Evaluation of overshooting errors in particle methods for diffusion by biased global random walk

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Nicolae Suciu Călin Vamoş

Abstract

The adjustment of grid steps which guarantees that particles methods yield no numerical diffusion inevitably induces overshooting errors in the solution of the parabolic partial differential equations with space variable coefficients. In this paper we give an evaluation of the overshooting errors of the "global random walk" algorithm (GRW), a computational efficient method used in simulations for transport in environmental problems. The evaluation is performed by comparisons between the GRW solutions and those of the "biased global random walk" algorithm (BGRW), a cellular automaton, which is computationally more expensive but is also free of overshooting errors. The reference problem was the diffusive transport in a random velocity field, a model for the transport of the contaminant solutes in groundwater. The evaluation reveals that, for an optimum choice of the parameters, GRW results for time intervals of practical interest lie in ranges of acceptable precision, for both the ensemble averaged observables and for their fluctuations.

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Keywords
overshooting; global random walk; groundwater contamination
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