Journal
MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY
Volume 505, Issue 4, Pages 5910-5940Publisher
OXFORD UNIV PRESS
DOI: 10.1093/mnras/stab1384
Keywords
accretion; accretion discs; hydrodynamics; shock waves
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Funding
- HGS-HIRe for FAIR
- LOEWE-Program in HIC for FAIR
- ` PHAROS', COST Action [CA16214]
- ERC Synergy Grant 'BlackHoleCam: Imaging the Event Horizon of Black Holes' [610058]
- Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) [315477589 -TRR 211]
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The text discusses the suitability of numerical integration in special-relativistic and general-relativistic scenarios, presenting a fully general, causal formulation of relativistic second-order dissipative hydrodynamics. The formulation is tested in specific scenarios and the results can be used as a testbed for numerical codes simulating non-perfect fluids on curved backgrounds.
We consider the relativistic hydrodynamics of non-perfect fluids with the goal of determining a formulation that is suited for numerical integration in special-relativistic and general-relativistic scenarios. To this end, we review the various formulations of relativistic second-order dissipative hydrodynamics proposed so far and present in detail a particular formulation that is fully general, causal, and can be cast into a 3+1 flux-conservative form, as the one employed in modern numerical-relativity codes. As an example, we employ a variant of this formulation restricted to a relaxation-type equation for the bulk viscosity in the generalrelativistic magnetohydrodynamics code BHAC. After adopting the formulation for a series of standard and non-standard tests in 1+1-dimensional special-relativistic hydrodynamics, we consider a novel general-relativistic scenario, namely, the stationary, spherically symmetric, viscous accretion on to a black hole. The newly developed solution - which can exhibit even considerable deviations from the inviscid counterpart - can be used as a testbed for numerical codes simulating non-perfect fluids on curved backgrounds.
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