research-article

Discrete viscous threads

Authors:

Miklós Bergou,

Eitan GrinspunAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 29, Issue 4

Article No.: 116, Pages 1 - 10

https://doi.org/10.1145/1778765.1778853

Published: 26 July 2010 Publication History

Abstract

We present a continuum-based discrete model for thin threads of viscous fluid by drawing upon the Rayleigh analogy to elastic rods, demonstrating canonical coiling, folding, and breakup in dynamic simulations. Our derivation emphasizes space-time symmetry, which sheds light on the role of time-parallel transport in eliminating---without approximation---all but an O(n) band of entries of the physical system's energy Hessian. The result is a fast, unified, implicit treatment of viscous threads and elastic rods that closely reproduces a variety of fascinating physical phenomena, including hysteretic transitions between coiling regimes, competition between surface tension and gravity, and the first numerical fluid-mechanical sewing machine. The novel implicit treatment also yields an order of magnitude speedup in our elastic rod dynamics.

Supplementary Material

JPG File (tp059-10.jpg)

Download
10.50 KB

Supplemental material. (116.zip)

Download
28.47 MB

MP4 File (tp059-10.mp4)

Download
39.55 MB

References

[1]

Andreassen, E., Gundersen, E., Hinrichsen, E. L., and Langtangen, H. P. 1997. Numerical Methods and Software Tools in Industrial Mathematics. Birkhäueser, Boston, ch. A mathematical model for the melt spinning of polymer fibers, 195--212.

[2]

Bargteil, A. W., Wojtan, C., Hodgins, J. K., and Turk, G. 2007. A Finite Element Method for Animating Large Viscoplastic Flow. ACM TOG 26, 3 (Jul), 16:1--16:8.

Digital Library

[3]

Batty, C., and Bridson, R. 2008. Accurate Viscous Free Surfaces for Buckling, Coiling, and Rotating Liquids. In SCA '08, 219--226.

Digital Library

[4]

Bergou, M., Wardetzky, M., Robinson, S., Audoly, B., and Grinspun, E. 2008. Discrete Elastic Rods. ACM TOG 27, 3 (Aug), 63:1--63:12.

Digital Library

[5]

Bertails, F., Audoly, B., Cani, M.-P., Querleux, B., Leroy, F., and Lévêque, J.-L. 2006. Super-helices for predicting the dynamics of natural hair. ACM TOG 25, 3 (Jul), 1180--1187.

Digital Library

[6]

Bonito, A., Picasso, M., and Laso, M. 2006. Numerical simulation of 3D viscoelastic flows with free surfaces. J. Comput. Phys. 215, 2, 691--716.

Digital Library

[7]

Boyer, F., and Primault, D. 2004. Finite element of slender beams in finite transformations: a geometrically exact approach. Int. J. Numer. Methods Eng. 59, 5, 669--702.

[8]

Bridson, R., and Müller-Fischer, M. 2007. Fluid Simulation. SIGGRAPH 2007 Course Notes.

Digital Library

[9]

Chang, Y., Bao, K., Liu, Y., Zhu, J., and Wu, E. 2009. A particle-based method for viscoelastic fluids animation. VRST '09 (Nov), 111--117.

Digital Library

[10]

Chentanez, N., Alterovitz, R., Ritchie, D., Cho, L., Hauser, K. K., Goldberg, K., Shewchuk, J. R., and O'Brien, J. F. 2009. Interactive Simulation of Surgical Needle Insertion and Steering. ACM TOG 28, 3 (Jul), 88:1--88:10.

Digital Library

[11]

Chiu-Webster, S., and Lister, J. R. 2006. The fall of a viscous thread onto a moving surface: a 'fluid-mechanical sewing machine'. J. Fluid Mech. 569, 89--111.

[12]

Clavet, S., Beaudoin, P., and Poulin, P. 2005. Particle-based Viscoelastic Fluid Simulation. In SCA '05.

Digital Library

[13]

Desbrun, M., and Gascuel, M. 1996. Smoothed particles: A new paradigm for animating highly deformable bodies. Computer Animation and Simulation (Jan), 61--76.

Digital Library

[14]

Dewynne, J. N., Ockendon, J. R., and Wilmott, P. 1992. A systematic derivation of the leading-order equations for extensional flows in slender geometries. J. Fluid Mech. 24, 323--338.

[15]

DiVerdi, S., Krishnaswamy, A., and Hadap, S. 2010. Industrial-Strength Painting with a Bristle Brush Simulation. submitted.

[16]

Eggers, J., and Dupont, T. F. 1994. Drop formation in a one-dimensional approximation of the Navier-Stokes equation. J. Fluid Mech. 262, 205--221.

[17]

Entov, V. M., and Yarin, A. L. 1984. The dynamics of thin liquid jets in air. J. Fluid Mech. 140, 91--111.

