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

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.

More information

Identifiers

Catalogue record

Export record

ASCII CitationAtomBibTeXData Cite XMLDublin CoreDublin CoreEP3 XMLEndNoteHTML CitationHTML CitationHTML ListJSONMETSMODSMPEG-21 DIDLOpenURL ContextObjectOpenURL ContextObject in SpanRDF+N-TriplesRDF+N3RDF+XMLRIOXX2 XMLReferReference ManagerSimple Metadata

Altmetrics