We present a method for simulating water and smoke on an unrestricted octree data structure exploiting mesh refinement techniques to capture the small scale visual detail. We propose a new technique for discretizing the Poisson equation on this octree grid. The resulting linear system is symmetric positive definite enabling the use of fast solution methods such as preconditioned conjugate gradients, whereas the standard approximation to the Poisson equation on an octree grid results in a non-symmetric linear system which is more computationally challenging to invert. The semi-Lagrangian characteristic tracing technique is used to advect the velocity, smoke density, and even the level set making implementation on an octree straightforward. In the case of smoke, we have multiple refinement criteria including object boundaries, optical depth, and vorticity concentration. In the case of water, we refine near the interface as determined by the zero isocontour of the level set function.

We describe a method for controlling smoke simulations through user-specified keyframes. To achieve the desired behavior, a continuous quasi-Newton optimization solves for appropriate "wind" forces to be applied to the underlying velocity field throughout the simulation. The cornerstone of our approach is a method to efficiently compute exact derivatives through the steps of a fluid simulation. We formulate an objective function corresponding to how well a simulation matches the user's keyframes, and use the derivatives to solve for force parameters that minimize this function. For animations with several keyframes, we present a novel multipleshooting approach. By splitting large problems into smaller overlapping subproblems, we greatly speed up the optimization process while avoiding certain local minima.

In this paper we introduce a method to simulate fluid flows on smooth surfaces of arbitrary topology: an effect never seen before. We achieve this by combining a two-dimensional stable fluid solver with an atlas of parametrizations of a Catmull-Clark surface. The contributions of this paper are: (i) an extension of the Stable Fluids solver to arbitrary curvilinear coordinates, (ii) an elegant method to handle cross-patch boundary conditions and (iii) a set of new external forces custom tailored for surface flows. Our techniques can also be generalized to handle other types of processes on surfaces modeled by partial differential equations, such as reactiondiffusion. Some of our simulations allow a user to interactively place densities and apply forces to the surface, then watch their effects in real-time. We have also computed higher resolution animations of surface flows off-line.

In this paper we present a new method for efficiently controlling animated smoke. Given a sequence of target smoke states, our method generates a smoke simulation in which the smoke is driven towards each of these targets in turn, while exhibiting natural-looking interesting smoke-like behavior. This control is made possible by two new terms that we add to the standard flow equations: (i) a driving force term that causes the fluid to carry the smoke towards a particular target, and (ii) a smoke gathering term that prevents the smoke from diffusing too much. These terms are explicitly defined by the instantaneous state of the system at each simulation timestep. Thus, no expensive optimization is required, allowing complex smoke animations to be generated with very little additional cost compared to ordinary flow simulations.

In this paper we present a simple and rapid implementation of a fluid dynamics solver for game engines. Our tools can greatly enhance games by providing realistic fluid-like effects such as swirling smoke past a moving character. The potential applications are endless. Our algorithms are based on the physical equations of fluid flow, namely the Navier-Stokes equations. These equations are notoriously hard to solve when strict physical accuracy is of prime importance. Our solvers on the other hand are geared towards visual quality. Our emphasis is on stability and speed, which means that our simulations can be advanced with arbitrary time steps. We also demonstrate that our solvers are easy to code by providing a complete C code implementation in this paper. Our algorithms run in real-time for reasonable grid sizes in both two and three dimensions on standard PC hardware, as demonstrated during the presentation of this paper at the conference.

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We propose the use of textured splats as the basic display primitives for an open surface fire model. The high-detail textures help to achieve a smooth boundary of the fire and gain the small-scale turbulence appearance. We utilize the Lattice Boltzmann Model (LBM) to simulate physically-based equations describing the fire evolution and its interaction with the environment (e.g., obstacles, wind and temperature). The property of fuel and non-burning objects are defined on the lattice of the computation domain. A temperature field is also incorporated to model the generation of smoke from the fire due to incomplete combustion. The linear and local characteristics of the LBM enable us to accelerate the computation with graphics hardware to reach real-time simulation speed, while the texture splat primitives enable interactive rendering frame rates.

Since the seminal work of [92] on coupling the level set method of [69] to the equations for two-phase incompressible flow, there has been a great deal of interest in this area. That work demonstrated the most powerful aspects of the level set method, i.e. automatic handling of topological changes such as merging and pinching, as well as robust geometric information such as normals and curvature. Interestingly, this work also demonstrated the largest weakness of the level set method, i.e. mass or information loss characteristic of most Eulerian capturing techniques. In fact, [92] introduced a partial differential equation for battling this weakness, without which their work would not have been possible. In this paper, we discuss both historical and most recent works focused on improving the computational accuracy of the level set method focusing in part on applications related to incompressible flow due to both its popularity and stringent accuracy requirements. Thus, we discuss higher order accurate numerical methods such as Hamilton-Jacobi WENO [46], methods for maintaining a signed distance function, hybrid methods such as the particle level set method [27] and the coupled level set volume of fluid method [91], and adaptive gridding techniques such as the octree approach to free surface flows proposed in [56].

This dissertation was presented by Gary D. Hart It was defended on

This paper considers the problem of reconstructing visually realistic 3D models of fire from a very small set of simultaneous views (even two). By modeling fire as a semi-transparent 3D density field, we show that fire reconstruction is equivalent to a severely under-constrained computerized tomography problem, for which traditional methods break down. Our approach is based on the observation that every pair of photographs of a semi-transparent scene defines a unique density field, called a Flame Sheet, that (1) concentrates all its density on one connected, semitransparent surface, (2) reproduces the two photos exactly, and (3) is the most spatially-coherent density field that does so. From this observation, we reduce fire reconstruction to the convex combination of sheet-like density fields, each of which is derived from the Flame Sheet of two input photos. Experimental results suggest that this method enables highquality view extrapolation without over-fitting artifacts. 1.