“The affine particle-in-cell method”

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

Conference:


Type:


Session Title:

    Wave-Particle Fluidity

Title:

    The affine particle-in-cell method

Moderator(s):



Presenter(s)/Author(s):



Abstract:


    Hybrid Lagrangian/Eulerian simulation is commonplace in computer graphics for fluids and other materials undergoing large deformation. In these methods, particles are used to resolve transport and topological change, while a background Eulerian grid is used for computing mechanical forces and collision responses. Particle-in-Cell (PIC) techniques, particularly the Fluid Implicit Particle (FLIP) variants have become the norm in computer graphics calculations. While these approaches have proven very powerful, they do suffer from some well known limitations. The original PIC is stable, but highly dissipative, while FLIP, designed to remove this dissipation, is more noisy and at times, unstable. We present a novel technique designed to retain the stability of the original PIC, without suffering from the noise and instability of FLIP. Our primary observation is that the dissipation in the original PIC results from a loss of information when transferring between grid and particle representations. We prevent this loss of information by augmenting each particle with a locally affine, rather than locally constant, description of the velocity. We show that this not only stably removes the dissipation of PIC, but that it also allows for exact conservation of angular momentum across the transfers between particles and grid.

References:


    1. Ando, R., and Tsuruno, R. 2011. A particle-based method for preserving fluid sheets. In Proc ACM SIGGRAPH/Eurographics Symp Comp Anim, SCA ’11, 7–16. Google ScholarDigital Library
    2. Ando, R., Thurey, N., and Tsuruno, R. 2012. Preserving fluid sheets with adaptively sampled anisotropic particles. IEEE Trans Vis Comp Graph 18, 8, 1202–1214. Google ScholarDigital Library
    3. Ando, R., Thurey, N., and Wojtan, C. 2013. Highly adaptive liquid simulations on tetrahedral meshes. ACM Trans Graph 32, 4, 103:1–103:10. Google ScholarDigital Library
    4. Bargteil, A., Wojtan, C., Hodgins, J., and Turk, G. 2007. A finite element method for animating large viscoplastic flow. ACM Trans Graph 26, 3. Google ScholarDigital Library
    5. Batty, C., and Bridson, R. 2008. Accurate viscous free surfaces for buckling, coiling, and rotating liquids. Proc ACM SIGGRAPH/ Eurograph Symp Comp Anim, 219–228. Google ScholarDigital Library
    6. Batty, C., Bertails, F., and Bridson, R. 2007. A fast variational framework for accurate solid-fluid coupling. ACM Trans Graph 26, 3. Google ScholarDigital Library
    7. Boyd, L., and Bridson, R. 2012. Multiflip for energetic two-phase fluid simulation. ACM Trans Graph 31, 2, 16:1–16:12. Google ScholarDigital Library
    8. Brackbill, J., and Ruppel, H. 1986. Flip: A method for adaptively zoned, particle-in-cell calculations of fluid flows in two dimensions. J Comp Phys 65, 314–343. Google ScholarDigital Library
    9. Brackbill, J., Kothe, D., and Ruppel, H. 1988. Flip: A low-dissipation, pic method for fluid flow. Comp Phys Comm 48, 25–38.Google ScholarCross Ref
    10. Brackbill, J. 1988. The ringing instability in particle-in-cell calculations of low-speed flow. J Comp Phys 75, 2, 469–492. Google ScholarDigital Library
    11. Bridson, R. 2008. Fluid simulation for computer graphics. Taylor & Francis. Google ScholarDigital Library
    12. Chentanez, N., and Muller, M. 2010. Real-time simulation of large bodies of water with small scale details. In Proc ACM SIGGRAPH/Eurograph Symp Comp Anim, SCA ’10, 197–206. Google ScholarDigital Library
    13. Chentanez, N., and Muller, M. 2011. Real-time eulerian water simulation using a restricted tall cell grid. ACM Trans Graph 30, 4, 82:1–82:10. Google ScholarDigital Library
    14. Chentanez, N., and Muller, M. 2014. Coupling 3d eulerian, height field and particle methods for the simulation of large scale liquid phenomena. In Proc ACM SIGGRAPH/Eurograph Symp Comp Anim, SCA ’14.Google Scholar
    15. Cornelis, J., Ihmsen, M., Peer, A., and Teschner, M. 2014. Iisph-flip for incompressible fluids. Comp Graph Forum 33, 2, 255–262. Google ScholarDigital Library
    16. Edwards, E., and Bridson, R. 2012. A high-order accurate particle-in-cell method. Int J Numer Meth Eng 90, 1073–1088.Google ScholarCross Ref
    17. Edwards, E., and Bridson, R. 2014. Detailed water with coarse grids: combining surface meshes and adaptive discontinuous galerkin. ACM Trans Graph 33, 4, 136:1–136:9. Google ScholarDigital Library
    18. Enright, D., Marschner, S., and Fedkiw, R. 2002. Animation and rendering of complex water surfaces. ACM Trans Graph 21, 3, 736–744. Google ScholarDigital Library
    19. Feldman, B., O’Brien, J., and Arikan, O. 2003. Animating suspended particle explosions. SIGGRAPH ’03 22, 3, 708–715. Google ScholarDigital Library
