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.