research-article

Open access

Surface-only liquids

Authors:

Christopher Batty,

Eitan GrinspunAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 35, Issue 4

Article No.: 78, Pages 1 - 12

https://doi.org/10.1145/2897824.2925899

Published: 11 July 2016 Publication History

Abstract

We propose a novel surface-only technique for simulating incompressible, inviscid and uniform-density liquids with surface tension in three dimensions. The liquid surface is captured by a triangle mesh on which a Lagrangian velocity field is stored. Because advection of the velocity field may violate the incompressibility condition, we devise an orthogonal projection technique to remove the divergence while requiring the evaluation of only two boundary integrals. The forces of surface tension, gravity, and solid contact are all treated by a boundary element solve, allowing us to perform detailed simulations of a wide range of liquid phenomena, including waterbells, droplet and jet collisions, fluid chains, and crown splashes.

Supplementary Material

ZIP File (a78-da-supp.zip)

Supplemental files.

Download
106.13 MB

MP4 File (a78.mp4)

Download
311.02 MB

References

[1]

Abraham, R., Marsden, J. E., and Ratiu, T. 1988. Manifolds, Tensor Analysis, and Applications. Springer.

Digital Library

[2]

Angelidis, A., and Neyret, F. 2005. Simulation of smoke based on vortex filament primitives. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation, 87--96.

Digital Library

[3]

Atkinson, K. E. 1997. The numerical solution of boundary integral equations. In The State of the Art in Numerical Analysis, pp. 223--259.

[4]

Batty, C., Bertails, F., and Bridson, R. 2007. A fast variational framework for accurate solid-fluid coupling. ACM Trans. Graph. 26, 3, 100.

Digital Library

[5]

Batty, C., Xenos, S., and Houston, B. 2010. Tetrahedral embedded boundary methods for accurate and flexible adaptive fluids. In Computer Graphics Forum, vol. 29, Wiley Online Library, 695--704.

[6]

Batty, C., Uribe, A., Audoly, B., and Grinspun, E. 2012. Discrete viscous sheets. ACM Trans. Graph. 31, 4, 113.

Digital Library

[7]

Bojsen-Hansen, M., and Wojtan, C. 2013. Liquid surface tracking with error compensation. ACM Trans. Graph. 32, 4, 68.

Digital Library

[8]

Brochu, T., Batty, C., and Bridson, R. 2010. Matching fluid simulation elements to surface geometry and topology. ACM Trans. Graph. 29, 4, 47.

Digital Library

[9]

Brochu, T., Keeler, T., and Bridson, R. 2012. Linear-time smoke animation with vortex sheet meshes. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation, 87--95.

Digital Library

[10]

Brochu, T. 2006. Fluid animation with explicit surface meshes and boundary-only dynamics. Master's thesis, University of British Columbia.

[11]

Bush, J. W., and Hasha, A. E. 2004. On the collision of laminar jets: fluid chains and fishbones. Journal of fluid mechanics 511, 285--310.

[12]

Chen, C., Golberg, M., and Schaback, R. 2003. Recent developments in the dual reciprocity method using compactly supported radial basis functions. Transformation of Domain Effects to the Boundary (YF Rashed and CA Brebbia, eds), WITPress, Southampton, Boston, 138--225.

[13]

Chentanez, N., Feldman, B. E., Labelle, F., O'Brien, J. F., and Shewchuk, J. R. 2007. Liquid simulation on lattice-based tetrahedral meshes. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer animation, 219--228.

Digital Library

[14]

Clausen, P., Wicke, M., Shewchuk, J. R., and O'brien, J. F. 2013. Simulating liquids and solid-liquid interactions with Lagrangian meshes. ACM Trans. Graph. 32, 2, 17.

Digital Library

[15]

Cohen-Steiner, D., and Morvan, J.-M. 2003. Restricted Delaunay triangulations and normal cycle. In Proceedings of the nineteenth annual Symposium on Computational Geometry, ACM, 312--321.

Digital Library

[16]

Da, F., Batty, C., and Grinspun, E. 2014. Multimaterial mesh-based surface tracking. ACM Trans. Graph. 33, 4, 112:1--112:11.

Digital Library

[17]

Da, F., Batty, C., Wojtan, C., and Grinspun, E. 2015. Double bubbles sans toil and trouble: discrete circulation-preserving vortex sheets for soap films and foams. ACM Trans. Graph. 34, 4, 149.

