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Issue No.01 - Jan. (2014 vol.20)
pp: 17-29
Nuttapong Chentanez , Nvidia PhysX Res., Zurich, Switzerland
Matthias Muller , Nvidia PhysX Res., Zurich, Switzerland
ABSTRACT
We present a GPU friendly, Eulerian, free surface fluid simulation method that conserves mass locally and globally without the use of Lagrangian components. Local mass conservation prevents small-scale details of the free surface from disappearing, a problem that plagues many previous approaches, while global mass conservation ensures that the total volume of the liquid does not decrease over time. Our method handles moving solid boundaries as well as cells that are partially filled with solids. Due to its stability, it allows the use of large time steps that makes it suitable for both offline and real-time applications. We achieve this by using density-based surface tracking with a novel, unconditionally stable, conservative advection scheme. We also propose mass conserving methods to sharpen the interface and to reveal subgrid features of the liquid. While our approach conserves mass, volume loss is still possible but only temporarily. With constant mass, local volume loss causes a local increase of the density used for surface tracking which we detect and correct over time. We show the effectiveness of the proposed methods in several practical examples all running either at interactive rates or in real time.
INDEX TERMS
Liquids, Level set, Interpolation, Computational modeling, Solids, Mathematical model, Graphics processing units,physics-based animation, Mass conservation, density sharpening, fluid simulation
CITATION
Nuttapong Chentanez, Matthias Muller, "Mass-Conserving Eulerian Liquid Simulation", IEEE Transactions on Visualization & Computer Graphics, vol.20, no. 1, pp. 17-29, Jan. 2014, doi:10.1109/TVCG.2013.19
REFERENCES
[1] C. Wojtan, M. Müller-Fischer, and T. Brochu, "Liquid Simulation with Mesh-Based Surface Tracking," Proc. ACM SIGGRAPH, pp. 8:1-8:84, 2011.
[2] N. Foster and R. Fedkiw, "Practical Animation of Liquids," Proc. ACM SIGGRAPH, pp. 23-30, Aug. 2001.
[3] D. Enright, S. Marschner, and R. Fedkiw, "Animation and Rendering of Complex Water Surfaces," ACM Trans. Graphics, vol. 21, no. 3, pp. 736-744, July 2002.
[4] A.W. Bargteil, T.G. Goktekin, J.F. O'Brien, and J.A. Strain, "A Semi-Lagrangian Contouring Method for Fluid Simulation," ACM Trans. Graphics, vol. 25, pp. 19-38, 2005.
[5] P. Mullen, A. McKenzie, Y. Tong, and M. Desbrun, "A Variational Approach to Eulerian Geometry Processing," Proc. ACM SIGGRAPH, 2007.
[6] M. Lentine, M. Aanjaneya, and R. Fedkiw, "Mass and Momentum Conservation for Fluid Simulation," Proc. ACM SIGGRAPH/Eurographics Symp. Computer Animation, pp. 91-100, Aug. 2011.
[7] N. Foster and D. Metaxas, "Realistic Animation of Liquids," Graphical Models Image Processing, vol. 58, no. 5, pp. 471-483, 1996.
[8] J. Stam, "Stable Fluids," Proc. ACM SIGGRAPH, pp. 121-128, Aug. 1999.
[9] N. Heo and H.-S. Ko, "Detail-Preserving Fully-Eulerian Interface Tracking Framework," ACM Trans. Graphics, vol. 29, pp. 176:1-176:8, Dec. 2010.
[10] Y. Zhu and R. Bridson, "Animating Sand as a Fluid," ACM Trans. Graphics, vol. 24, no. 3, pp. 965-972, July 2005.
[11] B. Adams, M. Pauly, R. Keiser, and L.J. Guibas, "Adaptively Sampled Particle Fluids," ACM Trans. Graphics, vol. 26, July 2007.
[12] J. Yu and G. Turk, "Enhancing Fluid Animation with Adaptive, Controllable and Intermittent Turbulence," Proc. ACM SIGGRAPH/Eurographics Symp. Computer Animation, 2010.
