Well-balanced high order finite difference WENO schemes for a first-order Z4 formulation of the Einstein field equations
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| Format: | Preprint |
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2024
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| _version_ | 1866914953167896576 |
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| author | Balsara, Dinshaw Bhoriya, Deepak Zanotti, Olindo Dumbser, Michael |
| author_facet | Balsara, Dinshaw Bhoriya, Deepak Zanotti, Olindo Dumbser, Michael |
| contents | In this work we aim at developing a new class of high order accurate well-balanced finite difference (FD) Weighted Essentially Non-Oscillatory (WENO) methods for numerical general relativity, which can be applied to any first-order reduction of the Einstein field equations, even if non-conservative terms are present. We choose the first-order non-conservative Z4 formulation of the Einstein equations, which has a built-in cleaning procedure that accounts for the Einstein constraints and that has already shown its ability in keeping stationary solutions stable over long timescales. Upon the introduction of auxiliary variables, the vacuum Einstein equations in first order form constitute a ... |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_05450 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Well-balanced high order finite difference WENO schemes for a first-order Z4 formulation of the Einstein field equations Balsara, Dinshaw Bhoriya, Deepak Zanotti, Olindo Dumbser, Michael General Relativity and Quantum Cosmology Instrumentation and Methods for Astrophysics Numerical Analysis 35L75, 65M06, 83C35, 83C05, 83C57 and 83-08 In this work we aim at developing a new class of high order accurate well-balanced finite difference (FD) Weighted Essentially Non-Oscillatory (WENO) methods for numerical general relativity, which can be applied to any first-order reduction of the Einstein field equations, even if non-conservative terms are present. We choose the first-order non-conservative Z4 formulation of the Einstein equations, which has a built-in cleaning procedure that accounts for the Einstein constraints and that has already shown its ability in keeping stationary solutions stable over long timescales. Upon the introduction of auxiliary variables, the vacuum Einstein equations in first order form constitute a ... |
| title | Well-balanced high order finite difference WENO schemes for a first-order Z4 formulation of the Einstein field equations |
| topic | General Relativity and Quantum Cosmology Instrumentation and Methods for Astrophysics Numerical Analysis 35L75, 65M06, 83C35, 83C05, 83C57 and 83-08 |
| url | https://arxiv.org/abs/2406.05450 |