Evaluation of overshooting errors in particle methods for diffusion by biased global random walk
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...
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| Format: | Article |
| Language: | English |
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Publishing House of the Romanian Academy
2006-02-01
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| Series: | Journal of Numerical Analysis and Approximation Theory |
| Subjects: | |
| Online Access: | https://www.ictp.acad.ro/jnaat/journal/article/view/1020 |
| _version_ | 1818520937627123712 |
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| author | Nicolae Suciu Călin Vamoş |
| author_facet | Nicolae Suciu Călin Vamoş |
| author_sort | Nicolae Suciu |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-11T01:44:20Z |
| format | Article |
| id | doaj.art-a7b17def0b1d4ce98eb74e8f83d95981 |
| institution | Directory Open Access Journal |
| issn | 2457-6794 2501-059X |
| language | English |
| last_indexed | 2024-12-11T01:44:20Z |
| publishDate | 2006-02-01 |
| publisher | Publishing House of the Romanian Academy |
| record_format | Article |
| series | Journal of Numerical Analysis and Approximation Theory |
| spelling | doaj.art-a7b17def0b1d4ce98eb74e8f83d959812022-12-22T01:24:56ZengPublishing House of the Romanian AcademyJournal of Numerical Analysis and Approximation Theory2457-67942501-059X2006-02-01351Evaluation of overshooting errors in particle methods for diffusion by biased global random walkNicolae Suciu0Călin Vamoş1Tiberiu Popoviciu, Institute of Numerical Analysis, Romanian AcademyTiberiu Popoviciu, Institute of Numerical Analysis, Romanian AcademyThe 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.https://www.ictp.acad.ro/jnaat/journal/article/view/1020overshootingglobal random walkgroundwater contamination |
| spellingShingle | Nicolae Suciu Călin Vamoş Evaluation of overshooting errors in particle methods for diffusion by biased global random walk Journal of Numerical Analysis and Approximation Theory overshooting global random walk groundwater contamination |
| title | Evaluation of overshooting errors in particle methods for diffusion by biased global random walk |
| title_full | Evaluation of overshooting errors in particle methods for diffusion by biased global random walk |
| title_fullStr | Evaluation of overshooting errors in particle methods for diffusion by biased global random walk |
| title_full_unstemmed | Evaluation of overshooting errors in particle methods for diffusion by biased global random walk |
| title_short | Evaluation of overshooting errors in particle methods for diffusion by biased global random walk |
| title_sort | evaluation of overshooting errors in particle methods for diffusion by biased global random walk |
| topic | overshooting global random walk groundwater contamination |
| url | https://www.ictp.acad.ro/jnaat/journal/article/view/1020 |
| work_keys_str_mv | AT nicolaesuciu evaluationofovershootingerrorsinparticlemethodsfordiffusionbybiasedglobalrandomwalk AT calinvamos evaluationofovershootingerrorsinparticlemethodsfordiffusionbybiasedglobalrandomwalk |