We present a study of numerical behavior of a thickened flame used in Flame Capturing (FC, Khokhlov (1995)) for tracking thin physical flames in deflagration simulations. This technique, used extensively in astrophysics, utilizes artificial flame variable to evolve flame region, width of which is resolved in simulations, with physically motivated propagation speed. We develop a steady-state procedure for calibrating flame model used in FC, and test it against analytical results. Original flame model is properly calibrated with taking matter expansion into consideration and keeping artificial flame width at predetermined value regardless of expansion.

We observe numerical noises generated by original realization of the technique. Alternative artificial burning rates are discussed, which produce acceptably quiet flames (relative dispersion in propagation speed within 0.1% at physically interesting ratios of fuel and ash densities).

Two new quiet models are calibrated to yield required “flame” speed and width, and further studied in 2D and 3D setting. Landau-Darrieus type instabilities of the flames are observed. One model also shows significantly anisotropic propagation speed on the grid, both effects increasingly pronounced at larger matter expansion as a result of burning; these 2D/3D effects make that model unacceptable for use in type Ia supernova simulations at fuel densities below about 100 tons per cubic centimeter. Another model, first presented here, looks promising for use in flame capturing at fuel to ash density ratio of order 3 and below, the interval of most interest for astrophysical applications. No model was found to significantly inhibit LD instability development at larger expansions without increasing flame width. The model we propose, “Model B”, yields flames completely localized within a region 6 cells wide at any expansion.

We study Markstein effect (speed of the flame dependence on its curvature) for flame models described, through direct numerical simulations and through quasi-steady technique developed. By comparing results obtained by the 2 approaches we demonstrate that Markstein effect dominates instability effects on curved flame speed for Model B in 2D simulations for fuel to ash density of about 2.5 and below. We find critical wavelength of LD instability by direct simulations of perturbed nearly planar flames; these agree with analytical predictions with Markstein number values found in this work. We conclude that the behavior of model B is well understood, and optimal for FC applications among all flame models proposed to date.