  A numerical method to efficiently solve for mixing and reaction of scalars in
a two-dimensional flow field at large P\'eclet numbers but otherwise arbitrary
Damk\"ohler numbers is reported. We consider a strip of one reactant in a pool
of another reactant, both of which are advected with the known velocity field.
We first establish that the system evolution for such a system under certain
conditions is described by a locally one-dimensional reaction-diffusion
problem. The approximation of a locally one-dimensional dynamics is true for
cases where the strip thickness is smaller than the local radius of curvature
and also when the strip thickness is smaller than the distance between adjacent
strips. We first demonstrate the method for the transport of a conservative
scalar under a linear shear flow, point vortex and a chaotic sine flow. We then
proceed to consider the situation with a simple bimolecular reaction between
two reactants to yield a single product. The methodology presented herewith
essentially generalizes nontrivially the Diffusive Strip Method developed by
Meunier and Villermaux (J. Fluid Mech. 662, 134-172 (2010)) to address passive
scalar transport, to the generalized situation with multiple reacting species.
In essence, the reduction of dimensionality of the problem, which renders the
2D problem 1D, allows one to efficiently model reactive transport under high
P\'eclet numbers which are otherwise prohibitively difficult to resolve from
classical finite difference or finite element based methods.