Digital Library

[18]

Davidson, M. R. 2000. Boundary integral prediction of the spreading of an inviscid drop impacting on a solid surface. Chemical Engineering Science 55, 6, 1159--1170.

[19]

Duffy, M. G. 1982. Quadrature over a pyramid or cube of integrands with a singularity at a vertex. SIAM journal on Numerical Analysis 19, 6, 1260--1262.

[20]

Enright, D., Fedkiw, R., Ferziger, J., and Mitchell, I. 2002. A hybrid particle level set method for improved interface capturing. Journal of Computational Physics 183, 1, 83--116.

Digital Library

[21]

Fedkiw, R. P., Aslam, T., Merriman, B., and Osher, S. 1999. A non-oscillatory Eulerian approach to interfaces in multi-material flows (the ghost fluid method). Journal of Computational Physics 152, 2, 457--492.

Digital Library

[22]

Florez, W., and Power, H. 2001. Comparison between continuous and discontinuous boundary elements in the multidomain dual reciprocity method for the solution of the two-dimensional Navier--Stokes equations. Engineering analysis with boundary elements 25, 1, 57--69.

[23]

Foster, N., and Fedkiw, R. 2001. Practical animation of liquids. In Proceedings of SIGGRAPH 01, Annual Conference Series, 23--30.

Digital Library

[24]

Foster, N., and Metaxas, D. 1996. Realistic animation of liquids. Graphical models and image processing 58, 5, 471--483.

Digital Library

[25]

Greengard, L., and Rokhlin, V. 1987. A fast algorithm for particle simulations. Journal of Computational Physics 73, 2, 325--348.

Digital Library

[26]

Hahn, D., and Wojtan, C. 2015. High-resolution brittle fracture simulation with boundary elements. ACM Trans. Graph. 34, 4, 151.

Digital Library

[27]

Hartmann, F. 2012. Introduction to boundary elements: theory and applications. Springer Science & Business Media.

[28]

Hong, J.-M., and Kim, C.-H. 2005. Discontinuous fluids. In ACM Trans. Graph., vol. 24, ACM, 915--920.

Digital Library

[29]

Ihmsen, M., Cornelis, J., Solenthaler, B., Horvath, C., and Teschner, M. 2014. Implicit incompressible SPH. Visualization and Computer Graphics, IEEE Transactions on 20, 3, 426--435.

Digital Library

[30]

Ihmsen, M., Orthmann, J., Solenthaler, B., Kolb, A., and Teschner, M. 2014. SPH Fluids in Computer Graphics. Eurographics 2014 - State of the Art Reports.

[31]

James, D. L., and Pai, D. K. 1999. ArtDefo: accurate real time deformable objects. In Proceedings of SIGGRAPH 99, Annual Conference Series, 65--72.

Digital Library

[32]

Keeler, T., and Bridson, R. 2014. Ocean waves animation using boundary integral equations and explicit mesh tracking. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation, 11--19.

Digital Library

[33]

Ladyzhenskaya, O. A. 1963. The mathematical theory of viscous incompressible flow. Gordon and Breach New York.

[34]

Mantič, V. 1993. A new formula for the C-matrix in the Somigliana identity. Journal of Elasticity 33, 3, 191--201.

[35]

Misztal, M. K., Bridson, R., Erleben, K., Bærentzen, J. A., and Anton, F. 2010. Optimization-based fluid simulation on unstructured meshes. In VRIPHYS, 11--20.

[36]

Narain, R., Samii, A., and O'Brien, J. F. 2012. Adaptive anisotropic remeshing for cloth simulation. ACM Trans. Graph. 31, 6, 152.

Digital Library

[37]

Osher, S., and Sethian, J. A. 1988. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics 79, 1, 12--49.

Digital Library

[38]

Pan, K.-L., Chou, P.-C., and Tseng, Y.-J. 2009. Binary droplet collision at high Weber number. Phys. Rev. E 80 (Sep), 036301.

[39]

Park, S. I., and Kim, M. J. 2005. Vortex fluid for gaseous phenomena. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation, 261--270.

Digital Library

[40]

Pfaff, T., Thuerey, N., and Gross, M. 2012. Lagrangian vortex sheets for animating fluids. ACM Trans. Graph. 31, 4, 112.

Digital Library

[41]

Phillips, H. B. 1933. Vector analysis. Wiley New York.

[42]

Power, H., and Partridge, P. W. 1994. The use of Stokes' fundamental solution for the boundary only element formulation of the three-dimensional Navier-Stokes equations for moderate Reynolds numbers. International journal for numerical methods in engineering 37, 11, 1825--1840.

