Reversible time-step adaptation for the integration of few-body systems
The time-step criterion plays a crucial role in direct N-body codes. If not chosen carefully, it will cause a secular drift in the energy error. Shared, adaptive time-step criteria commonly adopt the minimum pairwise time-step, which suffers from discontinuities in the time evolution of the time-ste...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Oxford University Press
2022
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| _version_ | 1797108675985276928 |
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| author | Boekholt, TCN Vaillant, T Correia, ACM |
| author_facet | Boekholt, TCN Vaillant, T Correia, ACM |
| author_sort | Boekholt, TCN |
| collection | OXFORD |
| description | The time-step criterion plays a crucial role in direct N-body codes. If not chosen carefully, it will cause a secular drift in the energy error. Shared, adaptive time-step criteria commonly adopt the minimum pairwise time-step, which suffers from discontinuities in the time evolution of the time-step. This has a large impact on the functioning of time-step symmetrization algorithms. We provide new demonstrations of previous findings that a smooth and weighted average over all pairwise time-steps in the N-body system, improves the level of energy conservation. Furthermore, we compare the performance of 27 different time-step criteria, by considering three methods for weighting time-steps and nine symmetrization methods. We present performance tests for strongly chaotic few-body systems, including unstable triples, giant planets in a resonant chain, and the current Solar System. We find that the harmonic symmetrization methods (methods A3 and B3 in our notation) are the most robust, in the sense that the symmetrized time-step remains close to the time-step function. Furthermore, based on our Solar System experiment, we find that our new weighting method based on direct pair-wise averaging (method W2 in our notation), is slightly preferred over the other methods. |
| first_indexed | 2024-03-07T07:30:26Z |
| format | Journal article |
| id | oxford-uuid:7659f96c-b592-46d0-94fe-00d4d1179550 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:30:26Z |
| publishDate | 2022 |
| publisher | Oxford University Press |
| record_format | dspace |
| spelling | oxford-uuid:7659f96c-b592-46d0-94fe-00d4d11795502023-01-17T11:19:27ZReversible time-step adaptation for the integration of few-body systemsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:7659f96c-b592-46d0-94fe-00d4d1179550EnglishSymplectic ElementsOxford University Press2022Boekholt, TCNVaillant, TCorreia, ACMThe time-step criterion plays a crucial role in direct N-body codes. If not chosen carefully, it will cause a secular drift in the energy error. Shared, adaptive time-step criteria commonly adopt the minimum pairwise time-step, which suffers from discontinuities in the time evolution of the time-step. This has a large impact on the functioning of time-step symmetrization algorithms. We provide new demonstrations of previous findings that a smooth and weighted average over all pairwise time-steps in the N-body system, improves the level of energy conservation. Furthermore, we compare the performance of 27 different time-step criteria, by considering three methods for weighting time-steps and nine symmetrization methods. We present performance tests for strongly chaotic few-body systems, including unstable triples, giant planets in a resonant chain, and the current Solar System. We find that the harmonic symmetrization methods (methods A3 and B3 in our notation) are the most robust, in the sense that the symmetrized time-step remains close to the time-step function. Furthermore, based on our Solar System experiment, we find that our new weighting method based on direct pair-wise averaging (method W2 in our notation), is slightly preferred over the other methods. |
| spellingShingle | Boekholt, TCN Vaillant, T Correia, ACM Reversible time-step adaptation for the integration of few-body systems |
| title | Reversible time-step adaptation for the integration of few-body systems |
| title_full | Reversible time-step adaptation for the integration of few-body systems |
| title_fullStr | Reversible time-step adaptation for the integration of few-body systems |
| title_full_unstemmed | Reversible time-step adaptation for the integration of few-body systems |
| title_short | Reversible time-step adaptation for the integration of few-body systems |
| title_sort | reversible time step adaptation for the integration of few body systems |
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