  Reactive transport in permeable porous media is relevant for a variety of
applications, but poses a significant challenge due to the range of length and
time scales. Multiscale methods that aim to link microstructure with the
macroscopic response of geo-materials have been developed, but require the
repeated solution of the small-scale problem and provide the motivation for
this work. We present an efficient computational method to study fluid flow and
solute transport problems in periodic porous media. Fluid flow is governed by
the Stokes equation, and the solute transport is governed by the
advection-diffusion equation. We follow the accelerated computational
micromechanics approach that leads to an iterative computational method where
each step is either local or the solution of a Poisson's equation. This enables
us to implement these methods on accelerators like graphics processing units
(GPUs) and exploit their massively parallel architecture. We verify the
approach by comparing the results against established computational methods and
then demonstrate the accuracy, efficacy, and performance by studying various
examples. This method efficiently calculates the effective transport properties
for complex pore geometries.
