Stability analysis and improvement of the covariant BSSN formulation against the FLRW spacetime background
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| Format: | Preprint |
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2024
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| _version_ | 1866916330348740608 |
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| author | Hoshino, Hidetomo Tsuchiya, Takuya Yoneda, Gen |
| author_facet | Hoshino, Hidetomo Tsuchiya, Takuya Yoneda, Gen |
| contents | In this study, we investigate the numerical stability of the covariant Baumgarte--Shapiro--Shibata--Nakamura (cBSSN) formulation against the Friedmann--Lemaître--Robertson--Walker spacetime. To evaluate the numerical stability, we calculate the constraint amplification factor by the eigenvalue analysis of the evolution of the constraint. We propose a modification to the time evolution equations of the cBSSN formulation for a higher numerical stability. Furthermore, we perform numerical simulations using the modified formulation to confirm its improved stability. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_14305 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability analysis and improvement of the covariant BSSN formulation against the FLRW spacetime background Hoshino, Hidetomo Tsuchiya, Takuya Yoneda, Gen General Relativity and Quantum Cosmology Numerical Analysis 83-08, 35Q76, 65M12 In this study, we investigate the numerical stability of the covariant Baumgarte--Shapiro--Shibata--Nakamura (cBSSN) formulation against the Friedmann--Lemaître--Robertson--Walker spacetime. To evaluate the numerical stability, we calculate the constraint amplification factor by the eigenvalue analysis of the evolution of the constraint. We propose a modification to the time evolution equations of the cBSSN formulation for a higher numerical stability. Furthermore, we perform numerical simulations using the modified formulation to confirm its improved stability. |
| title | Stability analysis and improvement of the covariant BSSN formulation against the FLRW spacetime background |
| topic | General Relativity and Quantum Cosmology Numerical Analysis 83-08, 35Q76, 65M12 |
| url | https://arxiv.org/abs/2407.14305 |