“Augmented MPM for phase-change and varied materials” by Stomakhin, Schroeder, Jiang, Chai, Teran, et al. …

  • ©Alexey Stomakhin, Craig Schroeder, Chenfanfu Jiang, Lawrence Chai, Joseph Teran, and Andrew Selle




    Augmented MPM for phase-change and varied materials


Session Title: Fluids



    In this paper, we introduce a novel material point method for heat transport, melting and solidifying materials. This brings a wider range of material behaviors into reach of the already versatile material point method. This is in contrast to best-of-breed fluid, solid or rigid body solvers that are difficult to adapt to a wide range of materials. Extending the material point method requires several contributions. We introduce a dilational/deviatoric splitting of the constitutive model and show that an implicit treatment of the Eulerian evolution of the dilational part can be used to simulate arbitrarily incompressible materials. Furthermore, we show that this treatment reduces to a parabolic equation for moderate compressibility and an elliptic, Chorin-style projection at the incompressible limit. Since projections are naturally done on marker and cell (MAC) grids, we devise a staggered grid MPM method. Lastly, to generate varying material parameters, we adapt a heat-equation solver to a material point framework.


    1. Bargteil, A. W., Wojtan, C., Hodgins, J. K., and Turk, G. 2007. A finite element method for animating large viscoplastic flow. ACM Trans. Graph. 26, 3. Google ScholarDigital Library
    2. Batty, C., and Bridson, R. 2008. Accurate viscous free surfaces for buckling, coiling, and rotating liquids. In Proc 2008 ACM/Eurographics Symp Comp Anim, 219–228. Google ScholarDigital Library
    3. Becker, M., Ihmsen, M., and Teschner, M. 2009. Corotated sph for deformable solids. In Eurographics Conf. Nat. Phen., 27–34. Google ScholarDigital Library
    4. Bonet, J., and Wood, R. 1997. Nonlinear Continuum Mechanics for Finite Element Analysis. Cambridge University Press.Google Scholar
    5. Carlson, M., Mucha, P. J., Van Horn, III, R. B., and Turk, G. 2002. Melting and flowing. In ACM SIGGRAPH/Eurographics Symp. Comp. Anim., 167–174. Google ScholarDigital Library
    6. Carlson, M., Mucha, P., and Turk, G. 2004. Rigid fluid: animating the interplay between rigid bodies and fluid. In ACM Trans. on Graph., vol. 23, 377–384. Google ScholarDigital Library
    7. Chang, Y., Bao, K., Liu, Y., Zhu, J., and Wu, E. 2009. A particle-based method for viscoelastic fluids animation. In ACM Symp. Virt. Real. Soft. Tech., 111–117. Google ScholarDigital Library
    8. Chentanez, N., Goktekin, T. G., Feldman, B. E., and O’Brien, J. F. 2006. Simultaneous coupling of fluids and deformable bodies. In ACM SIGGRAPH/Eurographics Symposium on Computer Animation, 83–89. Google ScholarDigital Library
    9. Choi, S.-C. T. 2006. Iterative Methods for Singular Linear Equations and Least-Squares Problems. PhD thesis, ICME, Stanford University, CA.Google Scholar
    10. Chorin, A. 1968. Numerical solution of the Navier-Stokes Equations. Math. Comp. 22, 745–762.Google ScholarCross Ref
    11. 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, 17:1–17:15. Google ScholarDigital Library
    12. Dagenais, F., Gagnon, J., and Paquette, E. 2012. A prediction-correction approach for stable sph fluid simulation from liquid to rigid. In Proc. of Comp. Graph. Intl.Google Scholar
    13. Desbrun, M., and Gascuel, M.-P. 1996. Smoothed particles: A new paradigm for animating highly deformable bodies. In Eurographics Workshop Comp. Anim. Sim., 61–76. Google ScholarDigital Library
    14. Goktekin, T. G., Bargteil, A. W., and O’Brien, J. F. 2004. A method for animating viscoelastic fluids. ACM Trans. Graph. 23, 3, 463–468. Google ScholarDigital Library
