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A dissipative extension to ideal hydrodynamics

A dissipative extension to ideal hydrodynamics
A dissipative extension to ideal hydrodynamics
We present a formulation of special relativistic dissipative hydrodynamics (SRDHD) derived from the well-established Müller–Israel–Stewart (MIS) formalism using an expansion in deviations from ideal behaviour. By re-summing the non-ideal terms, our approach extends the Euler equations of motion for an ideal fluid through a series of additional source terms that capture the effects of bulk viscosity, shear viscosity, and heat flux. For efficiency these additional terms are built from purely spatial derivatives of the primitive fluid variables. The series expansion is parametrized by the dissipation strength and time-scale coefficients, and is therefore rapidly convergent near the ideal limit. We show, using numerical simulations, that our model reproduces the dissipative fluid behaviour of other formulations. As our formulation is designed to avoid the numerical stiffness issues that arise in the traditional MIS formalism for fast relaxation time-scales, it is roughly an order of magnitude faster than standard methods near the ideal limit.
hydrodynamics, methods: numerical, neutron star mergers, relativistic processes, software: simulations, stars: neutron
47-64
Hatton, Marcus John
d2214492-6ca0-4796-a148-9e4dd20e99c1
Hawke, Ian
fc964672-c794-4260-a972-eaf818e7c9f4
Hatton, Marcus John
d2214492-6ca0-4796-a148-9e4dd20e99c1
Hawke, Ian
fc964672-c794-4260-a972-eaf818e7c9f4

Hatton, Marcus John and Hawke, Ian (2024) A dissipative extension to ideal hydrodynamics. MNRAS, 535 (1), 47-64. (doi:10.1093/mnras/stae2284).

Record type: Article

Abstract

We present a formulation of special relativistic dissipative hydrodynamics (SRDHD) derived from the well-established Müller–Israel–Stewart (MIS) formalism using an expansion in deviations from ideal behaviour. By re-summing the non-ideal terms, our approach extends the Euler equations of motion for an ideal fluid through a series of additional source terms that capture the effects of bulk viscosity, shear viscosity, and heat flux. For efficiency these additional terms are built from purely spatial derivatives of the primitive fluid variables. The series expansion is parametrized by the dissipation strength and time-scale coefficients, and is therefore rapidly convergent near the ideal limit. We show, using numerical simulations, that our model reproduces the dissipative fluid behaviour of other formulations. As our formulation is designed to avoid the numerical stiffness issues that arise in the traditional MIS formalism for fast relaxation time-scales, it is roughly an order of magnitude faster than standard methods near the ideal limit.

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Accepted/In Press date: 30 October 2024
Published date: 1 November 2024
Additional Information: Publisher Copyright: © 2024 The Author(s).
Keywords: hydrodynamics, methods: numerical, neutron star mergers, relativistic processes, software: simulations, stars: neutron

Identifiers

Local EPrints ID: 495990
URI: http://eprints.soton.ac.uk/id/eprint/495990
PURE UUID: 4dad8d29-12ac-47ee-b12c-07705d35de27
ORCID for Ian Hawke: ORCID iD orcid.org/0000-0003-4805-0309

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Date deposited: 28 Nov 2024 17:50
Last modified: 30 Nov 2024 02:41

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Contributors

Author: Marcus John Hatton
Author: Ian Hawke ORCID iD

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