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Center for Nonlinear Studies |
Numerical relativity codes that do not make assumptions on spatial symmetries most commonly adopt Cartesian coordinates. While these coordinates have many attractive features, spherical coordinates are much better suited to take advantage of approximate symmetries in a number of astrophysical objects, including single stars, black holes, and accretion disks. SphericalNR is a suite of thorns that enables the use of spherical coordinates in the Einstein Toolkit infrastructure, originally designed for Cartesian coordinates. This is done by providing appropriate MPI-parallelized parity boundary conditions at the internal boundaries of spherical coordinates. The evolution equations are written as a reference-metric version of the Baumgarte-Shapiro-Shibata-Nakamura formulation together with a proper rescaling of tensorial quantities. I will present numerical simulations for a disturbed Kerr black hole, the extracted the gravitational wave signal, and demonstrate that the noise in these signals is orders of magnitude smaller when computed on spherical grids rather than Cartesian grids. I will describe techniques to alleviate the so-called "pole-problem", namely the severe CFL condition as cell volumes are not constant in space in spherical coordinates. This is done by combining excision inside the black hole apparent horizon with an azimuthal FFT filter at high latitudes. I have recently started to adapt GRHydro, a general relativistic magnetohydrodynamics GRMHD code in the Einstein Toolkit, to use the reference metric formalism applied to the Valencia formulation of GRMHD. I will present first results showing the code maintains spherical symmetry to round off in the conserved fluxes in spherically symmetric accretion onto a Schwarzschild black hole.
Host: Oleg Korobkin