TITLE: Global random walk model of diffusion in random velocity fields

ABSTRACT:
 
Diffusion in random velocity fields is often used as stochastic model for transport processes in turbulent atmosphere, natural porous media or plasma physics. The stochastic process can be numerically simulated by sets of random walkers evolving in realizations of a random velocity field. Unlike the traditional methods which simulate and store all the random walkers trajectories, the Global Random Walk algorithm performs the spreading of all the particles lying at a grid node in a single computing step. In this way, we can use numbers of particles large enough for accurate simulations of diffusion in single realizations and we obtain large statistical ensembles corresponding to different realizations of the random field. Considering typical parameters from subsurface hydrology transport problems, we compute the effective diffusion coefficients for single realizations and their ensemble average and we find a bell shaped dependence of the longitudinal effective diffusion coefficient as function of Peclet number.

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