“A multi-scale model for simulating liquid-fabric interactions” by Fei, Batty, Grinspun and Zheng

  • ©Yun (Raymond) Fei, Christopher Batty, Eitan Grinspun, and Changxi Zheng



Entry Number: 51

Session Title:

    Cloth Encounters of the Shirt Kind


    A multi-scale model for simulating liquid-fabric interactions




    We propose a method for simulating the complex dynamics of partially and fully saturated woven and knit fabrics interacting with liquid, including the effects of buoyancy, nonlinear drag, pore (capillary) pressure, dripping, and convection-diffusion. Our model evolves the velocity fields of both the liquid and solid relying on mixture theory, as well as tracking a scalar saturation variable that affects the pore pressure forces in the fluid. We consider the porous microstructure implied by the fibers composing individual threads, and use it to derive homogenized drag and pore pressure models that faithfully reflect the anisotropy of fabrics. In addition to the bulk liquid and fabric motion, we derive a quasi-static flow model that accounts for liquid spreading within the fabric itself. Our implementation significantly extends standard numerical cloth and fluid models to support the diverse behaviors of wet fabric, and includes a numerical method tailored to cope with the challenging nonlinearities of the problem. We explore a range of fabric-water interactions to validate our model, including challenging animation scenarios involving splashing, wringing, and collisions with obstacles, along with qualitative comparisons against simple physical experiments.


    1. Keita Abe, Kenichi Soga, and Samila Bandara. 2013. Material point method for coupled hydromechanical problems. Journal of Geotechnical and Geoenvironmental Engineering 140, 3 (2013), 04013033.Google ScholarCross Ref
    2. KJ Ahn, JC Seferis, and JC Berg. 1991. Simultaneous measurements of permeability and capillary pressure of thermosetting matrices in woven fabric reinforcements. Polymer Composites 12, 3 (1991), 146–152.Google ScholarCross Ref
    3. Ömer Akgiray and Ahmet M Saatçi. 2001. A new look at filter backwash hydraulics. Water Science and Technology: Water Supply 1, 2 (2001), 65–72.Google ScholarCross Ref
    4. Nadir Akinci, Jens Cornelis, Gizem Akinci, and Matthias Teschner. 2013. Coupling elastic solids with smoothed particle hydrodynamics fluids. Computer Animation and Virtual Worlds 24, 3–4 (2013), 195–203.Google ScholarCross Ref
    5. SC Amico and C Lekakou. 2002. Axial impregnation of a fiber bundle. Part 2: theoretical analysis. Polymer composites 23, 2 (2002), 264–273.Google ScholarCross Ref
    6. T B Anderson and Roy Jackson. 1967. Fluid mechanical description of fluidized beds. Equations of motion. Industrial & Engineering Chemistry Fundamentals 6, 4 (1967), 527–539.Google ScholarCross Ref
    7. Omri Azencot, Orestis Vantzos, Max Wardetzky, Martin Rumpf, and Mirela Ben-Chen. 2015. Functional thin films on surfaces. In Proceedings of the 14th ACM SIGGRAPH/Eurographics Symposium on Computer Animation. ACM, 137–146. Google ScholarDigital Library
    8. Vinicius C Azevedo, Christopher Batty, and Manuel M Oliveira. 2016. Preserving geometry and topology for fluid flows with thin obstacles and narrow gaps. ACM Transactions on Graphics (TOG) 35, 4 (2016), 97. Google ScholarDigital Library
    9. P Bagchi and S Balachandar. 2002. Effect of free rotation on the motion of a solid sphere in linear shear flow at moderate Re. Physics of Fluids 14, 8 (2002), 2719–2737.Google ScholarCross Ref
    10. Samila Bandara and Kenichi Soga. 2015. Coupling of soil deformation and pore fluid flow using material point method. Computers and geotechnics 63 (2015), 199–214.Google Scholar
    11. Jacob Bear. 2013. Dynamics of fluids in porous media. Courier Corporation.Google Scholar