    20. Foster, N., and Metaxas, D. 1996. Realistic animation of liquids. Graph Mod Imag Proc 58, 471–483. Google ScholarDigital Library
    21. Gao, Y., li, C., Hu, S., and Barsky, B. 2009. Simulating gaseous fluids with low and high speeds. Comp Graph Forum 28, 28, 1845–1852.Google ScholarCross Ref
    22. Gerszewski, D., and Bargteil, A. 2013. Physics-based animation of large-scale splashing liquids. ACM Trans Graph 32, 6, 185:1–185:6. Google ScholarDigital Library
    23. Harlow, F., and Welch, E. 1965. Numerical calculation of time dependent viscous flow of fluid with a free surface. Phys Fluid 8, 12, 2182–2189.Google ScholarCross Ref
    24. Harlow, F. 1964. The particle-in-cell method for numerical solution of problems in fluid dynamics. Meth Comp Phys 3, 319–343.Google Scholar
    25. Hong, J., Lee, H., Yoon, J., and Kim, C. 2008. Bubbles alive. ACM Trans Graph 27, 3, 48:1–48:4. Google ScholarDigital Library
    26. Hong, W., House, D., and Keyser, J. 2008. Adaptive particles for incompressible fluid simulation. Vis Comp 24, 7, 535–543. Google ScholarDigital Library
    27. Hong, W., House, D., and Keyser, J. 2009. An adaptive sampling approach to incompressible particle-based fluid. Theory Pract Comp Graph, 69–76.Google Scholar
    28. Ihmsen, M., Cornelis, J., Solenthaler, B., Horvath, C., and Teschner, M. 2013. Implicit incompressible sph. IEEE Trans Vis Comp Graph 20, 3, 426–435. Google ScholarDigital Library
    29. Kim, J., Cha, D., Chang, B., Koo, B., and Ihm, I. 2006. Practical animation of turbulent splashing water. In Proc ACM SIGGRAPH/Eurograph Symp Comp Anim, SCA ’06, 335–344. Google ScholarDigital Library
    30. Lee, H., Hong, J., and Kim, C. 2009. Interchangeable sph and level set method in multiphase fluids. Vis Comp 25, 5, 713–718. Google ScholarDigital Library
    31. Losasso, F., Talton, J., Kwatra, N., and Fedkiw, R. 2008. Two-way coupled sph and particle level set fluid simulation. IEEE Trans Vis Comp Graph 14, 797–804. Google ScholarDigital Library
    32. Love, E., and Sulsky, D. 2006. An unconditionally stable, energy-momentum consistent implementation of the the material point method. Comp Meth App Mech Eng 195, 3903–3925.Google ScholarCross Ref
    33. Mihalef, V., Metaxas, D., and Sussman, M. 2007. Textured liquids based on the marker level set. Comp Graph Forum, 457–466.Google Scholar
    34. Muller, K., Fedosov, D., and Gompper, G. 2015. Smoothed dissipative particle dynamics with angular momentum conservation. J Comp Phys 281, 301–315.Google ScholarDigital Library
    35. Narain, R., Golas, A., and Lin, M. 2013. Free-flowing granular materials with two-way solid coupling. ACM Trans Graph 29, 6, 173:1–173:10. Google ScholarDigital Library
    36. Patkar, S., Aanjaneya, M., Karpman, D., and Fedkiw, R. 2013. A hybrid lagrangian-eulerian formulation for bubble generation and dynamics. In Proc ACM SIGGRAPH/Eurograp Symp Comp Anim, SCA ’13, 105–114. Google ScholarDigital Library
    37. Raveendran, K., Wojtan, C., and Turk, G. 2011. Hybrid sph. In Proc 2011 ACM SIGGRAPH/Eurograp Symp Comp Anim, SCA ’11, 33–42. Google ScholarDigital Library
    38. Sifakis, E., Shinar, T., Irving, G., and Fedkiw, R. 2007. Hybrid simulation of deformable solids. In Proc ACM SIGGRAPH/Eurograph Symp Comp Anim, 81–90. Google ScholarDigital Library
    39. Sin, F., Bargteil, A., and Hodgins, J. 2009. A point-based method for animating incompressible flow. In Proc ACM SIGGRAPH/Eurograph Symp Comp Anim, 247–255. Google ScholarDigital Library
    40. Song, O., Kim, D., and Ko, H. 2009. Derivative particles for simulating detailed movements of fluids. IEEE Trans Vis Comp Graph, 247–255. Google ScholarDigital Library
    41. Stomakhin, A., Schroeder, C., Chai, L., Teran, J., and Selle, A. 2013. A material point method for snow simulation. ACM Trans Graph 32, 4, 102:1–102:10. Google ScholarDigital Library
    42. Stomakhin, A., Schroeder, C., Jiang, C., Chai, L., Teran, J., and Selle, A. 2014. Augmented mpm for phasechange and varied materials. ACM Trans Graph 33, 4, 138:1–138:11. Google ScholarDigital Library
    43. Sulsky, D., Zhou, S., and Schreyer, H. 1995. Application of a pic method to solid mechanics. Comp Phys Comm 87, 1, 236–252.Google ScholarCross Ref
    44. Um, K., Baek, S., and Han, J. 2014. Advanced hybrid particle-grid method with sub-grid particle correction. Comp Graph Forum 33, 209–218. Google ScholarDigital Library
    45. Yabe, T., Xiao, F., and Utsumi, T. 2001. The constrained interpolation profile method for multiphase analysis. J Comp Phys 169, 556–593. Google ScholarDigital Library
    46. Zhu, Y., and Bridson, R. 2005. Animating sand as a fluid. ACM Trans Graph 24, 3, 965–972. Google ScholarDigital Library
    47. Zhu, B., Yang, X., and Fan, Y. 2010. Creating and preserving vortical details in sph fluid. Comp Graph Forum 29, 7, 2207–2214.Google ScholarCross Ref


ACM Digital Library Publication: