Flame-capturing technique. 1: Adaptation to gas expansion
  Various flame tracking techniques are often used in hydrodynamic simulations. Their use is indispensable when resolving actual scale of the flame is impossible. We show that parameters defining "artificial flame" propagation found from model systems may yield flame velocities several times distinct from the required ones, due to matter expansion being ignored in the models.   Integral effect of material expansion due to burning is incorporated into flame capturing technique (FCT) [Khokhlov(1995)]. Interpolation formula is proposed for the parameters governing flame propagation yielding 0.2% accurate speed and width for any expansion (and at least 0.01% accurate for expansions typical in type Ia supernova explosions.) Several models with simple burning rates are studied with gas expansion included. Plausible performance of the technique in simulations is discussed. Its modification ensuring finite flame width is found. Implementation suggestions are summarized, main criterion being the scheme performance being insensitive to expansion parameter (thus absence of systematic errors when the burning progresses from inner to outer layers); in this direction promising realizations are found, leading to flame structure not changing while flame evolves through the whole range of densities in the white dwarf. 
Andrey V. Zhiglo