    12. A Bedford and D S Drumheller. 1983. Theories of immiscible and structured mixtures. International Journal of Engineering Science 21, 8 (1983), 863–960.Google ScholarCross Ref
    13. Miklós Bergou, Basile Audoly, Etienne Vouga, Max Wardetzky, and Eitan Grinspun. 2010. Discrete viscous threads. ACM Transactions on Graphics (TOG) 29, 4 (2010), 116. Google ScholarDigital Library
    14. José Bico, Étienne Reyssat, and Benoît Roman. 2018. Elastocapillarity: When Surface Tension Deforms Elastic Solids. Annual Review of Fluid Mechanics 50, 1 (2018), 629–659.Google ScholarCross Ref
    15. Maurice A Biot. 1941. General theory of three-dimensional consolidation. Journal of applied physics 12, 2 (1941), 155–164.Google ScholarCross Ref
    16. Javier Bonet and Richard D Wood. 1997. Nonlinear continuum mechanics for finite element analysis. Cambridge university press.Google Scholar
    17. Ronaldo I Borja. 2006. On the mechanical energy and effective stress in saturated and unsaturated porous continua. International Journal of Solids and Structures 43, 6 (2006), 1764–1786.Google ScholarCross Ref
    18. Mario Botsch, Leif Kobbelt, Mark Pauly, Pierre Alliez, and Bruno Lévy. 2010. Polygon mesh processing. CRC press.Google Scholar
    19. Robert Bridson. 2015. Fluid simulation for computer graphics. CRC Press.Google ScholarDigital Library
    20. Royal Harvard Brooks and Arthur Thomas Corey. 1964. Hydraulic properties of porous media. Hydrology papers (Colorado State University) 3 (1964).Google Scholar
    21. Richard L Burden and J Douglas Faires. 1985. 2.2 Fixed-Point Iteration. Numerical Analysis (3rd ed.). PWS Publishers. ISBN 0-87150-857-5 (1985).Google Scholar
    22. Philip Crosbie Carman. 1937. Fluid flow through granular beds. Transactions-Institution of Chemical Engineeres 15 (1937), 150–166.Google Scholar
    23. Yujun Chen, Nadia Magnenat Thalmann, and Brian Foster Allen. 2012. Physical simulation of wet clothing for virtual humans. The Visual Computer 28, 6–8 (2012), 765–774. Google ScholarDigital Library
    24. Nelson S.-H. Chu and Chiew-Lan Tai. 2005. MoXi: Real-time Ink Dispersion in Absorbent Paper. ACM Transactions on Graphics (TOG) 24, 3 (July 2005), 504–511. Google ScholarDigital Library
    25. S Chwastiak. 1973. A wicking method for measuring wetting properties of carbon yarns. Journal of Colloid and Interface Science 42, 2 (1973), 298–309.Google ScholarCross Ref
    26. Gabriel Cirio, Jorge Lopez-Moreno, David Miraut, and Miguel A Otaduy. 2014. Yarn-level simulation of woven cloth. ACM Transactions on Graphics (TOG) 33, 6 (2014), 207. Google ScholarDigital Library
    27. Cassidy J. Curtis, Sean E. Anderson, Joshua E. Seims, Kurt W. Fleischer, and David H. Salesin. 1997. Computer-generated Watercolor. In Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH ’97). ACM Press/Addison-Wesley Publishing Co., New York, NY, USA, 421–430. Google ScholarDigital Library
    28. Trong Dang-Vu and Jan Hupka. 2005. Characterization of porous materials by capillary rise method. Physicochemical problems of mineral processing 39 (2005), 47–65.Google Scholar
    29. Henry Philibert Gaspard Darcy. 1856. Dètermination des lois d’ècoulement de l’eau à travers le sable.Google Scholar
    30. Brojeswari Das, A Das, VK Kothari, R Fanguiero, and M Araujo. 2007. Moisture transmission through textiles. Part II: evaluation methods and mathematical modeling. Autex Res J 7, 3 (2007), 194–216.Google Scholar
    31. Brojeswari Das, A Das, VK Kothari, R Fanguiero, and M De Araújo. 2008. Effect of fibre diameter and cross-sectional shape on moisture transmission through fabrics. Fibers and Polymers 9, 2 (2008), 225–231.Google ScholarCross Ref
    32. Gilles Daviet and Florence Bertails-Descoubes. 2017. Simulation of Drucker-Prager granular flows inside Newtonian fluids. (Feb. 2017). working paper or preprint.Google Scholar
