Generalized random walk algorithm for the numerical modeling of complex diffusion processes

Abstract

A generalized form of the random walk algorithm to simulate diffusion processes is introduced.

Unlike the usual approach, at a given time all the particles from a grid node are simultaneously scattered using the Bernoulli repartition. This procedure saves memory and computing time and no restrictions are imposed for the maximum number of particles to be used in simulations.

We prove that for simple diffusion the method generalizes the finite difference scheme and gives the same precision for large enough number of particles.

As an example, simulations of diffusion in random velocity field are performed and the main features of the stochastic mathematical model are numerically tested.

Authors

Călin Vamoş
Tiberiu Popoviciu Institute of Numerical Analysis (Romanian Academy)

Nicolae Suciu
Tiberiu Popoviciu Institute of Numerical Analysis (Romanian Academy)

Harry Vereecken

Keywords

Diffusion; random walk; groundwater; contaminant transport

Cite this paper as

C. Vamoş, N. Suciu, H. Vereecken (2003), Generalized random walk algorithm for the numerical modeling of complex diffusion processes, J. Comp. Phys., 186(2), 527-544, doi: 10.1016/S0021-9991(03)00073-1

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J. Comp. Phys.

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