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## The Lattice-Boltzmann method for simulating gaseous phenomena. Visualization and Computer Graphics (2004)

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Venue: | IEEE Transactions on |

Citations: | 17 - 1 self |

### Citations

683 |
An image synthesizer
- Perlin
- 1985
(Show Context)
Citation Context ...time rendering speed. Finally, we outline our implementation and describe several examples in Section 8. 2 PREVIOUS WORK A common approach to simulating gaseous phenomena is procedural modeling [11], =-=[26]-=-, [30], where fluid behaviors are described by procedural functions. This method is fast and easy to program, but it is difficult to find the proper parameter settings that achieve realistic results. ... |

567 | Stable fluids
- Stam
- 1999
(Show Context)
Citation Context ...e solution to simulate the turbulent rotational motion of gas. Because of the inherent instability of the finite difference method with a larger time step, the speed of this approach is limited. Stam =-=[31]-=- devised a fluid solver using a semi-Lagrangian advection scheme and implicit solver for the NS equations. Each term of the equations is handled in turn, starting with external force, then advection, ... |

443 |
Lattice Boltzmann method for fluid flows
- Chen, Doolen
- 1998
(Show Context)
Citation Context ...particles that move along each bond of the lattice, following the motion of an average distribution fqi of microscopic particles. This gives rise to a model known as the Lattice Boltzmann model (LBM) =-=[3]-=-. In the densities fqi, the index qi describes the D-dimensional sublattice defined by the permutations of (1; . . . ;1; 0; . . . 0), where q is the number of nonzero components and i counts the sub... |

235 |
Lattice-gas automata for the Navier–Stokes equation
- Frisch, Hasslacher, et al.
- 1986
(Show Context)
Citation Context ... count) and momentum. The main problem with this model is that the gaseous behavior it modeled is anisotropic. A historically important lattice gas model is the FHP model, introduced by Frisch et al. =-=[15]-=- in 1986. It is a 2D hexagonal lattice used to ensure macroscopic isotropy. In this model, each cell has six nearest neighbors and, consequently, six possible velocity directions. Updating the grid in... |

196 | Modeling the motion of a hot turbulent gas
- Foster, Metaxas
- 1997
(Show Context)
Citation Context ...] gave an analytic solution to the NS equations by using simple flow primitives. Chen and Lobo [2] solved a simplified NS equations in 2D using a finite difference approach. Later, Foster and Metaxas =-=[14]-=- presented a full 3D finite difference solution to simulate the turbulent rotational motion of gas. Because of the inherent instability of the finite difference method with a larger time step, the spe... |

189 |
The Nature of Mathematical Modeling
- Gershenfeld
- 1999
(Show Context)
Citation Context ...s the conservation of momentum. It describes the velocity changes in time, due to convection, spatial variations in pressure, viscous forces, and external forces. Many books and articles (e.g., [12], =-=[16]-=-) have been published on how to solve these equations numerically. The difficulty in solving the NS equations is due to their nonlinear terms. This complexity makes the solution of these equations in ... |

150 |
Partial Differential Equations for Scientists and Engineers,
- Farlow
- 1982
(Show Context)
Citation Context ...) shows the conservation of momentum. It describes the velocity changes in time, due to convection, spatial variations in pressure, viscous forces, and external forces. Many books and articles (e.g., =-=[12]-=-, [16]) have been published on how to solve these equations numerically. The difficulty in solving the NS equations is due to their nonlinear terms. This complexity makes the solution of these equatio... |

132 | Turbulent wind fields for gaseous phenomena
- Stam, Fiume
- 1993
(Show Context)
Citation Context ... an equally efficient way to add the small-scale turbulence details into the visual simulation and render these to the screen. One way to model the small-scale turbulence is through spectral analysis =-=[32]-=-. Turbulent motion is first defined in Fourier space and then it is transformed to give periodic and chaotic vector fields that can be combined with the global motions. Another approach is to take adv... |