    15. Gonzalez, O., and Stuart, A. 2008. A First Course in Continuum Mechanics. Cambridge texts in applied mathematics. Cambridge University Press.Google Scholar
    16. Harlow, F., and Welch, E. 1965. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys Fl 8, 2182.Google ScholarCross Ref
    17. Hirt, C., and Shannon, J. 1968. Free-surface stress conditions for incompressible-flow calculations. JCP 2, 4, 403–411.Google ScholarCross Ref
    18. Irving, G., Teran, J., and Fedkiw, R. 2004. Invertible finite elements for robust simulation of large deformation. In Proc. 2004 ACM SIGGRAPH/Eurographics Symp. Comp. Anim., 131–140. Google ScholarDigital Library
    19. Iwasaki, K., Uchida, H., Dobashi, Y., and Nishita, T. 2010. Fast particle-based visual simulation of ice melting. Comp. Graph. Forum 29, 7, 2215–2223.Google ScholarCross Ref
    20. Keiser, R., Adams, B., Gasser, D., Bazzi, P., Dutré, P., and Gross, M. 2005. A unified lagrangian approach to solid-fluid animation. In Eurographics/IEEE VGTC Conf. Point-Based Graph., 125–133. Google ScholarDigital Library
    21. Kim, T., Adalsteinsson, D., and Lin, M. C. 2006. Modeling ice dynamics as a thin-film stefan problem. In Proc 2006 ACM SIGGRAPH/Eurographics Symp Comp Anim, 167–176. Google ScholarDigital Library
    22. Kwatra, N., Su, J., Gretarsson, J., and Fedkiw, R. 2009. A method for avoiding the acoustic time-step restriction in compressible flow. J. Comp. Phys. 228, 4146–4161. Google ScholarDigital Library
    23. Lenaerts, T., and Dutre, P. 2009. Mixing fluids and granular materials. Comp. Graph. Forum 28, 2, 213–218.Google ScholarCross Ref
    24. Lii, S.-Y., and Wong, S.-K. 2013. Ice melting simulation with water flow handling. Vis. Comp., 1–8.Google Scholar
    25. Losasso, F., Irving, G., Guendelman, E., and Fedkiw, R. 2006. Melting and burning solids into liquids and gases. IEEE Trans. Vis. Comp. Graph. 12, 343–352. Google ScholarDigital Library
    26. Losasso, F., Shinar, T., Selle, A., and Fedkiw, R. 2006. Multiple interacting liquids. ACM Trans. Graph. 25, 3, 812–819. Google ScholarDigital Library
    27. Maréchal, N., Guérin, E., Galin, E., Mérillou, S., and Mérillou, N. 2010. Heat transfer simulation for modeling realistic winter sceneries. Comp. Graph. Forum 29, 2, 449–458.Google ScholarCross Ref
    28. Martin, S., Kaufmann, P., Botsch, M., Grinspun, E., and Gross, M. 2010. Unified simulation of elastic rods, shells, and solids. ACM Trans. Graph. 29, 4 (July), 39:1–39:10. Google ScholarDigital Library
    29. Mast, C., Mackenzie-Helnwein, P., Arduino, P., Miller, G., and Shin, W. 2012. Mitigating kinematic locking in the material point method. J. Comp. Phys. 231, 16, 5351–5373. Google ScholarDigital Library
    30. Monaghan, J. J. 1992. Smoothed particle hydrodynamics. Annual review of astronomy and astrophysics 30, 543–574.Google Scholar
    31. Müller, M., Keiser, R., Nealen, A., Pauly, M., Gross, M., and Alexa, M. 2004. Point based animation of elastic, plastic and melting objects. In ACM SIGGRAPH/Eurographics Symp. Comp. Anim., 141–151. Google ScholarDigital Library
    32. Müller, M., Heidelberger, B., Teschner, M., and Gross, M. 2005. Meshless deformations based on shape matching. ACM Trans. Graph. 24, 3, 471–478. Google ScholarDigital Library
    33. Paiva, A., Petronetto, F., Lewiner, T., and Tavares, G. 2006. Particle-based non-newtonian fluid animation for melting objects. In Conf. Graph. Patt. Images, 78–85.Google Scholar
    34. Paiva, A., Petronetto, F., Lewiner, T., and Tavares, G. 2009. Particle-based viscoplastic fluid/solid simulation. Comp. Aided Des. 41, 4, 306–314. Google ScholarDigital Library
