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We present a study of numerical behavior of a thickened flame used in FlameCapturing (FC, Khokhlov (1995)) for tracking thin unresolved physical flames indeflagration simulations. We develop a steady-state procedure for calibratingthe flame model used, and test it against analytical results.  We observe numerical noises generated by original realization of thetechnique. Alternative artificial burning rates are discussed, which produceacceptably quiet flames. 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 alsoshows significantly anisotropic propagation speed on the grid, both effectsincreasingly pronounced at larger matter expansion as a result of burning; thismakes the model unacceptable for use in type Ia supernova simulations. Anothermodel looks promising for use in flame capturing at fuel to ash density ratioof order 3 and below. That "Model B" yields flames completely localized withina region 6 cells wide at any expansion.  We study Markstein effect for flame models described, through directnumerical simulations and through quasi-steady technique developed. Comparisondemonstrates that Markstein effect dominates instability effects on curvedflame speed for Model B in 2D simulations for fuel to ash density ratio ofabout 2.5 and below. We find critical wavelength of LD instability by directsimulations of perturbed nearly planar flames; these agree with analyticalestimates when Markstein number values found in this work are used. We concludethat the behavior of model B is well understood, and optimal for FCapplications among all flame models proposed to date.

Analysis of Reaction-Diffusion Systems for Flame Capturing in Type Ia Supernova Simulations