126 | Texture splats for 3D scalar and vector field visualization
- Crawfis, Max
- 1993
(Show Context)
Citation Context ...into the LBM a number of physically accurate effects, such as the buoyancy effect of hot gases, additional realism can be provided. Our framework makes efficient use of the concept of textured splats =-=[6]-=-, which are associated with the macroscopic particles to represent the gaseous phenomena. The textured splats form the observable “display particles,” such as the smoke particles or dust particles, wh... |

118 | Particle Animation and Rendering Using Data Parallel Computation
- Sims
- 1990
(Show Context)
Citation Context ...endering speed. Finally, we outline our implementation and describe several examples in Section 8. 2 PREVIOUS WORK A common approach to simulating gaseous phenomena is procedural modeling [11], [26], =-=[30]-=-, where fluid behaviors are described by procedural functions. This method is fast and easy to program, but it is difficult to find the proper parameter settings that achieve realistic results. The in... |

106 | Rendering and Animation of Gaseous Phenomena by Combining Fast Volume and Scanline A-buffer Techniques
- Ebert, Parent
- 1990
(Show Context)
Citation Context ... real-time rendering speed. Finally, we outline our implementation and describe several examples in Section 8. 2 PREVIOUS WORK A common approach to simulating gaseous phenomena is procedural modeling =-=[11]-=-, [26], [30], where fluid behaviors are described by procedural functions. This method is fast and easy to program, but it is difficult to find the proper parameter settings that achieve realistic res... |

105 | Smoothed particles: a new paradigm for animating highly deformable bodies
- Desbrun, Gascuel
- 1996
(Show Context)
Citation Context ...next section, we present a complete framework for the LBM-based fluid simulation and how its calculation is implemented based on the fast growing GPU technology. Physically-based particle models [5], =-=[7]-=-, [22], [24], [33], [34], [35] have also been used to describe fluid behaviors. Particle systems were first introduced by Reeves [28] as a technique for modeling fuzzy objects, such as fire, clouds, s... |

98 |
HAUMANN D.: Animation aerodynamics
- WEJCHERT
- 1991
(Show Context)
Citation Context ...y correct manner. Physically-based modeling is another broadly used method; however, it usually requires a large amount of computation time and memory, especially in 3D. In 1991, Wejchert and Haumann =-=[38]-=- gave an analytic solution to the NS equations by using simple flow primitives. Chen and Lobo [2] solved a simplified NS equations in 2D using a finite difference approach. Later, Foster and Metaxas [... |

94 | Animating soft substances with implicit surfaces
- Desbrun, Cani
- 1995
(Show Context)
Citation Context ... interaction of particles due to the thermal energy. Terzopoulos et al. [34] implemented a similar approach. Particles and springs are utilized to render a series of blobbies. Desbrun and Gascue [7], =-=[8]-=- developed a paradigm extended from the Smoothed Particle Hydrodynamics approach used by physicists for cosmological fluid simulation. This technique defines a type of particle system which uses smoot... |

84 |
Heating and melting deformable models (from goop to glop
- Terzopoulos, Platt, et al.
- 1989
(Show Context)
Citation Context ...t a complete framework for the LBM-based fluid simulation and how its calculation is implemented based on the fast growing GPU technology. Physically-based particle models [5], [7], [22], [24], [33], =-=[34]-=-, [35] have also been used to describe fluid behaviors. Particle systems were first introduced by Reeves [28] as a technique for modeling fuzzy objects, such as fire, clouds, smoke, and water. Tonnese... |

72 |
Toward interactive-rate simulation of fluids with moving obstacles using Navier-Stokes equations. Graphical Models and Image Processing,
- Chen, Lobo
- 1995
(Show Context)
Citation Context ...quires a large amount of computation time and memory, especially in 3D. In 1991, Wejchert and Haumann [38] gave an analytic solution to the NS equations by using simple flow primitives. Chen and Lobo =-=[2]-=- solved a simplified NS equations in 2D using a finite difference approach. Later, Foster and Metaxas [14] presented a full 3D finite difference solution to simulate the turbulent rotational motion of... |