[18]

Fedkiw, R., Stam, J., and Jensen, H. W. 2001. Visual Simulation of Smoke. In SIGGRAPH 2001, 15--22.

Digital Library

[19]

Foster, N., and Fedkiw, R. 2001. Practical Animation of Liquids. In SIGGRAPH 2001, 23--30.

Digital Library

[20]

Foster, N., and Metaxas, D. 1997. Modeling the Motion of a Hot, Turbulent Gas. In SIGGRAPH 97, 181--188.

Digital Library

[21]

Gerszewski, D., Bhattacharya, H., and Bargteil, A. W. 2009. A Point-based Method for Animating Elastoplastic Solids. In SCA '09.

Digital Library

[22]

Goktekin, T. G., Bargteil, A. W., and O'Brien, J. F. 2004. A method for animating viscoelastic fluids. ACM TOG 23, 3 (Aug), 463--468.

Digital Library

[23]

Grégoire, M., and Schömer, E. 2007. Interactive simulation of one-dimensional flexible parts. Comput.-Aided Des. 39, 8, 694--707.

Digital Library

[24]

Hauth, M., Etzmuss, O., and Strasser, W. 2003. Analysis of numerical methods for the simulation of deformable models. Vis. Comp. 19, 7--8, 581--600.

Digital Library

[25]

Hong, J.-M., and Kim, C.-H. 2005. Discontinuous fluids. ACM TOG 24, 3 (Jul), 915--920.

Digital Library

[26]

Irving, G. 2007. Methods for the physically based simulation of solids and fluids. PhD thesis, Stanford University.

[27]

Kaldor, J. M., James, D. L., and Marschner, S. 2010. Efficient Yarn-based Cloth with Adaptive Contact Linearization. ACM TOG 29, 4 (Jul).

Digital Library

[28]

Kharevych, L., Yang, W., Tong, Y., Kanso, E., Marsden, J. E., Schröder, P., and Desbrun, M. 2006. Geometric, Variational Integrators for Computer Animation. In SCA '06, 43--51.

Digital Library

[29]

Kim, D., Song, O.-Y., and Ko, H.-S. 2009. Stretching and Wiggling Liquids. ACM TOG 28, 5 (Dec), 120:1--120:7.

Digital Library

[30]

Kirchhoff, G. 1859. Über das Gleichgewicht und die Bewegung eines unendlich dünnen elastischen Stabes. Journal für die reine und angewandte Mathematik 56, 285--313.

[31]

Landau, L. D., and Lifshitz, E. M. 1981. Theory of Elasticity (Course of Theoretical Physics), 2^nd ed. Pergamon Press.

[32]

Langer, J., and Singer, D. 1996. Lagrangian aspects of the Kirchhoff elastic rod. SIAM Review, 605--618.

Digital Library

[33]

Le Merrer, M., Seiwert, J., Quéré, D., and Clanet, C. 2008. Shapes of hanging viscous filaments. EPL 84, 56004.

[34]

Lee, S., Olsen, S., and Gooch, B. 2006. Interactive 3D fluid jet painting. NPAR '06 (Jun), 97--104.

Digital Library

[35]

Losasso, F., Gibou, F., and Fedkiw, R. 2004. Simulating water and smoke with an octree data structure. ACM TOG 23, 3 (Aug), 457--462.

Digital Library

[36]

Miller, G., and Pearce, A. 1989. Globular dynamics: A connected particle system for animating viscous fluids. COMP. GRAPH. (Jan), 305--309.

[37]

Morris, S. W., Dawes, J. H. P., Ribe, N. M., and Lister, J. R. 2008. Meandering instability of a viscous thread. Phys. Rev. E (Statistical, Nonlinear, and Soft Matter Physics) 77, 6, 066218.

[38]

Müller, M., Charypar, D., and Gross, M. 2003. Particle-based fluid simulation for interactive applications. In SCA '03, 154--159.

Digital Library

[39]

Müller, M., Keiser, R., Nealen, A., Pauly, M., Gross, M., and Alexa, M. 2004. Point based animation of elastic, plastic and melting objects. In SCA '04, 141--151.

Digital Library

[40]

Nealen, A., Müller, M., Keiser, R., Boxerman, E., and Carlson, M. 2006. Physically Based Deformable Models in Computer Graphics. CGF 25, 4, 809--836.

[41]

O'Brien, J. F., Bargteil, A. W., and Hodgins, J. K. 2002. Graphical Modeling and Animation of Ductile Fracture. ACM TOG 21, 3 (Jul), 291--294.

Digital Library

[42]

Oishi, C. M., Tomé, M. F., Cuminato, J. A., and McKee, S. 2008. An implicit technique for solving 3D low Reynolds number moving free surface flows. J. Comput. Phys. 227, 16, 7446--7468.

