  We present a study of numerical behavior of a thickened flame used in Flame
Capturing (FC, Khokhlov (1995)) for tracking thin unresolved physical flames in
deflagration simulations. We develop a steady-state procedure for calibrating
the flame model used, and test it against analytical results.
  We observe numerical noises generated by original realization of the
technique. Alternative artificial burning rates are discussed, which produce
acceptably 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 also
shows significantly anisotropic propagation speed on the grid, both effects
increasingly pronounced at larger matter expansion as a result of burning; this
makes the model unacceptable for use in type Ia supernova simulations. Another
model looks promising for use in flame capturing at fuel to ash density ratio
of order 3 and below. That "Model B" yields flames completely localized within
a region 6 cells wide at any expansion.
  We study Markstein effect for flame models described, through direct
numerical simulations and through quasi-steady technique developed. Comparison
demonstrates that Markstein effect dominates instability effects on curved
flame speed for Model B in 2D simulations for fuel to ash density ratio 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
estimates when Markstein number values found in this work are used. We conclude
that the behavior of model B is well understood, and optimal for FC
applications among all flame models proposed to date.
