Building animation tools for fluid-like motions is an important and challenging problem with many applications in computer graphics. The use of physics-based models for fluid flow can greatly assist in creating such tools. Physical models, unlike key frame or procedural based techniques, permit an animator to almost effortlessly create interesting, swirling fluid-like behaviors. Also, the interaction of flows with objects and virtual forces is handled elegantly. Until recently, it was believed that physical fluid models were too expensive to allow real-time interaction. This was largely due to the fact that previous models used unstable schemes to solve the physical equations governing a fluid. In this paper, for the first time, we propose an unconditionally stable model which still produces complex fluid-like flows. As well, our method is very easy to implement. The stability of our model allows us to take larger time steps and therefore achieve faster simulations. We have used our model in conjuction with advecting solid textures to create many fluid-like animations interactively in twoand three-dimensions. CR Categories: I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism—Animation

Stable fluids

This paper presents a new reflectance model for rendering computer synthesized images. The model accounts for the relative brightness of different materials and light sources in the same scene. It describes the directional distribution of the reflected light and a color shift that occurs as the reflectance changes with incidence angle. The paper presents a method for obtaining the spectral energy distribution of the light reflected from an object made of a specific real material and discusses a procedure for accurately reproducing the color associated with the spectral energy distribution. The model is applied to the simulation of a metal and a plastic.

A reflectance model for computer graphics

Realistically animated fluids can add substantial realism to interactive applications such as virtual surgery simulators or computer games. In this paper we propose an interactive method based on Smoothed Particle Hydrodynamics (SPH) to simulate fluids with free surfaces. The method is an extension of the SPH-based technique by Desbrun to animate highly deformable bodies. We gear the method towards fluid simulation by deriving the force density fields directly from the Navier-Stokes equation and by adding a term to model surface tension effects. In contrast to Eulerian grid-based approaches, the particle-based approach makes mass conservation equations and convection terms dispensable which reduces the complexity of the simulation. In addition, the particles can directly be used to render the surface of the fluid. We propose methods to track and visualize the free surface using point splatting and marching cubes-based surface reconstruction. Our animation method is fast enough to be used in interactive systems and to allow for user interaction with models consisting of up to 5000 particles.

/pdf/particle-based-fluid-simulation-for-interactive-applications-4vbgkze3bf.pdf

Particle-based fluid simulation for interactive applications

https://www.cs.ubc.ca/~mitchell/Papers/myJCP02.pdf

A hybrid particle level set method for improved interface capturing

In this paper, we propose a new approach to numerical smoke simulation for computer graphics applications. The method proposed here exploits physics unique to smoke in order to design a numerical method that is both fast and efficient on the relatively coarse grids traditionally used in computer graphics applications (as compared to the much finer grids used in the computational fluid dynamics literature). We use the inviscid Euler equations in our model, since they are usually more appropriate for gas modeling and less computationally intensive than the viscous Navier-Stokes equations used by others. In addition, we introduce a physically consistent vorticity confinement term to model the small scale rolling features characteristic of smoke that are absent on most coarse grid simulations. Our model also correctly handles the inter-action of smoke with moving objects.

/pdf/visual-simulation-of-smoke-5e6o2k5lr8.pdf

Visual simulation of smoke

We present a general method for modeling and animating liquids. The system is specifically designed for computer animation and handles viscous liquids as they move in a 3D environment and interact with graphics primitives such as parametric curves and moving polygons. We combine an appropriately modified semi-Lagrangian method with a new approach to calculating fluid flow around objects. This allows us to efficiently solve the equations of motion for a liquid while retaining enough detail to obtain realistic looking behavior. The object interaction mechanism is extended to provide control over the liquid s 3D motion. A high quality surface is obtained from the resulting velocity field using a novel adaptive technique for evolving an implicit surface.

/pdf/practical-animation-of-liquids-5dq4r7r9xa.pdf

Practical animation of liquids

We present a comprehensive methodology for realistically animating liquid phenomena Our approach unifies existing computer graphics techniques for simulating fluids and extends them by incorporating more complex behavior It is based on the Navier–Stokes equations which couple momentum and mass conservation to completely describe fluid motion Our starting point is an environment containing an arbitrary distribution of fluid, and submerged or semisubmerged obstacles Velocity and pressure are defined everywhere within this environment and updated using a set of finite difference expressions The resulting vector and scalar fields are used to drive a height field equation representing the liquid surface The nature of the coupling between obstacles in the environment and free variables allows for the simulation of a wide range of effects that were not possible with previous computer graphics fluid models Wave effects such as reflection, refraction, and diffraction, as well as rotational effects such as eddies, vorticity, and splashing are a natural consequence of solving the system In addition, the Lagrange equations of motion are used to place buoyant dynamic objects into a scene and track the position of spray and foam during the animation process Typical disadvantages to dynamic simulations such as poor scalability and lack of control are addressed by assuming that stationary obstacles align with grid cells during the finite difference discretization, and by appending terms to the Navier–Stokes equations to include forcing functions Free surfaces in our system are represented as either a collection of massless particles in 2D, or a height field which is suitable for many of the water rendering algorithms presented by researchers in recent years

Realistic animation of liquids

This paper describes a new animation technique for modeling the turbulent rotational motion that occurs when a hot gas interacts with solid objects and the surrounding medium. The method is especially useful for scenes involving swirling steam, rolling or billowing smoke, and gusting wind. It can also model gas motion due to fans and heat convection. The method combines specialized forms of the equations of motion of a hot gas with an efficient method for solving volumetric differential equations at low resolutions. Particular emphasis is given to issues of computational efficiency and ease-of-use of the method by an animator. We present the details of our model, together with examples illustrating its use.

Modeling the motion of a hot, turbulent gas

A methodology for controlling fluid animations is developed using the concept of an embedded controller. A controller acts as an interface between the animator and a general tool for calculating three dimensional fluid flow. The major contribution of this paper is that for the first time, it is possible for computer graphics animators, to specify and control a three dimensional fluid animation, without knowledge of the underlying equations or the method used to solve them. In addition the technique is stable, physically accurate, and can be integrated with other animation tools that deal with dynamic objects. To illustrate the method, animations of moving objects fountains, and explosions, together with the straightforward control functions that are used to create them, are presented.

Controlling fluid animation

In this paper we describe a system for animating flames. Stochastic models of flickering and buoyant diffusion provide realistic local appearance while physics-based wind fields and Kolmogorov noise add controllable motion and scale. Procedural mechanisms are developed for animating all aspects of flame behavior including moving sources, combustion spread, flickering, separation and merging, and interaction with stationary objects. At all stages in the process the emphasis is on total artistic and behavioral control while maintaining interactive animation rates. The final system is suitable for a high volume production pipeline.

Nick Foster

Papers

Practical animation of liquids

Realistic animation of liquids

Modeling the motion of a hot, turbulent gas

Controlling fluid animation

Structural modeling of flames for a production environment