Dissemin is shutting down on January 1st, 2025

Published in

IOP Publishing, Classical and Quantum Gravity, 10(40), p. 105002, 2023

DOI: 10.1088/1361-6382/acc828

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A new formulation of general-relativistic hydrodynamic equations using primitive variables

Journal article published in 2023 by Gaël Servignat ORCID, Jérôme Novak ORCID, Isabel Cordero-Carrión ORCID
This paper was not found in any repository, but could be made available legally by the author.
This paper was not found in any repository, but could be made available legally by the author.

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Abstract

Abstract We present the derivation of hydrodynamical equations for a perfect fluid in General Relativity, within the 3 + 1 decomposition of spacetime framework, using only primitive variables. Primitive variables are opposed to conserved variables, as defined in the widely used Valencia formulation of the same hydrodynamical equations. The equations are derived in a covariant way, so that they can be used to describe any configuration of the perfect fluid. Once derived, the equations are tested numerically. We implement them in an evolution code for spherically symmetric self-gravitating compact objects. The code uses pseudospectral methods for both the metric and the hydrodynamics. First, convergence tests are performed, then the frequencies of radial modes of polytropes are recovered with and without the Cowling approximation, and finally the performance of our code in the black hole collapse and migration tests are described. The results of the tests and the comparison with a reference core-collapse and neutron star oscillations code suggests that not only our code can handle very strong gravitational fields, but also that this new formulation helps gaining a significant amount of computational time in hydrodynamical simulations of smooth flows in General Relativity.