  The problem of front propagation in flowing media is addressed for laminar
velocity fields in two dimensions. Three representative cases are discussed:
stationary cellular flow, stationary shear flow, and percolating flow.
Production terms of Fisher-Kolmogorov-Petrovskii-Piskunov type and of Arrhenius
type are considered under the assumption of no feedback of the concentration on
the velocity. Numerical simulations of advection-reaction-diffusion equations
have been performed by an algorithm based on discrete-time maps. The results
show a generic enhancement of the speed of front propagation by the underlying
flow. For small molecular diffusivity, the front speed $V_f$ depends on the
typical flow velocity $U$ as a power law with an exponent depending on the
topological properties of the flow, and on the ratio of reactive and advective
time-scales. For open-streamline flows we find always $V_f \sim U$, whereas for
cellular flows we observe $V_f \sim U^{1/4}$ for fast advection, and $V_f \sim
U^{3/4}$ for slow advection.