[13] M. Müller, "Fast and Robust Tracking of Fluid Surfaces," Proc. ACM SIGGRAPH/Eurographics Symp. Computer Animation, 2009.
[14] T. Brochu and R. Bridson, "Robust Topological Operations for Dynamic Explicit Surfaces," SIAM J. Scientific Computing, vol. 31, no. 4, pp. 2472-2493, http://link.aip.org/link/?SCE/31/24721, 2009.
[15] C. Wojtan, N. Thürey, M. Gross, and G. Turk, "Physics-Inspired Topology Changes for Thin Fluid Features," ACM Trans. Graphics, vol. 29, pp. 50:1-50:8, July 2010.
[16] B.E. Feldman, J.F. O'Brien, and O. Arikan, "Animating Suspended Particle Explosions," ACM Trans. Graphics, vol. 22, no. 3, pp. 708-715, July 2003.
[17] B. Kim, Y. Liu, I. Llamas, X. Jiao, and J. Rossignac, "Simulation of Bubbles in Foam with the Volume Control Method," ACM Trans. Graphics, vol. 26, July 2007.
[18] G. Irving, C. Schroeder, and R. Fedkiw, "Volume Conserving Finite Element Simulations of Deformable Models," ACM SIGGRAPH, 2007.
[19] B. Kim, Y. Liu, I. Llamas, and J. Rossignac, "FlowFixer: Using BFECC for Fluid Simulation," Proc. First Eurographics Conf. Natural Phenomena (NPH), pp. 51-56, 2005.
[20] A. Selle, R. Fedkiw, B. Kim, Y. Liu, and J. Rossignac, "An Unconditionally Stable MacCormack Method," J. Science Computing, vol. 35, nos. 2/3, pp. 350-371, 2008.
[21] D. Kim, O.-Y. Song, and H.-S. Ko, "A Semi-Lagrangian Cip Fluid Solver without Dimensional Splitting," Computer Graphics Forum, vol. 27, no. 2, pp. 467-475, Apr. 2008.
[22] M. Lentine, J.T. Grétarsson, and R. Fedkiw, "An Unconditionally Stable Fully Conservative Semi-Lagrangian Method," J. Computational Physics, vol. 230, pp. 2857-2879, Apr. 2011.
[23] C.W. Hirt and B.D. Nichols, "Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries," J. Computational Physics, vol. 39, no. 1, pp. 201-225, Jan. 1981.
[24] J.E. Pilliod Jr and E.G. Puckett, "Second-Order Accurate Volume-of-Fluid Algorithms for Tracking Material Interfaces," J. Computational Physics, vol. 199, no. 2, pp. 465-502, Sept. 2004.
[25] J.C. Anderson, C. Garth, M.A. Duchaineau, and K. Joy, "Discrete Multi-Material Interface Reconstruction for Volume Fraction Data," Computer Graphics Forum vol. 27, no. 3,http://graphics. cs.ucdavis.educobalt, 2008.
[26] M. Sussman and E.G. Puckett, "A Coupled Level Set and Volume-of-Fluid Method for Computing 3D and Axisymmetric Incompressible Two-Phase Flows," J. Computational Physics, vol. 162, no. 2, pp. 301-337, Aug. 2000.
[27] N. Kang, J. Park, J. yong Noh, and S.Y. Shin, "A Hybrid Approach to Multiple Fluid Simulation Using Volume Fractions," Computer Graphics Forum, vol. 29, no. 2, pp. 685-694, 2010.
[28] K.K. So, X.Y. Hu, and N.A. Adams, "Anti-Diffusion Method for Interface Steepening in Two-Phase Incompressible Flow," J. Computational Physics, vol. 230, no. 13, pp. 5155-5177, June 2011.
[29] Z. Xu and C.-W. Shu, "Anti-Diffusive Flux Corrections for High Order Finite Difference WENO Schemes," J. Computational Physics, vol. 205, no. 2, pp. 458-485, 2005.
[30] H. Rusche, "Computational Fluid Dynamics of Dispersed Two-Phase Flows at High Phase Fractions," PhD dissertation, Imperial College of Science, Technology and Medicine, 2002.
