A point-based method for animating incompressible flow

In this paper, we present a point-based method for animating incompressible flow. The advection term is handled by moving the sample points through the flow in a Lagrangian fashion. However, unlike most previous approaches, the pressure term is handled by performing a projection onto a divergence-free field. To perform the pressure projection, we compute a Voronoi diagram with the sample points as input. Borrowing from Finite Volume Methods, we then invoke the divergence theorem and ensure that each Voronoi cell is divergence free. To handle complex boundary conditions, Voronoi cells are clipped against obstacle boundaries and free surfaces. The method is stable, flexible and combines many of the desirable features of point-based and grid-based methods. We demonstrate our approach on several examples of splashing and streaming liquid and swirling smoke.

[1]  F. Harlow,et al.  Numerical Calculation of Time‐Dependent Viscous Incompressible Flow of Fluid with Free Surface , 1965 .

[2]  J. Monaghan,et al.  Smoothed particle hydrodynamics: Theory and application to non-spherical stars , 1977 .

[3]  James F. Blinn,et al.  A Generalization of Algebraic Surface Drawing , 1982, TOGS.

[4]  J. Brackbill,et al.  FLIP: A method for adaptively zoned, particle-in-cell calculations of fluid flows in two dimensions , 1986 .

[5]  William E. Lorensen,et al.  Marching cubes: A high resolution 3D surface construction algorithm , 1987, SIGGRAPH.

[6]  V. Rich.  Personal communication , 1989, Nature.

[7]  N. Taniguchi,et al.  Construction of a Flow-Simulating Method with Finite Volume Based on a Voronoi Diagram , 1991 .

[8]  S. Koshizuka.  A particle method for incompressible viscous flow with fluid fragmentation , 1995 .

[9]  Mathieu Desbrun,et al.  Smoothed particles: a new paradigm for animating highly deformable bodies , 1996 .

[10]  Mark A Fleming,et al.  Meshless methods: An overview and recent developments , 1996 .

[11]  David P. Dobkin,et al.  The quickhull algorithm for convex hulls , 1996, TOMS.

[12]  Dimitris N. Metaxas,et al.  Realistic Animation of Liquids , 1996, Graphics Interface.

[13]  P. Colella,et al.  A Cartesian Grid Embedded Boundary Method for Poisson's Equation on Irregular Domains , 1998 .

[14]  Jos Stam,et al.  Stable fluids , 1999, SIGGRAPH.

[15]  Marie-Paule Cani,et al.  Animating Lava Flows , 1999, Graphics Interface.

[16]  S. Cummins,et al.  An SPH Projection Method , 1999 .

[17]  G. Dilts.  MOVING-LEAST-SQUARES-PARTICLE HYDRODYNAMICS-I. CONSISTENCY AND STABILITY , 1999 .

[18]  J. Kuhnert,et al.  Grid Free Method For Solving The Poisson Equation , 2001 .

[19]  Ross T. Whitaker,et al.  Particle‐Based Simulation of Fluids , 2003, Comput. Graph. Forum.

[20]  Markus H. Gross,et al.  Particle-based fluid simulation for interactive applications , 2003, SCA '03.

[21]  Markus H. Gross,et al.  Interaction of fluids with deformable solids , 2004, Comput. Animat. Virtual Worlds.

[22]  E. Oñate,et al.  The particle finite element method. An overview , 2004 .

[23]  João Flávio Vieira de Vasconcellos,et al.  A FINITE-VOLUME METHOD BASED ON VORONOI DISCRETIZATION FOR FLUID FLOW PROBLEMS , 2004 .

[24]  Matthias Teschner,et al.  Interaction of fluids with deformable solids: Research Articles , 2004 .

[25]  Ronald Fedkiw,et al.  Simulating water and smoke with an octree data structure , 2004, ACM Trans. Graph..

[26]  Gernot Schaller,et al.  Kinetic and dynamic Delaunay tetrahedralizations in three dimensions , 2004, Comput. Phys. Commun..

[27]  James F. O'Brien,et al.  Animating gases with hybrid meshes , 2005, SIGGRAPH 2005.

[28]  James F. O'Brien,et al.  Fluids in deforming meshes , 2005, SCA '05.