Digital Library

[43]

Pai, D. K. 2002. STRANDS: Interactive Simulation of Thin Solids using Cosserat Models. CGF 21, 3, 347--352.

[44]

Panda, S., Marheineke, N., and Wegener, R. 2008. Systematic derivation of an asymptotic model for the dynamics of curved viscous fibers. Math. Meth. Appl. Sci. 31, 10, 1153--1173.

[45]

Radovitzky, R., and Ortiz, M. 1999. Error estimation and adaptive meshing in strongly nonlinear dynamic problems. Comput. Methods Appl. Mech. Eng 172, 1--4, 203--240.

[46]

Rafiee, A., Manzari, M. T., and Hosseini, M. 2007. An incompressible SPH method for simulation of unsteady viscoelastic free-surface flows. Int. J. Non Linear Mech. 42, 10, 1210--1223.

[47]

Ribe, N. M., Huppert, H. E., Hallworth, M. A., Habibi, M., and Bonn, D. 2006. Multiple coexisting states of liquid rope coiling. J. Fluid Mech. 555, 1, 275--297.

[48]

Ribe, N. M. 2004. Coiling of viscous jets. Proc. Math., Phys. and Eng. Sci., 3223--3239.

[49]

Skorobogatiy, M., and Mahadevan, L. 2000. Folding of viscous sheets and filaments. EPL 52, 5, 532--538.

[50]

Spillmann, J., and Teschner, M. 2007. CORDE: Cosserat Rod Elements for the Dynamic Simulation of One-Dimensional Elastic Objects. In SCA '07, 63--72.

Digital Library

[51]

Spillmann, J., and Teschner, M. 2008. An Adaptive Contact Model for the Robust Simulation of Knots. CGF 27, 2, 497--506.

[52]

Stam, J. 1999. Stable Fluids. In SIGGRAPH 99, 121--128.

Digital Library

[53]

Steele, K., Cline, D., Egbert, P., and Dinerstein, J. 2004. Modeling and rendering viscous liquids. CAVW (Jan), 183--192.

Digital Library

[54]

Stora, D., Agliati, P.-O., Cani, M.-P., Neyret, F., and Gascuel, J.-D. 1999. Animating lava flows. GI '99 (Jan), 203--210.

Digital Library

[55]

Strutt, J. W. 1945. Theory of Sound, vol. 2. Dover Publications.

[56]

Taylor, G. I. 1968. Instability of jets, threads, and sheets of viscous fluid. In Proc. 12th Intl Congr. Appl. Mech., Stanford, Springer, Ed., 382.

[57]

Terzopoulos, D., and Fleischer, K. 1988. Modeling Inelastic Deformation: Viscoelasticity, Plasticity, Fracture. In SIGGRAPH 88, 269--278.

Digital Library

[58]

Terzopoulos, D., Platt, J., and Fleischer, K. 1991. Heating and melting deformable models. J. Visual. Comp. Animat. 2, 2, 68--73.

[59]

Theetten, A., Grisoni, L., Duriez, C., and Merlhiot, X. 2007. Quasi-dynamic splines. In SPM '07, ACM, New York, 409--414.

Digital Library

[60]

Theetten, A., Grisoni, L., Andriot, C., and Barsky, B. 2008. Geometrically exact dynamic splines. Comput.-Aided Des. 40, 1, 35--48.

Digital Library

[61]

Trouton, F. R. S. 1906. On the coefficient of viscous traction and its relation to that of viscosity. Proc. Royal Soc. London, A 77, 426--440.

[62]

Witkin, A., and Baraff, D. 2001. Physically Based Modeling: Principles and Practice. SIGGRAPH 2001 Course Notes.

[63]

Wojtan, C., and Turk, G. 2008. Fast Viscoelastic Behavior with Thin Features. ACM TOG 27, 3 (Aug), 47:1--47:8.

Digital Library

Cited By

Sze WDoedel EKarimfazli IYousefzadeh B(2025)Pattern formation in coiling of falling viscous threads: Revisiting the geometric modelPhysical Review Fluids10.1103/PhysRevFluids.10.02390110:2Online publication date: 5-Feb-2025
https://doi.org/10.1103/PhysRevFluids.10.023901
Jallon ARecho PÉtienne J(2025)Mechanics and Thermodynamics of Contractile Entropic Biopolymer NetworksJournal of Elasticity10.1007/s10659-024-10102-8157:1Online publication date: 10-Jan-2025
https://doi.org/10.1007/s10659-024-10102-8
Tong DChoi AQin LHuang WJoo JJawed M(2024)Sim2Real Neural Controllers for Physics-Based Robotic Deployment of Deformable Linear ObjectsInternational Journal of Robotics Research10.1177/0278364923121455343:6(791-810)Online publication date: 1-May-2024
https://dl.acm.org/doi/10.1177/02783649231214553
Show More Cited By

