A covariant approach to relativistic large-eddy simulations: The fibration picture
| Autor: | Nils Andersson, G.L. Comer, Ian Hawke, Thomas Celora |
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| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Physics
High Energy Astrophysical Phenomena (astro-ph.HE) Spacetime General relativity Fluid Dynamics (physics.flu-dyn) Equations of motion FOS: Physical sciences General Relativity and Quantum Cosmology (gr-qc) Physics - Fluid Dynamics General Relativity and Quantum Cosmology Dissipative system Fluid dynamics Covariant transformation Closure problem Statistical physics Astrophysics - High Energy Astrophysical Phenomena Smoothing |
| Popis: | 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 modelling of dissipative relativistic fluids, and crucially, demonstrate the linear stability of the proposed model. Version as published on Phys. Rev. D |
| Databáze: | OpenAIRE |
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