[29]  Markus H. Gross,et al.  Particle-based fluid-fluid interaction , 2005, SCA '05.

[30]  Philippe Beaudoin,et al.  Particle-based viscoelastic fluid simulation , 2005, SCA '05.

[31]  James F. O'Brien,et al.  Animating gases with hybrid meshes , 2005, ACM Trans. Graph..

[32]  Nafees Bin Zafar,et al.  Cartesian grid fluid simulation with irregular boundary voxels , 2005, SIGGRAPH '05.

[33]  Robert Bridson,et al.  Animating sand as a fluid , 2005, ACM Trans. Graph..

[34]  Markus H. Gross,et al.  Eurographics Symposium on Point-based Graphics (2005) a Unified Lagrangian Approach to Solid-fluid Animation , 2022 .

[35]  Ulrich Rüde,et al.  Detail-preserving fluid control , 2006, Symposium on Computer Animation.

[36]  James F. O'Brien,et al.  Fluid animation with dynamic meshes , 2006, SIGGRAPH 2006.

[37]  James F. O'Brien,et al.  Fluid animation with dynamic meshes , 2006, ACM Trans. Graph..

[38]  Yiying Tong,et al.  Stable, circulation-preserving, simplicial fluids , 2006, SIGGRAPH Courses.

[39]  Gavin S. P. Miller,et al.  Particle-Based Fluid Simulation on the GPU , 2006, International Conference on Computational Science.

[40]  S. Shao,et al.  Incompressible SPH simulation of wave breaking and overtopping with turbulence modelling , 2006 .

[41]  Rüdiger Westermann,et al.  Realistic and interactive simulation of rivers , 2006, Graphics Interface.

[42]  Fabrice Colin,et al.  Computing a null divergence velocity field using smoothed particle hydrodynamics , 2006, J. Comput. Phys..

[43]  Nikolaus A. Adams,et al.  An incompressible multi-phase SPH method , 2007, J. Comput. Phys..

[44]  J. Levesley,et al.  Enhancing SPH using Moving Least-Squares and Radial Basis Functions , 2007, 0705.4374.

[45]  James F. O'Brien,et al.  Liquid simulation on lattice-based tetrahedral meshes , 2007 .

[46]  Renato Pajarola,et al.  A unified particle model for fluid–solid interactions , 2007, Comput. Animat. Virtual Worlds.

[47]  Soon Hyoung Pyo,et al.  Bubbling and frothing liquids , 2007, SIGGRAPH 2007.

[48]  Pep Español,et al.  Incompressible smoothed particle hydrodynamics , 2007, J. Comput. Phys..

[49]  Renato Pajarola,et al.  A unified particle model for fluid–solid interactions: Research Articles , 2007 .

[50]  Leonidas J. Guibas,et al.  Adaptively sampled particle fluids , 2007, ACM Trans. Graph..

[51]  Matthias Teschner,et al.  Eurographics/ Acm Siggraph Symposium on Computer Animation (2007) Weakly Compressible Sph for Free Surface Flows , 2022 .

[52]  Paul W. Cleary,et al.  Bubbling and frothing liquids , 2007, ACM Trans. Graph..

[53]  Robert Bridson,et al.  A fast variational framework for accurate solid-fluid coupling , 2007, ACM Trans. Graph..

[54]  Renato Pajarola,et al.  Adaptive Sampling and Rendering of Fluids on the GPU , 2008, VG/PBG@SIGGRAPH.

[55]  Brent Warren Williams,et al.  Fluid surface reconstruction from particles , 2008 .

[56]  Donald H. House,et al.  Adaptive particles for incompressible fluid simulation , 2008, The Visual Computer.

[57]  Ronald Fedkiw,et al.  Two-Way Coupled SPH and Particle Level Set Fluid Simulation , 2008, IEEE Transactions on Visualization and Computer Graphics.

[58]  Renato Pajarola,et al.  Eurographics/ Acm Siggraph Symposium on Computer Animation (2008) , 2022 .

[59]  Philip Dutré,et al.  Porous flow in particle-based fluid simulations , 2008, ACM Trans. Graph..

[60]  R. Pajarola,et al.  Predictive-corrective incompressible SPH , 2009, SIGGRAPH 2009.