  In this paper, a new fractional step method is proposed for simulating stiff
and nonstiff chemically reacting flows. In stiff cases, a well-known spurious
numerical phenomenon, i.e. the incorrect propagation speed of discontinuities,
may be produced by general fractional step methods due to the under-resolved
discretization in both space and time. The previous random projection method
has been successfully applied for stiff detonation capturing in under-resolved
conditions. Not to randomly project the intermediate state into two presumed
equilibrium states (completely burnt or unburnt) as in the random projection
method, the present study is to randomly choose the time-dependent advance or
stop of a reaction process. Each one-way reaction has been decoupled from the
multi-reaction kinetics using operator splitting and the local smeared
temperature due to numerical dissipation of shock-capturing schemes is compared
with a random one within two limited temperatures corresponding to the advance
and its inverse states, respectively, to control the random reaction. The
random activation or deactivation in the reaction step is thus promising to
correct the deterministic accumulative error of the propagation of
discontinuities. Extensive numerical experiments, including model problems and
realistic reacting flows in one and two dimensions, demonstrate this
expectation as well as the effectiveness and robustness of the method.
Meanwhile, for nonstiff problems when spatial and temporal resolutions are
fine, the proposed random method recovers the results as general fractional
step methods, owing to the increasing possibility of activation with
diminishing randomness by adding a shift term.