[31] E. Olsson and G. Kreiss, "A Conservative Level Set Method for Two Phase Flow," J. Computational Physics, vol. 210, no. 1, pp. 225-246, 2005.
[32] E. Olsson, G. Kreiss, and S. Zahedi, "A Conservative Level Set Method for Two Phase Flow Ii," J. Computational Physics, vol. 225, no. 1, pp. 785-807, 2007.
[33] N. Thürey and U. Rüde, "Free Surface Lattice-Boltzmann Fluid Simulations with and without Level Sets," Proc. Vision, Modelling, and Visualization Workshop (VMV), pp. 199-207, 2004.
[34] N. Thürey and U. Rüde, "Stable Free Surface Flows with the Lattice Boltzmann Method on Adaptively Coarsened Grids," Computing and Visualization in Science, vol. 12, no. 5, pp. 247-263, May 2009.
[35] B. Long and E. Reinhard, "Real-Time Fluid Simulation Using Discrete Sine/Cosine Transforms," Proc. ACM SIGGRAPH Symp. Interactive 3D Graphics and Games, pp. 99-106, 2009.
[36] M. Müller, D. Charypar, and M. Gross, "Particle-Based Fluid Simulation for Interactive Applications," ACM SIGGRAPH/Eurographics Symp. Computer Animation, pp. 154-159, 2003.
[37] S. Premoze, T. Tasdizen, J. Bigler, A.E. Lefohn, and R.T. Whitaker, "Particle-Based Simulation of Fluids," Computer Graphics Forum, vol. 22, no. 3, pp. 401-410, 2003.
[38] B. Solenthaler and R. Pajarola, "Predictive-Corrective Incompressible SPH," ACM Trans. Graphics, vol. 28, no. 3, pp. 40:1-40:6, July 2009.
[39] B. Solenthaler and M. Gross, "Two-Scale Particle Simulation," ACM Trans. Graphics, vol. 30, pp. 81:1-81:8, Aug. 2011.
[40] M. Lentine, M. Cong, S. Patkar, and R. Fedkiw, "Simulating Free Surface Flow with Very Large Time Steps," Proc. ACM SIGGRAPH/Eurographics Symp. Computer Animation, pp. 107-116, 2012.
[41] F. Harlow and J. Welch, "Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with a Free Surface," The Physics of Fluids, vol. 8, pp. 2182-2189, 1965.
[42] N. Chentanez and M. Müller, "Real-Time Eulerian Water Simulation Using a Restricted Tall Cell Grid," ACM Trans. Graphics, vol. 30, no. 4, pp. 82:1-82:10, July 2011.
[43] W.-K. Jeong, Ross, and T. Whitaker, "A Fast Eikonal Equation Solver for Parallel Systems," Proc. SIAM Conf. Computational Science and Eng., 2007.
[44] C. Batty, F. Bertails, and R. Bridson, "A Fast Variational Framework for Accurate Solid-Fluid Coupling," ACM Trans. Graphics, vol. 26, no. 3, July 2007.
[45] D. Enright, D. Nguyen, F. Gibou, and R. Fedkiw, "Using the Particle Level Set Method and a Second Order Accurate Pressure Boundary Condition for Free Surface Flows," Proc. Fourth ASME-JSME Joint Fluids Eng. Conf., Number FEDSM2003-45144, 2003.
[46] N. Chentanez and M. Müller, "A Multigrid Fluid Pressure Solver Handling Separating Solid Boundary Conditions," Proc. ACM SIGGRAPH/Eurographics Symp. Computer Animation, pp. 83-90, 2011.
[47] W.E. Lorensen and H.E. Cline, "Marching Cubes: A High Resolution 3D Surface Construction Algorithm," SIGGRAPH Computer Graphics, vol. 21, pp. 163-169, Aug. 1987.
[48] E. Mokberi and P. Faloutsos, "A Particle Level Set Library."
[49] D. Kim, O.-Y. Song, and H.-S. Ko, "Stretching and Wiggling Liquids," ACM Trans. Graphics, vol. 28, no. 5, pp. 120:1-120:7, Dec. 2009.
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