2009), 3478–3489. 5.
- [TWGT10] Thürey N., Wojtan C., Gross M., Turk G.: A multiscale approach to mesh-based surface tension flows. ACM Trans. Graph. 29, 4 (July 2010), 48:1–48:10. 3.
- [WMFB11] Wojtan C., Müller-Fischer M., Brochu T.: Liquid simulation with mesh-based surface tracking. In ACM SIGGRAPH 2011 Courses (2011), SIGGRAPH '11, ACM, pp. 8:1–8:84. 7.
- [WTGT09] Wojtan C., Thürey N., Gross M., Turk G.: Deforming meshes that split and merge. ACM Trans. Graph. 28, 3 (2009), 1–10. 3.
- [WTGT10] Wojtan C., Thürey N., Gross M., Turk G.: Physics-inspired topology changes for thin fluid features. ACM Trans. Graph. 29, 4 (2010), 1–8. 3.
- [YT10] Yu J., Turk G.: Reconstructing surfaces of particle-based fluids using anisotropic kernels. In Proceedings of the 2010 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (2010), Eurographics Association, pp. 217–225. 2.
- [YWTY12] Yu J., Wojtan C., Turk G., Yap C.: Explicit mesh surfaces for particle based fluids. EUROGRAPHICS 2012 30 (2012), 41–48. 2.
- [ZB05] Zhu Y., Bridson R.: Animating sand as a fluid. ACM Trans. Graph. 24, 3 (2005), 965–972. 2, 3.