  We study the evolution of a reactive field advected by a one-dimensional
compressible velocity field and subject to an ignition-type nonlinearity. In
the limit of small molecular diffusivity the problem can be described by a
spatially discretized system, and this allows for an efficient numerical
simulation. If the initial field profile is supported in a region of size l <
lc one has quenching, i.e., flame extinction, where lc is a characteristic
length-scale depending on the system parameters (reacting time, molecular
diffusivity and velocity field). We derive an expression for lc in terms of
these parameters and relate our results to those obtained by other authors for
different flow settings.