    33. Reint De Boer. 2012. Theory of porous media: highlights in historical development and current state. Springer Science & Business Media.Google ScholarCross Ref
    34. M de Saint-Venant. 1856. Mémoire sur la torsion des prismes: avec des considérations sur leur flexion ainsi que sur l’équilibre intérieur des solides élastiques en général: et des formules pratiques pour le calcul de leur résistance à divers efforts s’ exerçant simultanément. Imprimerie nationale.Google Scholar
    35. Sabri Ergun. 1952. Fluid flow through packed columns. Chem. Eng. Prog. 48 (1952), 89–94.Google Scholar
    36. Yun (Raymond) Fei, Henrique Teles Maia, Christopher Batty, Changxi Zheng, and Eitan Grinspun. 2017. A Multi-scale Model for Simulating Liquid-hair Interactions. ACM Transactions on Graphics (TOG) 36, 4, Article 56 (July 2017), 17 pages. Google ScholarDigital Library
    37. Adolf Fick. 1855. Ueber diffusion. Annalen der Physik 170, 1 (1855), 59–86.Google ScholarCross Ref
    38. Paul Fillunger. 1913. Der auftrieb in talsperren. Osterr. Wochenschrift fur den offentl. Baudienst 19, 32 (1913), 532–555.Google Scholar
    39. PH Forchheimer. 1901. Wasserbewegung durch boden. Zeitz. Ver. Duetch Ing. 45 (1901), 1782–1788.Google Scholar
    40. Eitan Grinspun, Anil N. Hirani, Mathieu Desbrun, and Peter Schröder. 2003. Discrete Shells. In Proceedings of the 2003 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA ’03). Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, 62–67. Google ScholarDigital Library
    41. Eran Guendelman, Andrew Selle, Frank Losasso, and Ronald Fedkiw. 2005. Coupling water and smoke to thin deformable and rigid shells. ACM Transactions on Graphics (TOG) 24, 3 (2005), 973–981. Google ScholarDigital Library
    42. Henry Selby Hele-Shaw. 1898. The flow of water. Nature 58, 1489 (1898), 33–36.Google Scholar
    43. Markus Huber, Bernhard Eberhardt, and Daniel Weiskopf. 2015. Boundary handling at cloth-fluid contact. Computer Graphics Forum 34, 1 (2015), 14–25. Google ScholarDigital Library
    44. Markus Huber, Simon Pabst, and Wolfgang Straßer. 2011. Wet cloth simulation. In ACM SIGGRAPH 2011 Posters. ACM, 10. Google ScholarDigital Library
    45. Markus Ihmsen, Jens Cornelis, Barbara Solenthaler, Christopher Horvath, and Matthias Teschner. 2014. Implicit incompressible SPH. IEEE Transactions on Visualization and Computer Graphics 20, 3 (2014), 426–435. Google ScholarDigital Library
    46. Chenfanfu Jiang, Theodore Gast, and Joseph Teran. 2017. Anisotropic elastoplasticity for cloth, knit and hair frictional contact. ACM Transactions on Graphics (TOG) 36, 4 (2017), 152. Google ScholarDigital Library
    47. 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), 51. Google ScholarDigital Library
    48. Jonathan M. Kaldor, Doug L. James, and Steve Marschner. 2008. Simulating Knitted Cloth at the Yarn Level. ACM Transactions on Graphics (TOG) 27, 3, Article 65 (Aug. 2008), 9 pages. Google ScholarDigital Library
    49. Jonathan M. Kaldor, Doug L. James, and Steve Marschner. 2010. Efficient Yarn-based Cloth with Adaptive Contact Linearization. ACM Transactions on Graphics (TOG) 29, 4, Article 105 (July 2010), 10 pages. Google ScholarDigital Library
    50. HS Kim. 2003. In-plane liquid distribution in nonwoven fabrics: Part 2–simulation. Int. Nonwoven J. 12 (2003), 29–33.Google Scholar
    51. Erik Kissa. 1996. Wetting and wicking. Textile Research Journal 66, 10 (1996), 660–668.Google ScholarCross Ref
    52. Mark Landeryou, Ian Eames, and A Cottenden. 2005. Infiltration into inclined fibrous sheets. Journal of Fluid Mechanics 529 (2005), 173–193.Google ScholarCross Ref
    53. C Lekakou and MG Bader. 1998. Mathematical modelling of macro-and micro-infiltration in resin transfer moulding (RTM). Composites Part A: Applied Science and Manufacturing 29, 1–2 (1998), 29–37.Google ScholarCross Ref