[43]

Quan, S., Lou, J., and Schmidt, D. P. 2009. Modeling merging and breakup in the moving mesh interface tracking method for multiphase flow simulations. Journal of Computational Physics 228, 7, 2660--2675.

Digital Library

[44]

Sauter, S. A., and Schwab, C. 2011. Boundary element methods. Springer.

[45]

Schroeder, C., Zheng, W., and Fedkiw, R. 2012. Semi-implicit surface tension formulation with a Lagrangian surface mesh on an Eulerian simulation grid. Journal of Computational Physics 231, 4, 2092--2115.

Digital Library

[46]

Selle, A., Rasmussen, N., and Fedkiw, R. 2005. A vortex particle method for smoke, water and explosions. In ACM Trans. Graph., vol. 24, ACM, 910--914.

Digital Library

[47]

Stam, J. 1999. Stable fluids. In Proceedings of SIGGRAPH 99, Annual Conference Series, ACM Press/Addison-Wesley Publishing Co., 121--128.

Digital Library

[48]

Stock, M. J. 2006. A regularized inviscid vortex sheet method for three dimensional flows with density interfaces. PhD thesis, Worcester Polytechnic Institute.

[49]

Thürey, N., Wojtan, C., Gross, M., and Turk, G. 2010. A multiscale approach to mesh-based surface tension flows. In ACM Trans. Graph., vol. 29, ACM, 48.

Digital Library

[50]

Wang, H., Mucha, P. J., and Turk, G. 2005. Water drops on surfaces. In ACM Trans. Graph., vol. 24, ACM, 921--929.

Digital Library

[51]

Weissmann, S., and Pinkall, U. 2010. Filament-based smoke with vortex shedding and variational reconnection. ACM Trans. Graph. 29, 4, 115.

Digital Library

[52]

Wojtan, C., Müller-Fischer, M., and Brochu, T. 2011. Liquid simulation with mesh-based surface tracking. In ACM SIGGRAPH 2011 Courses, ACM, 8.

Digital Library

[53]

Xue, M., Xü, H., Liu, Y., and Yue, D. K. 2001. Computations of fully nonlinear three-dimensional wave--wave and wave--body interactions. Part 1. Dynamics of steep three-dimensional waves. Journal of Fluid Mechanics 438, 11--39.

[54]

Zhang, X., and Bridson, R. 2014. A PPPM fast summation method for fluids and beyond. ACM Trans. Graph. 33, 6, 206.

Digital Library

[55]

Zhang, Y., Wang, H., Wang, S., Tong, Y., and Zhou, K. 2012. A deformable surface model for real-time water drop animation. Visualization and Computer Graphics, IEEE Transactions on 18, 8, 1281--1289.

Digital Library

[56]

Zhang, X., Bridson, R., and Greif, C. 2015. Restoring the missing vorticity in advection-projection fluid solvers. ACM Trans. Graph. 34, 4.

Digital Library

[57]

Zhu, B., Quigley, E., Cong, M., Solomon, J., and Fedkiw, R. 2014. Codimensional surface tension flow on simplicial complexes. ACM Trans. Graph. 33, 4, 111.

Digital Library

[58]

Zhu, Y., Bridson, R., and Greif, C. 2015. Simulating rigid body fracture with surface meshes. ACM Trans. Graph. 34, 4, 150.

Digital Library

Cited By

Chen JSchaefer FDesbrun M(2024)Lightning-fast Method of Fundamental SolutionsACM Transactions on Graphics10.1145/365819943:4(1-16)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658199
Ni XWang RWang BChen B(2024)An Induce-on-Boundary Magnetostatic Solver for Grid-Based FerrofluidsACM Transactions on Graphics10.1145/365812443:4(1-14)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658124
Gomes Haetinger GTang JOrtiz RKanyuk PAzevedo V(2024)Controllable Neural Style Transfer for Dynamic MeshesACM SIGGRAPH 2024 Conference Papers10.1145/3641519.3657474(1-11)Online publication date: 13-Jul-2024
https://dl.acm.org/doi/10.1145/3641519.3657474
Show More Cited By

Index Terms

Surface-only liquids
1. Computing methodologies
  1. Computer graphics
    1. Animation
      1. Physical simulation
  2. Modeling and simulation
    1. Simulation types and techniques
      1. Continuous simulation

