# Global Random Walk simulations of diffusion

## Abstract

Random walk methods are suitable to build up convergent solutions for reaction-diffusion problems and were successfully applied to simulations of transport processes in a random environment. The disadvantage is that, for realistic cases, these methods become time and memory expensive.

To increase the computation speed and to reduce the required memory, we derived a “global random walk” method in which the particles at a given site of the grid are simultaneously scattered following the binomial Bernoulli repartition. It was found that the computation time is reduced three orders of magnitude with respect to individual random walk methods. Moreover, by suitable “microscopic balance” boundary conditions, we obtained good simulations of transport in unbounded domains, using normal size grids. The global random walk improves the statistical quality of simulations for diffusion processes in random fields. The method was tested by comparisons with analytical and finite difference solutions as well as with concentrations measured in “column experiments”, used in laboratory study of soils’ hydrogeological and chemical properties.

## Authors

C. Vamos
“Tiberiu Popoviciu” Institute of Numerical Analysis, Romanian Academy

N. Suciu
“Tiberiu Popoviciu” Institute of Numerical Analysis, Romanian Academy

H. Vereecken

O. Nitzsche

H. Hardelauf

## Keywords

diffusion; unbounded domains; random fields

## Cite this paper as

C. Vamoş, N. Suciu, H. Vereecken, O. Nitzsche, H. Hardelauf, Global Random Walk simulations of diffusion, pp. 343-354 in Scientific Computing, Validated Numerics, Interval Methods, Ed. Krämer and Wolff von Gudenberg, Kluwer Academic/Plenum Publishers, New York, 2001.
doi: 10.1007/978-1-4757-6484-0_28

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##### Journal

Scientific Computing, Validated Numerics, Interval Methods

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