    35. Rasmussen, N., Enright, D., Nguyen, D., Marino, S., Sumner, N., Geiger, W., Hoon, S., and Fedkiw, R. 2004. Directable photorealistic liquids. In ACM SIGGRAPH/Eurographics Symp. Comp. Anim., 193–202. Google ScholarDigital Library
    36. Robinson-Mosher, A., Shinar, T., Gretarsson, J., Su, J., and Fedkiw, R. 2008. Two-way coupling of fluids to rigid and deformable solids and shells. ACM Trans. Graph. 27, 3 (Aug.), 46:1–46:9. Google ScholarDigital Library
    37. Serway, R. A., and Jewett, J. W. 2009. Physics for Scientists and Engineers. Cengage Learning. Google ScholarDigital Library
    38. Solenthaler, B., and Pajarola, R. 2009. Predictive-corrective incompressible sph. In ACM transactions on graphics (TOG), vol. 28, ACM, 40. Google ScholarDigital Library
    39. Solenthaler, B., Schläfli, J., and Pajarola, R. 2007. A unified particle model for fluid-solid interactions: Research articles. Comp. Anim. Virt. Worlds 18, 1, 69–82. Google ScholarDigital Library
    40. Steffen, M., Kirby, R., and Berzins, M. 2008. Analysis and reduction of quadrature errors in the material point method (MPM). Int. J. Numer. Meth. Engng 76, 6, 922–948.Google ScholarCross Ref
    41. Stomakhin, A., Howes, R., Schroeder, C., and Teran, J. 2012. Energetically consistent invertible elasticity. In ACM SIGGRAPH/Eurographics Symp. Comp. Anim., 25–32. Google ScholarDigital Library
    42. Stomakhin, A., Schroeder, C., Chai, L., Teran, J., and Selle, A. 2013. A material point method for snow simulation. ACM Trans. Graph. 32, 4 (July), 102:1–102:10. Google ScholarDigital Library
    43. Stora, D., Agliati, P.-O., Cani, M.-P., Neyret, F., and Gascuel, J.-D. 1999. Animating lava flows. In Graph. Int., 203–210. Google ScholarDigital Library
    44. Sulsky, D., Zhou, S.-J., and Schreyer, H. 1995. Application of particle-in-cell method to solid mechanics. Comp. Phys. Comm. 87, 236–252.Google ScholarCross Ref
    45. Terzopoulos, D., Platt, J., and Fleischer, K. 1991. Heating and melting deformable models. J. Vis. Comp. Anim. 2, 2, 68–73.Google ScholarCross Ref
    46. Teschner, M., Heidelberger, B., Muller, M., and Gross, M. 2004. A versatile and robust model for geometrically complex deformable solids. In Comp. Graph. Int., 312–319. Google ScholarDigital Library
    47. Wei, X., Li, W., and Kaufman, A. 2003. Melting and flowing of viscous volumes. In Intl. Conf. Comp. Anim. Social Agents, 54–60. Google ScholarDigital Library
    48. Wicke, M., Ritchie, D., Klingner, B. M., Burke, S., Shewchuk, J. R., and O’Brien, J. F. 2010. Dynamic local remeshing for elastoplastic simulation. ACM Transactions on Graphics 29, 4 (July), 49:1–11. Proc. of ACM SIGGRAPH 2010. Google ScholarDigital Library
    49. Wojtan, C., and Turk, G. 2008. Fast viscoelastic behavior with thin features. ACM Trans. Graph. 27, 3, 47:1–47:8. Google ScholarDigital Library
    50. Wojtan, C., Carlson, M., Mucha, P. J., and Turk, G. 2007. Animating corrosion and erosion. In Eurographics Conf. Nat. Phen., 15–22. Google ScholarDigital Library
    51. Wojtan, C., Thürey, N., Gross, M., and Turk, G. 2009. Deforming meshes that split and merge. ACM Trans. Graph. 28, 3, 76:1–76:10. Google ScholarDigital Library
    52. Yu, J., and Turk, G. 2010. Reconstructing surfaces of particle-based fluids using anisotropic kernels. In Proc. of the 2010 ACM SIGGRAPH/Eurographics Symp. on Comp. Anim., Eurographics Association, 217–225. Google ScholarDigital Library
    53. Zhao, Y., Wang, L., Qiu, F., Kaufman, A., and Mueller, K. 2006. Melting and flowing in multiphase environment. Comp. Graph. 30, 2006.Google ScholarCross Ref
    54. Zhu, Y., and Bridson, R. 2005. Animating sand as a fluid. ACM Trans. on Graph. 24, 3, 965–972. Google ScholarDigital Library

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