71 | Implementing lattice Boltzmann computation on graphics hardware. The Visual Computer
- Li, Wei, et al.
- 2003
(Show Context)
Citation Context ...ture value. 6 MAPPING LBM TO GRAPHICS HARDWARE We briefly review in this section the basic ideas of mapping LBM to graphics hardware, that is, a graphics processing unit (GPU). (For more details, see =-=[21]-=-.) To compute the LBM equations on GPU, we divide the LBM grid and group the packet distributions fqi into arrays according to their velocity directions. All the packet distributions with the same vel... |

67 |
Modeling liquids and solids using thermal particles.
- Tonnesen
- 1991
(Show Context)
Citation Context ...mplete framework for the LBM-based fluid simulation and how its calculation is implemented based on the fast growing GPU technology. Physically-based particle models [5], [7], [22], [24], [33], [34], =-=[35]-=- have also been used to describe fluid behaviors. Particle systems were first introduced by Reeves [28] as a technique for modeling fuzzy objects, such as fire, clouds, smoke, and water. Tonnesen [35]... |

62 |
Mathematical Methods in Kinetic Theory
- Cercignani
- 1969
(Show Context)
Citation Context ...to a small numerical range, which makes the range scaling effective. Besides, the property of the LBM that the macroscopic dynamics is insensitive to the underlying details of the microscopic physics =-=[1]-=- relaxes the requirement on the accuracy of the computation. In the new generation of GPUs, such as ATI’s R300 and Nvidia’s NV30, floating-point computation is available throughout the fragment shader... |

57 |
Molecular dynamics of a classical lattice gas: transport properties and time correlation functions, Physical Review A
- Hardy, Pazzis, et al.
- 1976
(Show Context)
Citation Context ... in the LGA, the physical evolution rules are discrete, while, in the latter, the discretization is performed on the level of the macroscopic flow equations. The first LGA, introduced by Hardy et al. =-=[17]-=-, was called the HPP model, defined on a square lattice. In this model, microscopic particles of unit mass and unit speed move along the lattice links. Not more than one particle in a given direction ... |

38 | An accurate curved boundary treatment in the lattice Boltzmann method
- Mei, Luo, et al.
- 1999
(Show Context)
Citation Context ...as the boundary conditions become complicated, such as a fast moving boundary object or a complex geometric structure. In our work, we implemented the boundary conditions based on Mei et al.’s method =-=[23]-=- for curved boundaries. In their approach, the problem is solved in another way. Instead of directly setting the microscopic values, they calculate the macroscopic variables of density and velocity at... |

36 |
Lattice Gas Methods for Partial Differential Equations, Addison-Wesley Pub- lishing
- DOOLEN, EDITOR
- 1989
(Show Context)
Citation Context ...et the continuum macroscopic equations of fluid dynamics in two and three dimensions. The class of cellular automata used for the simulation of fluid dynamics is called the Lattice Gas Automata (LGA) =-=[10]-=-. The main difference between the LGA and the traditional numerical approaches of the NS equations is that, in the LGA, the physical evolution rules are discrete, while, in the latter, the discretizat... |

36 | Simulating fire with texture splats
- Wei, Li, et al.
- 2002
(Show Context)
Citation Context ...bjects in the flow, such as the leaves blowing in the wind. Besides gaseous phenomena, our model can also be used to simulate liquid [36], heat in a solid, and the like, and be extended to model fire =-=[37]-=-. ACKNOWLEDGMENTS This work is partially supported by US Office of Naval Research grant N000140110034, US National Science Foundation (NSF) grants IIS-0097646 and CCR-0306438 and NSF CAREER grant ACI-... |

13 |
Visual Simulation of Water Currents Using a Particle-Based Bahavioural Model
- Chiba, Sanakanishi, et al.
- 1995
(Show Context)
Citation Context ... the next section, we present a complete framework for the LBM-based fluid simulation and how its calculation is implemented based on the fast growing GPU technology. Physically-based particle models =-=[5]-=-, [7], [22], [24], [33], [34], [35] have also been used to describe fluid behaviors. Particle systems were first introduced by Reeves [28] as a technique for modeling fuzzy objects, such as fire, clou... |

