  Flow and multicomponent reactive transport in saturated/unsaturated porous
media are modeled by ensembles of computational particles moving on regular
lattices according to specific random walk rules. The occupation number of the
lattice sites is updated with a global random walk (GRW) procedure which
spreads the particles from a lattice site with computational costs comparable
to those for a single random walk step in sequential procedures. To cope with
the nonlinearity and the degeneracy of the Richards equation the GRW flow
solver uses linearization techniques similar to the $L$-scheme developed in
finite element/volume approaches. Numerical schemes for reactive transport,
coupled with the flow solver via numerical solutions for saturation and water
flux, are implemented in splitting procedures. Diffusion-advection steps are
solved by GRW algorithms using either biased or unbiased random walk
probabilities. Since the number of particles in GRW simulations can be as large
as the number of molecules involved in chemical reactions, one avoids the
cumbersome problem of rescaling particle densities to approximate
concentrations. Reaction steps are therefore formulated in terms of
concentrations, as in deterministic approaches. The numerical convergence of
the new schemes is demonstrated by comparisons with manufactured analytical
solutions. Coupled flow and reactive transport problems of contaminant
biodegradation described by the Monod model are further solved and the
influence of flow nonlinearity/degeneracy and of the spatial heterogeneity of
the medium is investigated numerically.
