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Flame-capturing Technique. I. Adaptation to Gas Expansion

Various flame-tracking techniques are used in hydrodynamic simulations. Their use is indispensable when resolving the actual scale of the flame is impossible. We show that parameters defining "artificial flame" propagation found from model systems in use may yield flame velocities several times those required, due to matter expansion being ignored in the models. The integral effect of material expansion due to burning is incorporated into flame-capturing technique. 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. Specific realizations are proposed that feature flame structure insensitive to the expansion parameter; these ensure consistent scheme performance at different stages of burning. An 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.) Implementation suggestions are summarized. Proposed realizations are tested with the ALLA hydrodynamic code used for supernovae simulations.