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

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 computational 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

Authors

N. Suciu
Friedrich-Alexander University of Erlangen-Nurnberg
C. Vamos
Tiberiu Popoviciu Institute of Numerical Analysis (Romanian Academy)

Keywords

Overshooting; global random walk; groundwater contamination

References

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Paper coordinates

N. Suciu, C. Vamoş, Evaluation of overshooting errors in particle methods for diffusion by biased global random walk, Rev. Anal. Numér. Théor. Approx., 35 (2006), pp. 119-126

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About this paper

Journal

Rev. Anal. Numer. Theor. Approx.

Publisher Name

Editura Academiei Romane

DOI

not available yet.

Print ISSN

1222-9024

Online ISSN

2457-8126

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