Recommendations

Surface-only ferrofluids

We devise a novel surface-only approach for simulating the three dimensional free-surface flow of incompressible, inviscid, and linearly magnetizable ferrofluids. A Lagrangian velocity field is stored on a triangle mesh capturing the fluid's surface. ...
High-order surface tension VOF-model for 3D bubble flows with high density ratio

An improved Volume of Fluid (VOF) method is presented which is applicable to high density ratio 3D flows for a large range of bubble Reynolds number (Re). The method is based on the Navier-Stokes equations for incompressible multi-phase flows which are ...
A finite-volume HLLC-based scheme for compressible interfacial flows with surface tension

Shock waves are often used in experiments to create a shear flow across liquid droplets to study secondary atomization. Similar behavior occurs inside of supersonic combustors (scramjets) under startup conditions, but it is challenging to study these ...

Comments

Information & Contributors

Information

Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 35, Issue 4

July 2016

1396 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/2897824

Issue’s Table of Contents

Copyright © 2016 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 11 July 2016

Published in TOG Volume 35, Issue 4

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article

Funding Sources

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

59
Total Citations
View Citations
1,654
Total Downloads

Downloads (Last 12 months)253
Downloads (Last 6 weeks)30

Reflects downloads up to 20 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

Chen JSchaefer FDesbrun M(2024)Lightning-fast Method of Fundamental SolutionsACM Transactions on Graphics10.1145/365819943:4(1-16)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658199
Ni XWang RWang BChen B(2024)An Induce-on-Boundary Magnetostatic Solver for Grid-Based FerrofluidsACM Transactions on Graphics10.1145/365812443:4(1-14)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658124
Gomes Haetinger GTang JOrtiz RKanyuk PAzevedo V(2024)Controllable Neural Style Transfer for Dynamic MeshesACM SIGGRAPH 2024 Conference Papers10.1145/3641519.3657474(1-11)Online publication date: 13-Jul-2024
https://dl.acm.org/doi/10.1145/3641519.3657474
Wang XXu YLiu SRen BKosinka JTelea AWang JSong CChang JLi CZhang JBan X(2024)Physics-based fluid simulation in computer graphics: Survey, research trends, and challengesComputational Visual Media10.1007/s41095-023-0368-y10:5(803-858)Online publication date: 27-Apr-2024
https://doi.org/10.1007/s41095-023-0368-y
Xiong YWang XXu YZhang YChang JZhang JBan X(2024)Dual-mechanism surface tension model for SPH-based simulationThe Visual Computer: International Journal of Computer Graphics10.1007/s00371-024-03474-440:7(4765-4776)Online publication date: 1-Jul-2024
https://dl.acm.org/doi/10.1007/s00371-024-03474-4
Mathaiyan V(2023)FLUID LEAVES: EFFECTS OF FLUID FLOW ON LEAF SHAPES AND FIBONACCI SERIESInternational Journal of Fluid Mechanics Research10.1615/InterJFluidMechRes.202304941550:5(33-50)Online publication date: 2023
https://doi.org/10.1615/InterJFluidMechRes.2023049415
De Lambilly ABenedetti GRizk NHanqi CHuang SQiu JLouapre DGranier De Cassagnac RRohmer D(2023)Heat Simulation on Meshless Crafted-Made ShapesProceedings of the 16th ACM SIGGRAPH Conference on Motion, Interaction and Games10.1145/3623264.3624457(1-7)Online publication date: 15-Nov-2023
https://dl.acm.org/doi/10.1145/3623264.3624457
Bang SSerkh KStein OJacobson A(2023)An Adaptive Fast-Multipole-Accelerated Hybrid Boundary Integral Equation Method for Accurate Diffusion CurvesACM Transactions on Graphics10.1145/361837442:6(1-28)Online publication date: 5-Dec-2023
https://dl.acm.org/doi/10.1145/3618374
Su HLi XXue TJiang CAanjaneya M(2023)A Generalized Constitutive Model for Versatile MPM Simulation and Inverse Learning with Differentiable PhysicsProceedings of the ACM on Computer Graphics and Interactive Techniques10.1145/36069256:3(1-20)Online publication date: 24-Aug-2023
https://dl.acm.org/doi/10.1145/3606925
Gross OSoliman YPadilla MKnöppel FPinkall USchröder P(2023)Motion from Shape ChangeACM Transactions on Graphics10.1145/359241742:4(1-11)Online publication date: 26-Jul-2023
https://dl.acm.org/doi/10.1145/3592417
Show More Cited By

View Options

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Article

Media

Figures

Other

Tables

View Issue’s Table of Contents