    54. Toon Lenaerts, Bart Adams, and Philip Dutré. 2008. Porous flow in particle-based fluid simulations. ACM Transactions on Graphics (TOG) 27, 3 (2008), 49. Google ScholarDigital Library
    55. Wei-Chin Lin. 2014. Coupling Hair with Smoothed Particle Hydrodynamics Fluids. In Workshop on Virtual Reality Interaction and Physical Simulation, Jan Bender, Christian Duriez, Fabrice Jaillet, and Gabriel Zachmann (Eds.). The Eurographics Association.Google Scholar
    56. Wei-Chin Lin. 2015. Boundary handling and porous flow for fluid-hair interactions. Computers & Graphics 52 (2015), 33–42. Google ScholarDigital Library
    57. Lin Lou, Feng Ji, and Yiping Qiu. 2015. Simulating adhesion of wet fabrics to water: surface tension-based theoretical model and experimental verification. Textile Research Journal 85, 19 (2015), 1987–1998.Google ScholarCross Ref
    58. Lin Lou, Yiping Qiu, Feng Ji, and Xiaohang Zhu. 2018. The influence of surface hydrophilicity on the adhesion properties of wet fabrics or films to water. Textile Research Journal 88, 1 (2018), 108–117.Google ScholarCross Ref
    59. Lin Lou, Jianfei Xie, Feng Ji, Yiping Qiu, Xiaohang Zhu, and Jing Xu. 2017. Simulating adhesion of wet fabrics to water: Gravity of liquid bridge-based theoretical model and experimental verification. Textile Research Journal 87, 7 (2017), 769–779.Google ScholarCross Ref
    60. R Lucas. 1918. Rate of capillary ascension of liquids. Kolloid Z 23, 15 (1918), 15–22.Google ScholarCross Ref
    61. Hernán A Makse, David L Johnson, and Lawrence M Schwartz. 2000. Packing of compressible granular materials. Physical review letters 84, 18 (2000), 4160.Google Scholar
    62. Reza Masoodi and Krishna M Pillai. 2012a. A general formula for capillary suction-pressure in porous media. Journal of Porous Media 15, 8 (2012).Google ScholarCross Ref
    63. Reza Masoodi and Krishna M Pillai. 2012b. Wicking in porous materials: traditional and modern modeling approaches. CRC Press.Google Scholar
    64. Reza Masoodi, Krishna M Pillai, and Padma Prabodh Varanasi. 2008. Role of hydraulic and capillary radii in improving the effectiveness of capillary model in wicking. In ASME Summer Conference, Jacksonville, FL, USA.Google ScholarCross Ref
    65. Joe J Monaghan. 1994. Simulating free surface flows with SPH. Journal of computational physics 110, 2 (1994), 399–406. Google ScholarDigital Library
    66. Matthias Müller, David Charypar, and Markus Gross. 2003. Particle-based fluid simulation for interactive applications. In Proceedings of the 2003 ACM SIGGRAPH/Eurographics symposium on Computer animation. Eurographics Association, 154–159. Google ScholarDigital Library
    67. Michael B Nielsen and Ole Østerby. 2013. A two-continua approach to Eulerian simulation of water spray. ACM Transactions on Graphics (TOG) 32, 4 (2013), 67. Google ScholarDigital Library
    68. P Nithiarasu, KN Seetharamu, and T Sundararajan. 1997. Natural convective heat transfer in a fluid saturated variable porosity medium. International Journal of Heat and Mass Transfer 40, 16 (1997), 3955–3967.Google ScholarCross Ref
    69. Hilary Ockendon and John R Ockendon. 1995. Viscous flow. Vol. 13. Cambridge University Press.Google Scholar
    70. Alexander Oron, Stephen H Davis, and S George Bankoff. 1997. Long-scale evolution of thin liquid films. Reviews of modern physics 69, 3 (1997), 931.Google Scholar
    71. Oktar Ozgen, Marcelo Kallmann, Lynnette Es Ramirez, and Carlos Fm Coimbra. 2010. Underwater cloth simulation with fractional derivatives. ACM Transactions on Graphics (TOG) 29, 3 (2010), 23. Google ScholarDigital Library
