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Explosions | Fluid Dynamics Explosion Animation | Explosion Program Explosions - Fluid Dynamics Explosion Animation Much of the information presented on this page was derived from a paper by Gary D. Yngve, James F. O'Brien, and Jessica K. Hodgins. Their paper, entitled Animating Explosions is available online at http://www.gvu.gatech.edu/animation/Papers/yngve:2000:AE.pdf. Motivation for using Fluid Dynamics As stated by Gary Yngve, et al., "Explosions are among the most dramatic phenomena in nature." To model explosions appropriately, a physically-based system must be implemented. Although particle systems can often provide accurate and stunning results, they are still limited in their abilities. Particle systems ignore several key issues:
With all of the severe limitations of the particle system method, other options were investigated. An empirical view of the blast wave was investigated next, which helped provide features like dust clouds and refraction of light to rendered scenes. However, the empirical view also maintains several problems. Damages and forces applied to objects in a scene are assumed to be universal over an entire surface, rather than centering on specific locations. Additionally, the reflected waves from the blast are ignored, which significantly limits the accuracy of the explosion from the perspective of physics. Therefore, the empirical view also yields artificial effects that leave the renderings inaccurate. Gary Yngve, et al., while working at the GVU Center and Georgia Tech's College of Computing, extended explosions in computer graphics with computational fluid dynamics "by modeling the pressure wave and the surrounding air as a fluid discretized over a three-dimensional rectilinear grid." A three-dimensional space was maintained, and key properties including density, fluid mass, pressure, velocity, temperature, and energy were maintained. Unlike the previous empirical and analytical views of a blast wave, they chose a fluid-based approach to modeling the wave. This technique seems to overcome the limitations of both previous approaches, and it is computationally acceptable. Graphics and Fluid Dynamics Computational fluid dynamics (CFD) is an approach for simulating explosions that has gained wide acceptance recently, due to its potential for providing a much higher degree of accuracy in describing real world scenarios. One of its primary advantages is its ability to describe a model which will behave in a true-to-life manner without relying on drastic approximations and simplifications. This is not to say that these models are perfect however, as they are still subject to limitations inherent to the underlying physical sub-models and accuracy of the numerical method used. Additionally, properties of the CFD model are determined for the most part on empirical coefficients and values obtained through real world experimentation. Therefore in order to ensure an accurate model, values obtained through experimentation with the actual type of event being simulated should be used, which limits the applications of this approach. (2) According to the generally accepted theory of CFD, fluids are modeled as a continuum. In other words, a fluid is defined by equations which describe its properties:
These properties and equations are evaluated on a continuous basis according to an Eulerian based definition, in which the equations apply to a region of space associated with the fluid, rather than to the fluid itself. Additional equations are needed relate to other physical properties of fluids, such as conservation of momentum, mass, and energy, its thermodynamic state, changes in the chemical equilibrium of the air, and effects related to dissociation and ionization. Most of these additional equations can be neglected by using assumptions that generalize to constants many of the time-varying properties dealing with the temperature. This is possible through the use of high temperatures in the simulations, which allow aesthetically pleasing results despite the use of slightly inaccurate values.
The first principle of fluid dynamics results from conservation of mass.
The second principle involves conservation of momentum.
The third principle comes from conservation of energy.
where 
In order to relate to each other the energy, temperature, density,
and pressure of the fluid, the following equation must be used.
Here, cv is specific heat, and R represents the gas constant of air. In general, the motivations for simulating explosions differ between the engineering and graphics communities differ fundamentally. Engineering applications usually involve concentrating on one element in the system, and considering other elements only in the context of how they affect the element in question. For this reason, many engineering simulations take place in a two-dimensional environment, with symmetry being assumed for the third. In contrast, the motivation for the graphics community is to create a depiction of the simulation which is all inclusive. The behavior and interactions of all the elements in the scene are relevant, as the accuracy of single elements in the scene are less important than the accuracy of the scene as a whole. As opposed to engineering simulations, which seek to determine a scientifically accurate depiction of a model, the primary purpose of the graphics approach is to create aesthetically pleasing simulations which are perceptually accurate rather than intrinsically accurate. Applying Computational Fluid Dynamics in a Graphics Implementation In practice, implementing an approach based on CFD requires some tinkering with the model, due to the fact that CFD was designed from an engineering standpoint, the needs of which differ from that of one rooted in graphics. The primary issue concerns the modeling of fluids as a continuum. While this approach ensures a high degree of accuracy, total accuracy is not always of paramount concern. First, animations by nature do not describe behavior as it changes on a continual basis, but only in discrete intervals (i.e. frames). Second, the goal of a simulation in graphics is to produce aesthetic results. Thus, a discretized model may be used in place of a continuous one provided they are visually indistinguishable to an appropriate degree. Finally, from a practical standpoint, it is preferable to discretize the model in order to allow for numerical computation. It is also necessary to develop a method for integrating the relevant equations from fluid dynamics.
