General relativistic hydrodynamics on a moving-mesh I: static space–times

• Published in: Monthly notices of the Royal Astronomical Society Vol. 496; no. 1; pp. 206 - 214
• Main Authors: Chang, Philip, Etienne, Zachariah B
• Format: Journal Article
• Language: English
• Published: Oxford University Press 21.07.2020
• Subjects: gravitational waves; hydrodynamics; methods: numerical; stars: neutron
• ISSN: 0035-8711; 1365-8711; 1365-2966; 1365-2966
• DOI: 10.1093/mnras/staa1532

ABSTRACT We present the moving-mesh general relativistic hydrodynamics solver for static space–times as implemented in the code, MANGA. Our implementation builds on the architectures of MANGA and the numerical relativity python package NRPy+. We review the general algorithm to solve these equations and, in particular, detail the time-stepping; Riemann solution across moving faces; conversion between primitive and conservative variables; validation and correction of hydrodynamic variables; and mapping of the metric to a Voronoi moving-mesh grid. We present test results for the numerical integration of an unmagnetized Tolman–Oppenheimer–Volkoff star for 24 dynamical times. We demonstrate that at a resolution of 106 mesh generating points, the star is stable and its central density drifts downwards by 2 per cent over this time-scale. At a lower resolution, the central density drift increases in a manner consistent with the adopted second-order spatial reconstruction scheme. These results agree well with the exact solutions, and we find the error behaviour to be similar to Eulerian codes with second-order spatial reconstruction. We also demonstrate that the new code recovers the fundamental mode frequency for the same TOV star but with its initial pressure depleted by 10 per cent.