    72. Claudio Paniconi, Alvaro A Aldama, and Eric F Wood. 1991. Numerical evaluation of iterative and noniterative methods for the solution of the nonlinear Richards equation. Water Resources Research 27, 6 (1991), 1147–1163.Google ScholarCross Ref
    73. Saket Patkar and Parag Chaudhuri. 2013. Wetting of porous solids. IEEE transactions on visualization and computer graphics 19, 9 (2013), 1592–1604. Google ScholarDigital Library
    74. Amalendu Patnaik, RS Rengasamy, VK Kothari, and A Ghosh. 2006. Wetting and wicking in fibrous materials. Textile Progress 38, 1 (2006), 1–105.Google ScholarCross Ref
    75. Krishna M Pillai and Suresh G Advani. 1996. Wicking across a fiber-bank. Journal of colloid and interface science 183, 1 (1996), 100–110.Google ScholarCross Ref
    76. E Bruce Pitman and Long Le. 2005. A two-fluid model for avalanche and debris flows. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 363, 1832 (2005), 1573–1601.Google Scholar
    77. Kumbakonam Ramamani Rajagopal and Lu Tao. 1995. Mechanics of mixtures. World Scientific.Google Scholar
    78. Bo Ren, Chenfeng Li, Xiao Yan, Ming C Lin, Javier Bonet, and Shi-Min Hu. 2014. Multiple-fluid SPH simulation using a mixture model. ACM Transactions on Graphics (TOG) 33, 5 (2014), 171. Google ScholarDigital Library
    79. Lorenzo Adolph Richards. 1931. Capillary conduction of liquids through porous mediums. Physics 1, 5 (1931), 318–333.Google ScholarCross Ref
    80. 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 Transactions on Graphics (TOG) 27, 3, Article 46 (Aug. 2008), 9 pages. Google ScholarDigital Library
    81. Witawat Rungjiratananon, Zoltan Szego, Yoshihiro Kanamori, and Tomoyuki Nishita. 2008. Real-time Animation of Sand-Water Interaction. Computer Graphics Forum 27, 7 (2008), 1887–1893.Google ScholarCross Ref
    82. Luc Scholtès, P-Y Hicher, François Nicot, Bruno Chareyre, and Félix Darve. 2009. On the capillary stress tensor in wet granular materials. International journal for numerical and analytical methods in geomechanics 33, 10 (2009), 1289–1313.Google ScholarCross Ref
    83. Aviv Segall, Orestis Vantzos, and Mirela Ben-Chen. 2016. Hele-shaw Flow Simulation with Interactive Control Using Complex Barycentric Coordinates. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA ’16). Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, 85–95. Google ScholarDigital Library
    84. MT Senoguz, FD Dungan, AM Sastry, and JT Klamo. 2001. Simulations and experiments on low-pressure permeation of fabrics: Part II—The variable gap model and prediction of permeability. Journal of composite materials 35, 14 (2001), 1285–1322.Google Scholar
    85. Toshihiro Shinohara, Jun-ya Takayama, Shinji Ohyama, and Akira Kobayashi. 2010. Extraction of yarn positional information from a three-dimensional CT image of textile fabric using yarn tracing with a filament model for structure analysis. Textile Research Journal 80, 7 (2010), 623–630.Google ScholarCross Ref
    86. Xiaoyu Song and Ronaldo I Borja. 2014. Mathematical framework for unsaturated flow in the finite deformation range. Internat. J. Numer. Methods Engrg. 97, 9 (2014), 658–682.Google ScholarCross Ref
    87. Alexey Stomakhin, Craig Schroeder, Chenfanfu Jiang, Lawrence Chai, Joseph Teran, and Andrew Selle. 2014. Augmented MPM for phase-change and varied materials. ACM Transactions on Graphics (TOG) 33, 4 (2014), 138. Google ScholarDigital Library
    88. Triantafyllos Stylianopoulos, Andrew Yeckel, Jeffrey J Derby, Xiao-Juan Luo, Mark S Shephard, Edward A Sander, and Victor H Barocas. 2008. Permeability calculations in three-dimensional isotropic and oriented fiber networks. Physics of Fluids 20, 12 (2008), 123601.Google ScholarCross Ref
    89. Deborah Sulsky, Zhen Chen, and Howard L Schreyer. 1994. A particle method for history-dependent materials. Computer methods in applied mechanics and engineering 118, 1–2 (1994), 179–196.Google Scholar
