We propose a physics-based combustion simulation method for computer graphics that extends the mathematical models of previous efforts to automatically capture more realistic flames as well as temperature and soot distributions. Our method includes mathematical models for the thermodynamic properties of real-world fuels which enables, for example, the prediction of adiabatic flame temperatures. We couple this with a model of heat transfer that includes convection, conduction as well as both radiative cooling and heating. This facilitates among other things ignition at a distance without heating up the intermediate air. We model the combustion as infinitely fast chemistry and couple this with the thin flame model, spatially varying laminar burning velocities based on local species and empirical measurements, physically validated soot formation and oxidation as well as water vapor production and condensation. We implement this on adaptive octree-like grids with collocated state variables, a new SBDF2-derived semi-Lagrangian time integrator for velocity, and a multigrid scheme used for multiple solver components. In combination, these models enable us to simulate deflagration phenomena ranging from small scale premixed and diffusion flames to fireballs and subsonic explosions which we demonstrate by several examples. In addition, we validate several of the results based on reference footage and measurements and discuss the relation of prevalent heuristic techniques arising in visual effects production to some of the physics-based models we propose.

When aiming to seamlessly integrate a fluid simulation into a larger scenario (like an open ocean), careful attention must be paid to boundary conditions. In particular, one must implement special "non-reflecting" boundary conditions, which dissipate out-going waves as they exit the simulation. Unfortunately, the state of the art in non-reflecting boundary conditions (perfectly-matched layers, or PMLs) only permits trivially simple inflow/outflow conditions, so there is no reliable way to integrate a fluid simulation into a more complicated environment like a stormy ocean or a turbulent river. This paper introduces the first method for combining non-reflecting boundary conditions based on PMLs with inflow/outflow boundary conditions that vary arbitrarily throughout space and time. Our algorithm is a generalization of state-of-the-art mean-flow boundary conditions in the computational fluid dynamics literature, and it allows for seamless integration of a fluid simulation into much more complicated environments. Our method also opens the door for previously-unseen post-process effects like retroactively changing the location of solid obstacles, and locally increasing the visual detail of a pre-existing simulation.

Our work concerns the combination of an Eulerian liquid simulation with a high-resolution surface tracker (e.g. the level set method or a Lagrangian triangle mesh). The naive application of a high-resolution surface tracker to a low-resolution velocity field can produce many visually disturbing physical and topological artifacts that limit their use in practice. We address these problems by defining an error function which compares the current state of the surface tracker to the set of physically valid surface states. By reducing this error with a gradient descent technique, we introduce a novel physics-based surface fairing method. Similarly, by treating this error function as a potential energy, we derive a new surface correction force that mimics the vortex sheet equations. We demonstrate our results with both level set and mesh-based surface trackers.

We present a method for recovering a temporally coherent, deforming triangle mesh with arbitrarily changing topology from an incoherent sequence of static closed surfaces. We solve this problem using the surface geometry alone, without any prior information like surface templates or velocity fields. Our system combines a proven strategy for triangle mesh improvement, a robust multi-resolution non-rigid registration routine, and a reliable technique for changing surface mesh topology. We also introduce a novel topological constraint enforcement algorithm to ensure that the output and input always have similar topology. We apply our technique to a series of diverse input data from video reconstructions, physics simulations, and artistic morphs. The structured output of our algorithm allows us to efficiently track information like colors and displacement maps, recover velocity information, and solve PDEs on the mesh as a post process.