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We present a physically based method for modeling and animating fire. Our method is suitable for both smooth (laminar) and turbulent flames, and it can be used to animate the burning of either solid or gas fuels. We use the incompressible Navier-Stokes equations to independently model both vaporized fuel and hot gaseous products. We develop a physically based model for the expansion that takes place when a vaporized fuel reacts to form hot gaseous products, and a related model for the similar expansion that takes place when a solid fuel is vaporized into a gaseous state. The hot gaseous products, smoke and soot rise under the influence of buoyancy and are rendered using a blackbody radiation model. We also model and render the blue core that results from radicals in the chemical reaction zone where fuel is converted into products. Our method allows the fire and smoke to interact with objects, and flammable objects can catch on fire.

In this paper, we propose a new numerical method for treating two phase incompressible flow where one phase is being converted into the other, e.g. the vaporization of liquid water. We consider this numerical method in the context of treating discontinuously thin flame fronts for incompressible flow. This method was designed as an extension of the Ghost Fluid Method [4] and relies heavily on the boundary condition capturing technology developed in [13] for the variable coefficient Poisson equation and in [12] for multiphase incompressible flow. Our new numerical method admits a sharp interface representation similar to the method proposed in [9]. Since the interface boundary conditions are handled in a simple and straightforward fashion, the code is very robust, e.g. no special treatment is required to treat the merging of flame fronts. The method is presented in three spatial dimensions, with numerical examples in one, two and three spatial dimensions.

In this paper, we present an enhanced resolution capturing method for topologically complex two and three dimensional incompressible free surface flows. The method is based upon the level set method of Osher and Sethian to represent the interface combined with two recent advances in the treatment of the interface, a second order accurate discretization of the Dirichlet pressure boundary condition at the free surface (2002, J. Comput. Phys. 176, 205) and the use of massless marker particles to enhance the resolution of the interface through the use of the particle level set method (2002, J. Comput. Phys., 183, 83). Use of these methods allow for the accurate movement of the interface while at the same time preserving the mass of the the liquid, even on coarse computational grids. Also, these methods complement the level set method in its ability to handle changes in interface topology in a robust manner. Surface tension effects can be easily included in our method. The method is presented in three spatial dimensions, with numerical examples in both two and three spatial dimensions. Governing EquationsWe solve for inviscid, incompressible flow. The governing equations for momentum and mass conservation arewhere t is the time, u = (u, v, w) is the velocity field, p is the pressure, g = (0, g, 0) is gravity, ρ is the constant density of the liquid, and ∇ = (We use the free surface assumption so that the air has a constant pressure, p air , in space and time.The location of the liquid free surface is defined as the set of points where the level set function φ = 0, and the region occupied by the liquid is given by φ < 0. The level set equation [1],determines the evolution of the free surface in space and time. Geometrical information about the interface, e.g. normals and curvature, can be easily obtained from φ which we take as the signed distance to the interface. The unit outward normal is N = ∇φ/|∇φ| and the curvature is κ = ∇ · N. See [2] for more details.

We present a method for the directable animation of photorealistic liquids using the particle level set method to obtain smooth, visually pleasing complex liquid surfaces. We also provide for a degree of control common to particle-only