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 two- and three-dimensions.

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 semi-submerged 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.

The realistic depiction of smoke, steam, mist and water reacting to a turbulent field such as wind is an attractive and challenging problem. Its solution requires interlocking models for turbulent fields, gaseous flow, and realistic illumination. We present a model for turbulent wind flow having a deterministic component to specify large-scale behaviour, and a stochastic component to model turbulent small-scale behaviour. The small-scale component is generated using space-time Fourier synthesis. Turbulent wind fields can be superposed interactively to create subtle behaviour. An advection-diffusion model is used to animate particle-based gaseous phenomena embedded in a wind field, and we derive an efficient physically-based illumination model for rendering the system. Because the number of particles can be quite large, we present a clustering algorithm for efficient animation and rendering. CR Categories and Subject Descriptors: I.3.7 [Com- puter Graphics]: Three-Dimensional Graphics...

Abstract: In this paper we describe a method for modeling the dynamic behavior of splashing fluids. The model simulates the behavior of a fluid when objects impact or float on its surface. The forces generated by the objects create waves and splashes on the surface of the fluid. To demonstrate the realism and limitations of the model, images from a computergenerated animation are presented and compared with video frames of actual splashes occuring under similar initial conditions. 1

We present a fast and stable system for animating materials that melt, flow, and solidify. Examples of real-world materials that exhibit these phenomena include melting candles, lava flow, the hardening of cement, icicle formation, and limestone deposition. We animate such phenomena by physical simulation of fluids -- in particular the incompressible viscous Navier-Stokes equations with free surfaces, treating solid and nearly-solid materials as very high viscosity fluids. The computational method is a modification of the Marker-and-Cell (MAC) algorithm in order to rapidly simulate fluids with variable and arbitrarily high viscosity. This allows the viscosity of the material to change in space and time according to variation in temperature, water content, or any other spatial variable, allowing different locations in the same continuous material to exhibit states ranging from the absolute rigidity or slight bending of hardened wax to the splashing and sloshing of water. We create detailed polygonal models of the fluid by splatting particles into a volumetric grid and we render these models using ray tracing with sub-surface scattering. We demonstrate the method with examples of several viscous materials including melting wax and sand drip castles.

The motion of fluids has been a topic of study for hundredsof years. In its most general setting, fluid flow is governed by a system of non-linear partial differential equations known as the Navier-Stokes equations. However, in several important settings, these equations degenerate into simpler systems of linear partial differential equations. This paper will show that flows corresponding to these linear equations can be modeled using subdivision schemes for vector fields. Given an initial, coarse vector field, these schemes generate an increasingly dense sequence of vector fields. The limit of this sequence is a continuous vector field defining a flow that follows the initial vector field. The beauty of this approach is that realistic flows can now be modeled and manipulated in real time using their associated subdivision schemes.

One of nature's greatest beauties is the way fresh snowcovers the world in a perfect blanket of crystalline white. Snow replaces sharp angles with gentle curves, and clings to surfaces to form ghostly silhouettes. It is said the Inuit have 50 di#erentwords for snow, yet even they can be left speechless, as snow is one of the most complex natural materials in existence.

We present an adaptive scheme for the interactive animation and display of ocean waves far from the coast. Relying on a procedural wave model, the method restricts computations to the visible part of the ocean surface, adapts the geometric resolution to the viewing distance and only considers the visible waves wavelengths. This yields real-time performances, even when the camera moves. The method allows the user to interactively fly over an unbounded animated ocean, which was not possible using previous approaches.

This paper proposes a simplified position-based physics that allows us to rapidly generate "piles" or "clumps" of many objects: local energy minima under a variety of potential energy functions. We can also generate plausible motions for many highly interacting objects from arbitrary starting positions to a local energy minimum. We present an efficient and numerically stable algorithm for carrying out position-based physics on spheres and non-rotating polyhedra through the use of linear programming. This algorithm is a generalization of an algorithm for finding tight packings of (nonrotating) polygons in two dimensions. This work introduces linear programming as a useful tool for graphics animation. As its name implies, position-based physics does not contain a notion of velocity, and thus it is not suitable for simulating the motion of free-flying, unencumbered objects. However, it generates realistic motions of "crowded" sets of objects in confined spaces, and it does so at least two...

As simulation and rendering capabilities continue to increase, volumetric effects like smoke, fire or explosions will be frequently encountered in computer games and virtual environments. In this paper, we present techniques for the visual simulation and rendering of such effects that keep up with the demands for frame rates imposed by such environments. This is achieved by leveraging functionality on recent graphics programming units (GPUs) in combination with a novel approach to model non physics-based, yet realistic variations in flow fields. We show how to use this mechanism for simulating effects as demonstrated in Figure 1. Physics-based simulation is performed on 2D proxy geometries, and simulation results are extruded to 3D using particle or texture based approaches. Our method allows the animator to model and to flexibly control the dynamic behavior of volumetric effects, and it can be used to create plausible animations of a variety of natural phenomena.