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

2020 ◽  
Vol 496 (1) ◽  
pp. 206-214
Author(s):  
Philip Chang ◽  
Zachariah B Etienne

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.

2021 ◽  
Vol 148 ◽  
pp. 103841
Author(s):  
Sana Keita ◽  
Abdelaziz Beljadid ◽  
Yves Bourgault

2012 ◽  
Vol 27 (22) ◽  
pp. 1250125 ◽  
Author(s):  
YU NAKAYAMA

We show that relativistic hydrodynamics in Minkowski space–time has intrinsic ambiguity in second-order viscosity parameters in the Landau–Lifshitz frame. This stems from the possibility of improvements of energy–momentum tensor. There exist at least two viscosity parameters which can be removed by using this ambiguity in scale invariant hydrodynamics in (1+3) dimension, and seemingly nonconformal hydrodynamic theories can be hiddenly conformal invariant.


1991 ◽  
Vol 113 (3) ◽  
pp. 185-192 ◽  
Author(s):  
K. F. Cheung ◽  
M. Isaacson

The present paper set out a nonlinear boundary value problem involving the interaction of surface waves with large submerged structures in two dimensions. The problem is solved to second order by a time-stepping procedure on the basis of two alternative methods. Both of these involve the application of Green’s theorem, a Taylor series expansion of variables at the free surface and a perturbation series representation of the pertinent variables. Differences between the two solutions are associated with alternative integral equations applicable to second-order terms. The two second-order solutions are compared with each other and with previous theoretical and experimental results, and their applicability is assessed.


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