The preferred method of discretization involves dividing the
volume into a system of cube shaped cells, called voxels. Then, instead
of integrating across a continuum, the fundamental equations can be
integrated explicitly across the voxels by approximating on them using
central differences. An example of this uses the equation
For each voxel, properties of the fluid are held constant. In order to address problems associated with steep pressure gradients, a technique called the donor-acceptor method is used. This method specifies that the transfer of mass between voxels be proportional to the mass of the donor. The scheme for updating voxels is based on the following algorithm, which occurs at each timestep:
Thus, the process for setting up an explosion simulation involves first specifying a portion of the space to be the center of the explosion. Then, a lattice of voxels is defined surrounding the area. The voxels at the center are explicitly declared to have certain properties, such as high temperature and pressure, which would be appropriate for describing the initial state of an explosion. Then, the fundamental equations are integrated explicitly over the system of voxels, updating each one with new properties at each timestep. Interacting with Solid Objects When considering the interaction of an explosion with solid objects, there are two related scenarios: applying a solid to a fluid, and vice versa. An example of the first scenario occurs when a piston compresses gas. An example of the second occurs when a bullet is fired from a gun. There are two representations of objects at work when incorporating these interactions. When applying a solid to a fluid, it is necessary to use a representation in voxels of the volume of the fluid, so that it may be displaced upon interaction with an object. When applying a fluid to a solid, a polygonal mesh is employed to transfer force from the fluid to the object. These two scenarios are incorporated into the system in the same way:
Modeling the Visible Effects of an Explosion An important aspect of modeling explosions in computer graphics is making it look like an explosion. The effects of an explosion could be seen without file-balls and dust-clouds, but then it wouldn't be much fun. With the fluid dynamics approach to explosion animation, these effects can be rendered after the actual explosion computation has taken place. Light Refraction by the Blast Wave As the blast wave travels outward from the explosion, once can see a bending of the light as it passes through the blast wave. This refraction of the light is a result of the bending of the light as it passes through the blast wave, which has a higher density than the air surrounding it. This higher density causes the blast wave to have a higher index of refraction than the surrounding air. The fluid dynamics technique models this phenomenon with ray tracing using refraction. The index of refraction for each position in the volume in the ray tracing process using [link]trilinear interpolation[/link] of the densities of neighboring voxels. Computation of the index of refraction is done according to the Dale-Gladstone law. If this index of refraction is beyond a certain threshold, then the direction of the ray cast from this position is recalculated according to Snell's law. Fireballs To render the fireball created by the explosion, particles are placed inside the shape to be exploded, and this material is used to determine the shape and color of the fireball. It's often the case that you want to show the fireball that results from an explosion. To render the fireball created by the explosion, particles are placed inside the shape to be exploded, and this material is used to determine the shape and color of the fireball. In order for the fireball to take on realistic characteristics, the particles detonating in the fireball are mass-less and flow with this fluid representing the explosion. Each particle has an associated temperature whose value is calculated according to its position in the explosion fluid. Color values are assigned to the particle with blackbody radiation. Dust Since the blast wave affects the environment surrounding it, in a real life simulation its useful to model how these surrounding particles are affected. A concrete representation of these surrounding particles is dust. These particles are hard to empirically study, so the behavior of the environment particles is a parameter to be set by the animator, although the simulation takes over once a particle becomes airborne. The behavior of the particle once airborne is determined by that particle's size: smaller particles are more affected by drag forces, and less so by inertial forces. Sources
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