13 |
Fast Volume Rendering and Animation of Amorphous Phenomena,” Volume Graphics
- King, Crawfis, et al.
- 2000
(Show Context)
Citation Context ...tor fields that can be combined with the global motions. Another approach is to take advantage of commodity texture mapping hardware, using textured splats [6] as the rendering primitive. King et al. =-=[20]-=- first used this technique to achieve fluid animation based on simple and local dynamics. A drawback of their model is, however, that it lacks the interaction of the fluid with environmental influence... |

10 |
Efficient Method for Realistic Animation of Clouds
- Dobashi, Kaneda, et al.
- 2000
(Show Context)
Citation Context ...linear and local rules, it is proven that the global behavior is the same as the one achieved by directly solving the heavy NS equations, which is the common approach in graphics [19]. Dobashi et al. =-=[9]-=- implemented a realistic animation of clouds based on a cellular automata model. Our work is fundamentally different from theirs. Dobashi et al.’s model can only be used to model clouds. In contrast, ... |

10 |
Large Scale Lattice-Boltzmann Simulations
- Kandhai
- 1999
(Show Context)
Citation Context ...egular grid based on linear and local rules, it is proven that the global behavior is the same as the one achieved by directly solving the heavy NS equations, which is the common approach in graphics =-=[19]-=-. Dobashi et al. [9] implemented a realistic animation of clouds based on a cellular automata model. Our work is fundamentally different from theirs. Dobashi et al.’s model can only be used to model c... |

10 | Melting and Flowing of Viscous Volumes
- Wei, Li, et al.
- 2003
(Show Context)
Citation Context ...prove the fluid animation. We also plan to model the behaviors of objects in the flow, such as the leaves blowing in the wind. Besides gaseous phenomena, our model can also be used to simulate liquid =-=[36]-=-, heat in a solid, and the like, and be extended to model fire [37]. ACKNOWLEDGMENTS This work is partially supported by US Office of Naval Research grant N000140110034, US National Science Foundation... |

9 |
Particle System—A Technique for Modeling a Class of Fuzzy Objects
- Reeves
- 1983
(Show Context)
Citation Context ... fast growing GPU technology. Physically-based particle models [5], [7], [22], [24], [33], [34], [35] have also been used to describe fluid behaviors. Particle systems were first introduced by Reeves =-=[28]-=- as a technique for modeling fuzzy objects, such as fire, clouds, smoke, and water. Tonnesen [35] used a discrete model for the heat transfer equations to describe the interaction of particles due to ... |

8 |
Three-Dimensional Parallel Lattice Boltzmann Hydrodynamics Simulations of Turbulent Flows in Interstellar Dark Clouds
- Muders
- 1995
(Show Context)
Citation Context ...ivation as this paper. To the best of our knowledge, we pioneered the introduction and use of the LBM to simulate gaseous phenomena in the graphics literature. 3 LATTICE BOLTZMANN MODEL The LBM [19], =-=[25]-=- is a lattice model similar to a cellular automata. It is defined on a 2D or 3D discrete grid, where the time and the state of each cell are also discrete. Fluid behavior can be understood as a self-o... |

3 |
TwoDimensional Visual Simulation of Flames
- Chiba, Muraoka, et al.
- 1994
(Show Context)
Citation Context ...the temperature of the smoke in the air can be characterized as a combination of the convection and diffusion of heat in neighboring cells. To achieve fast speed, we use a linear equation, similar to =-=[4]-=-, instead of an accurate differential equation, to approximate the change of temperature for the display primitives. Our model is governed by the following heat formula: TkðtÞ Tkðt 1Þ þ X j 6k ... |

2 |
Globular Dynamics: A Connected System for Animating Viscous Fluids
- Miller, Pearce
- 1998
(Show Context)
Citation Context ...n, we present a complete framework for the LBM-based fluid simulation and how its calculation is implemented based on the fast growing GPU technology. Physically-based particle models [5], [7], [22], =-=[24]-=-, [33], [34], [35] have also been used to describe fluid behaviors. Particle systems were first introduced by Reeves [28] as a technique for modeling fuzzy objects, such as fire, clouds, smoke, and wa... |