Index Terms

Discrete viscous threads
1. Computing methodologies
  1. Computer graphics
    1. Animation

Recommendations

CoRdE: Cosserat rod elements for the dynamic simulation of one-dimensional elastic objects
SCA '07: Proceedings of the 2007 ACM SIGGRAPH/Eurographics symposium on Computer animation

Simulating one-dimensional elastic objects such as threads, ropes or hair strands is a difficult problem, especially if material torsion is considered. In this paper, we present CoRdE(french 'rope'), a novel deformation model for the dynamic interactive ...
Discrete viscous threads
SIGGRAPH '10: ACM SIGGRAPH 2010 papers

We present a continuum-based discrete model for thin threads of viscous fluid by drawing upon the Rayleigh analogy to elastic rods, demonstrating canonical coiling, folding, and breakup in dynamic simulations. Our derivation emphasizes space-time ...
Discrete viscous sheets

We present the first reduced-dimensional technique to simulate the dynamics of thin sheets of viscous incompressible liquid in three dimensions. Beginning from a discrete Lagrangian model for elastic thin shells, we apply the Stokes-Rayleigh analogy to ...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 29, Issue 4

July 2010

942 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/1778765

Issue’s Table of Contents

Copyright © 2010 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: 26 July 2010

Published in TOG Volume 29, 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

264
Total Citations
View Citations
2,583
Total Downloads

Downloads (Last 12 months)240
Downloads (Last 6 weeks)29

Reflects downloads up to 27 Feb 2025

Other Metrics

View Author Metrics

Citations

Cited By

Sze WDoedel EKarimfazli IYousefzadeh B(2025)Pattern formation in coiling of falling viscous threads: Revisiting the geometric modelPhysical Review Fluids10.1103/PhysRevFluids.10.02390110:2Online publication date: 5-Feb-2025
https://doi.org/10.1103/PhysRevFluids.10.023901
Jallon ARecho PÉtienne J(2025)Mechanics and Thermodynamics of Contractile Entropic Biopolymer NetworksJournal of Elasticity10.1007/s10659-024-10102-8157:1Online publication date: 10-Jan-2025
https://doi.org/10.1007/s10659-024-10102-8
Tong DChoi AQin LHuang WJoo JJawed M(2024)Sim2Real Neural Controllers for Physics-Based Robotic Deployment of Deformable Linear ObjectsInternational Journal of Robotics Research10.1177/0278364923121455343:6(791-810)Online publication date: 1-May-2024
https://dl.acm.org/doi/10.1177/02783649231214553
Dandy LVidulis MRen YPauly M(2024)TensCERs: Tension-Constrained Elastic RodsACM Transactions on Graphics10.1145/368796743:6(1-13)Online publication date: 19-Dec-2024
https://dl.acm.org/doi/10.1145/3687967
Darke AOlander IKim TBurbano AWest R(2024)More Than Killmonger Locs: A Style Guide for Black Hair (in Computer Graphics)ACM SIGGRAPH 2024 Courses10.1145/3664475.3664535(1-251)Online publication date: 27-Jul-2024
https://dl.acm.org/doi/10.1145/3664475.3664535
Zhou ATan KYan ZDeng Q(2024)Modeling Magneto-Active Soft Robots in Vessels Based on Discrete Differential Geometry of Framed CurvesJournal of Applied Mechanics10.1115/1.406720592:2Online publication date: 18-Dec-2024
https://doi.org/10.1115/1.4067205
Huang WXu PLiu Z(2024)Dynamic modeling of a sliding ring on an elastic rod with incremental potential formulationJournal of Applied Mechanics10.1115/1.4065625(1-13)Online publication date: 29-May-2024
https://doi.org/10.1115/1.4065625
Fang YLi MCao YLi XWolper JYang YJiang C(2024)Augmented Incremental Potential Contact for Sticky InteractionsIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2023.329565630:8(5596-5608)Online publication date: 1-Aug-2024
https://dl.acm.org/doi/10.1109/TVCG.2023.3295656
Choi AJing RSabelhaus AJawed M(2024)DisMech: A Discrete Differential Geometry-Based Physical Simulator for Soft Robots and StructuresIEEE Robotics and Automation Letters10.1109/LRA.2024.33652929:4(3483-3490)Online publication date: Apr-2024
https://doi.org/10.1109/LRA.2024.3365292
Law WToro Wyetzner SZhen RFollmer S(2024)A Multi-Stable Curved Line Shape Display2024 IEEE International Conference on Robotics and Automation (ICRA)10.1109/ICRA57147.2024.10610902(9696-9703)Online publication date: 13-May-2024
https://doi.org/10.1109/ICRA57147.2024.10610902
Show More Cited By

View Options

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

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Figures

Tables

Media

View Issue’s Table of Contents