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Covariant approach to relativistic large-eddy simulations: The fibration picture

Covariant approach to relativistic large-eddy simulations: The fibration picture
Covariant approach to relativistic large-eddy simulations: The fibration picture

Models of turbulent flows require the resolution of a vast range of scales, from large eddies to small-scale features directly associated with dissipation. As the required resolution is not within reach of large scale numerical simulations, standard strategies involve a smoothing of the fluid dynamics, either through time averaging or spatial filtering. These strategies raise formal issues in general relativity, where the split between space and time is observer dependent. To make progress, we develop a new covariant framework for filtering/averaging based on the fibration of spacetime associated with fluid elements and the use of Fermi coordinates to facilitate a meaningful local analysis. We derive the resolved equations of motion, demonstrating how "effective"dissipative terms arise because of the coarse-graining, and paying particular attention to the thermodynamical interpretation of the resolved quantities. Finally, as the smoothing of the fluid dynamics inevitably leads to a closure problem, we propose a new closure scheme inspired by recent progress in the modeling of dissipative relativistic fluids, and crucially, demonstrate the linear stability of the proposed model.

2470-0010
Celora, T.
b15e9792-aae0-479a-83c5-b5c874b19fa6
Andersson, N.
2dd6d1ee-cefd-478a-b1ac-e6feedafe304
Hawke, I.
fc964672-c794-4260-a972-eaf818e7c9f4
Comer, G. L.
e78ae434-e576-4b39-93cd-679b6f30432d
Celora, T.
b15e9792-aae0-479a-83c5-b5c874b19fa6
Andersson, N.
2dd6d1ee-cefd-478a-b1ac-e6feedafe304
Hawke, I.
fc964672-c794-4260-a972-eaf818e7c9f4
Comer, G. L.
e78ae434-e576-4b39-93cd-679b6f30432d

Celora, T., Andersson, N., Hawke, I. and Comer, G. L. (2021) Covariant approach to relativistic large-eddy simulations: The fibration picture. Physical Review D, 104 (8), [084090]. (doi:10.1103/PhysRevD.104.084090).

Record type: Article

Abstract

Models of turbulent flows require the resolution of a vast range of scales, from large eddies to small-scale features directly associated with dissipation. As the required resolution is not within reach of large scale numerical simulations, standard strategies involve a smoothing of the fluid dynamics, either through time averaging or spatial filtering. These strategies raise formal issues in general relativity, where the split between space and time is observer dependent. To make progress, we develop a new covariant framework for filtering/averaging based on the fibration of spacetime associated with fluid elements and the use of Fermi coordinates to facilitate a meaningful local analysis. We derive the resolved equations of motion, demonstrating how "effective"dissipative terms arise because of the coarse-graining, and paying particular attention to the thermodynamical interpretation of the resolved quantities. Finally, as the smoothing of the fluid dynamics inevitably leads to a closure problem, we propose a new closure scheme inspired by recent progress in the modeling of dissipative relativistic fluids, and crucially, demonstrate the linear stability of the proposed model.

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2107.01083 - Accepted Manuscript
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Accepted/In Press date: 16 September 2021
e-pub ahead of print date: 26 October 2021
Published date: 26 October 2021

Identifiers

Local EPrints ID: 453268
URI: http://eprints.soton.ac.uk/id/eprint/453268
ISSN: 2470-0010
PURE UUID: b40956ab-51a5-4f36-90a7-4e8ed9351914
ORCID for T. Celora: ORCID iD orcid.org/0000-0002-6515-3644
ORCID for N. Andersson: ORCID iD orcid.org/0000-0001-8550-3843
ORCID for I. Hawke: ORCID iD orcid.org/0000-0003-4805-0309

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Date deposited: 11 Jan 2022 17:51
Last modified: 17 Mar 2024 03:02

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Contributors

Author: T. Celora ORCID iD
Author: N. Andersson ORCID iD
Author: I. Hawke ORCID iD
Author: G. L. Comer

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