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Well-balanced high-order finite difference weighted essentially nonoscillatory schemes for a first-order Z4 formulation of the Einstein field equations

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dc.contributor.author Bhoriya, Deepak
dc.date.accessioned 2025-09-18T09:55:01Z
dc.date.available 2025-09-18T09:55:01Z
dc.date.issued 2024-11
dc.identifier.uri https://iopscience.iop.org/article/10.3847/1538-4365/ad7d0d/meta
dc.identifier.uri http://dspace.bits-pilani.ac.in:8080/jspui/handle/123456789/19442
dc.description.abstract We develop a new class of high-order accurate well-balanced finite difference (FD) weighted essentially nonoscillatory (WENO) methods for numerical general relativity (GR), which can be applied to any first-order reduction of the Einstein field equations, even if nonconservative terms are present. We choose the first-order nonconservative 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. By introducing auxiliary variables, the vacuum Einstein equations in first-order form constitute a partial differential equation system of 54 equations that is naturally nonconservative. We show how to design FD-WENO schemes that can handle nonconservative products. Different variants of FD WENO are discussed, with an eye to their suitability for higher-order accurate formulations for numerical GR. We successfully solve a set of fundamental tests of numerical GR with up to ninth-order spatial accuracy. Due to their intrinsic robustness, flexibility, and ease of implementation, FD-WENO schemes can effectively replace traditional central finite differencing in any first-order formulation of the Einstein field equations, without any artificial viscosity. When used in combination with well-balancing, the new numerical schemes preserve stationary equilibrium solutions of the Einstein equations exactly. This is particularly relevant in view of the numerical study of the quasi-normal modes of oscillations of relevant astrophysical sources. In conclusion, general relativistic high-energy astrophysics could benefit from this new class of numerical schemes and the ecosystem of desirable capabilities built around them. en_US
dc.language.iso en en_US
dc.publisher IOP en_US
dc.subject Mathematics en_US
dc.subject Numerical general relativity (GR) en_US
dc.subject Einstein field equations en_US
dc.subject Z4 formulation en_US
dc.subject Nonconservative systems en_US
dc.subject Finite difference WENO methods en_US
dc.title Well-balanced high-order finite difference weighted essentially nonoscillatory schemes for a first-order Z4 formulation of the Einstein field equations en_US
dc.type Article en_US


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