Flame capturing with an advection-reaction-diffusion model

We conduct several verification tests of the advection-reaction-diffusion flame-capturing model, developed by Khokhlov in 1995 for subsonic nuclear burning fronts in supernova simulations. We find that energy conservation is satisfied, but there is systematic error in the computed flame speed due to thermal expansion, which was neglected in the original model. We decouple the model from the full system, determine the necessary corrections for thermal expansion, and then demonstrate that these corrections produce the correct flame speed. The flame-capturing model is an alternative to other popular interface tracking techniques, and might be useful for applications beyond astrophysics.