    90. Andre Pradhana Tampubolon, Theodore Gast, Gergely Klár, Chuyuan Fu, Joseph Teran, Chenfanfu Jiang, and Ken Museth. 2017. Multi-species simulation of porous sand and water mixtures. ACM Transactions on Graphics (TOG) 36, 4 (2017), 105. Google ScholarDigital Library
    91. Karl von Terzaghi. 1923. Die berechnung der durchlassigkeitsziffer des tones aus dem verlauf der hydrodynamischen spannungserscheinungen. Sitzungsberichte der Akademie der Wissenschaften in Wien, Mathematisch-Naturwissenschaftliche Klasse, Abteilung IIa 132 (1923), 125–138.Google Scholar
    92. Karl von Terzaghi. 1943. Theoretical soil mechanics. Vol. 18. Wiley Online Library.Google Scholar
    93. Bernhard Thomaszewski, Markus Wacker, Wolfgang Straßer, Etienne Lyard, C. Luible, Pascal Volino, M. Kasap, V. Muggeo, and Nadia Magnenat-Thalmann. 2007. Advanced Topics in Virtual Garment Simulation. In Eurographics 2007 – Tutorials, Karol Myszkowski and Vlastimil Havran (Eds.). The Eurographics Association.Google Scholar
    94. Kiwon Um, Xiangyu Hu, and Nils Thuerey. 2017. Perceptual evaluation of liquid simulation methods. ACM Transactions on Graphics (TOG) 36, 4 (2017), 143. Google ScholarDigital Library
    95. Kiwon Um, Tae-Yong Kim, Youngdon Kwon, and JungHyun Han. 2013. Porous deformable shell simulation with surface water flow and saturation. Computer Animation and Virtual Worlds 24, 3–4 (2013), 247–254.Google ScholarCross Ref
    96. M Th Van Genuchten. 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil science society of America journal 44, 5 (1980), 892–898.Google Scholar
    97. Orestis Vantzos, Omri Azencot, Max Wardeztky, Martin Rumpf, and Mirela Ben-Chen. 2017. Functional Thin Films on Surfaces. IEEE transactions on visualization and computer graphics 23, 3 (2017), 1179–1192. Google ScholarDigital Library
    98. Huamin Wang, Gavin Miller, and Greg Turk. 2007. Solving general shallow wave equations on surfaces. In Proceedings of the 2007 ACM SIGGRAPH/Eurographics symposium on Computer animation. Eurographics Association, 229–238. Google ScholarDigital Library
    99. Yongxin Wang, Stephen Michielsen, and Hoon Joo Lee. 2013. Symmetric and asymmetric capillary bridges between a rough surface and a parallel surface. Langmuir 29, 35 (2013), 11028–11037.Google ScholarCross Ref
    100. Edward W Washburn. 1921. The dynamics of capillary flow. Physical review 17, 3 (1921), 273.Google Scholar
    101. JG Williams, CEM Morris, and BC Ennis. 1974. Liquid flow through aligned fiber beds. Polymer Engineering & Science 14, 6 (1974), 413–419.Google ScholarCross Ref
    102. Reinhard Woltmann. 1792. Beitrdge zur Hydraulischen Architectur. Vol. 2. Dieterich.Google Scholar
    103. Xiao Yan, Yun-Tao Jiang, Chen-Feng Li, Ralph R Martin, and Shi-Min Hu. 2016. Multi-phase sph simulation for interactive fluids and solids. ACM Transactions on Graphics (TOG) 35, 4 (2016), 79. Google ScholarDigital Library
    104. Tao Yang, Jian Chang, Ming C Lin, Ralph R Martin, Jian J Zhang, and Shi-Min Hu. 2017. A unified particle system framework for multi-phase, multi-material visual simulations. ACM Transactions on Graphics (TOG) 36, 6 (2017), 224. Google ScholarDigital Library
    105. Tao Yang, Jian Chang, Bo Ren, Ming C Lin, Jian Jun Zhang, and Shi-Min Hu. 2015. Fast multiple-fluid simulation using Helmholtz free energy. ACM Transactions on Graphics (TOG) 34, 6 (2015), 201. Google ScholarDigital Library
    106. K Yazdchi and Stefan Luding. 2012. Towards unified drag laws for inertial flow through fibrous materials. Chemical engineering journal 207 (2012), 35–48.Google Scholar
    107. Xinxin Zhang. 2015. A TBB Parallelized Liquid Solver Featuring Simple FLIP and AMGPCG Pressure Solver. https://github.com/zhxx1987/tbb_liquid_amgpcg. (2015).Google Scholar

ACM Digital Library Publication: